# AP Physics 1 & 2 Simple Harmonic Motion

Section 2: Mechanics: Lecture 21 | 58:30 min

Simple harmonic motion (SHM) is the motion a spring follows. It’s an oscillatory motion with a graph that resembles a sine curve. SHM has tons of implications in more advanced topics of physics but for now just understand the basics. It’s best to think of SHM as another form of motion, much like rotational dynamics and linear movement. You’ll use these SHM equations for any circumstance where you have an oscillating body (most of the time denoted by a mass-on-a-spring problem). It’s important to note when you can use these equations as well as what they are. With this topic we’ve covered all of mechanics and will move onto fluids.

Table of Contents

7m 38s

- Intro0:00
- Objectives0:12
- What is Physics?0:31
- What is Matter, Energy, and How to They Interact0:55
- Why?0:58
- Physics Answers the 'Why' Questions.1:05
- Matter1:23
- Matter1:29
- Mass1:33
- Inertial Mass1:53
- Gravitational Mass2:12
- A Spacecraft's Mass2:58
- Energy3:37
- Energy: The Ability or Capacity to Do Work3:39
- Work: The Process of Moving an Object3:45
- The Ability or Capacity to Move an Object3:54
- Mass-Energy Equivalence4:51
- Relationship Between Mass and Energy E=mc25:01
- The Mass of An Object is Really a Measure of Its Energy5:05
- The Study of Everything5:42
- Introductory Course6:19
- Next Steps7:15

24m 12s

- Intro0:00
- Outline0:10
- Objectives0:28
- Why Do We Need Units?0:52
- Need to Set Specific Standards for Our Measurements1:01
- Physicists Have Agreed to Use the Systeme International1:24
- The Systeme International1:50
- Based on Powers of 101:52
- 7 Fundamental Units: Meter, Kilogram, Second, Ampere, Candela, Kelvin, Mole2:02
- The Meter2:18
- Meter is a Measure of Length2:20
- Measurements Smaller than a Meter, Use: Centimeter, Millimeter, Micrometer, Nanometer2:25
- Measurements Larger Than a Meter, Use Kilometer2:38
- The Kilogram2:46
- Roughly Equivalent to 2.2 English Pounds2:49
- Grams, Milligrams2:53
- Megagram2:59
- Seconds3:10
- Base Unit of Time3:12
- Minute, Hour, Day3:20
- Milliseconds, Microseconds3:33
- Derived Units3:41
- Velocity3:45
- Acceleration3:57
- Force4:04
- Prefixes for Powers of 104:21
- Converting Fundamental Units, Example 14:53
- Converting Fundamental Units, Example 27:18
- Two-Step Conversions, Example 18:24
- Two-Step Conversions, Example 210:06
- Derived Unit Conversions11:29
- Multi-Step Conversions13:25
- Metric Estimations15:04
- What are Significant Figures?16:01
- Represent a Manner of Showing Which Digits In a Number Are Known to Some Level of Certainty16:03
- Example16:09
- Measuring with Sig Figs16:36
- Rule 116:40
- Rule 216:44
- Rule 316:52
- Reading Significant Figures16:57
- All Non-Zero Digits Are Significant17:04
- All Digits Between Non-Zero Digits Are Significant17:07
- Zeros to the Left of the Significant Digits17:11
- Zeros to the Right of the Significant Digits17:16
- Non-Zero Digits17:21
- Digits Between Non-Zeros Are Significant17:45
- Zeroes to the Right of the Sig Figs Are Significant18:17
- Why Scientific Notation?18:36
- Physical Measurements Vary Tremendously in Magnitude18:38
- Example18:47
- Scientific Notation in Practice19:23
- Example 119:28
- Example 219:44
- Using Scientific Notation20:02
- Show Your Value Using Correct Number of Significant Figures20:05
- Move the Decimal Point20:09
- Show Your Number Being Multiplied by 10 Raised to the Appropriate Power20:14
- Accuracy and Precision20:23
- Accuracy20:36
- Precision20:41
- Example 1: Scientific Notation w/ Sig Figs21:48
- Example 2: Scientific Notation - Compress22:25
- Example 3: Scientific Notation - Compress23:07
- Example 4: Scientific Notation - Expand23:31

25m 5s

- Intro0:00
- Objectives0:05
- Scalars0:29
- Definition of Scalar0:39
- Temperature, Mass, Time0:45
- Vectors1:12
- Vectors are Quantities That Have Magnitude and Direction1:13
- Represented by Arrows1:31
- Vector Representations1:47
- Graphical Vector Addition2:42
- Graphical Vector Subtraction4:58
- Vector Components6:08
- Angle of a Vector8:22
- Vector Notation9:52
- Example 1: Vector Components14:30
- Example 2: Vector Components16:05
- Example 3: Vector Magnitude17:26
- Example 4: Vector Addition19:38
- Example 5: Angle of a Vector24:06

30m 11s

- Intro0:00
- Objectives0:07
- Position0:40
- An Object's Position Cab Be Assigned to a Variable on a Number Scale0:43
- Symbol for Position1:07
- Distance1:13
- When Position Changes, An Object Has Traveled Some Distance1:14
- Distance is Scalar and Measured in Meters1:21
- Example 1: Distance1:34
- Displacement2:17
- Displacement is a Vector Which Describes the Straight Line From Start to End Point2:18
- Measured in Meters2:27
- Example 2: Displacement2:39
- Average Speed3:32
- The Distance Traveled Divided by the Time Interval3:33
- Speed is a Scalar3:47
- Example 3: Average Speed3:57
- Average Velocity4:37
- The Displacement Divided by the Time Interval4:38
- Velocity is a Vector4:53
- Example 4: Average Velocity5:06
- Example 5: Chuck the Hungry Squirrel5:55
- Acceleration8:02
- Rate At Which Velocity Changes8:13
- Acceleration is a Vector8:26
- Example 6: Acceleration Problem8:52
- Average vs. Instantaneous9:44
- Average Values Take Into Account an Entire Time Interval9:50
- Instantaneous Value Tells the Rate of Change of a Quantity at a Specific Instant in Time9:54
- Example 7: Average Velocity10:06
- Particle Diagrams11:57
- Similar to the Effect of Oil Leak from a Car on the Pavement11:59
- Accelerating13:03
- Position-Time Graphs14:17
- Shows Position as a Function of Time14:24
- Slope of x-t Graph15:08
- Slope Gives You the Velocity15:09
- Negative Indicates Direction16:27
- Velocity-Time Graphs16:45
- Shows Velocity as a Function of Time16:49
- Area Under v-t Graphs17:47
- Area Under the V-T Graph Gives You Change in Displacement17:48
- Example 8: Slope of a v-t Graph19:45
- Acceleration-Time Graphs21:44
- Slope of the v-t Graph Gives You Acceleration21:45
- Area Under the a-t Graph Gives You an Object's Change in Velocity22:24
- Example 10: Motion Graphing24:03
- Example 11: v-t Graph27:14
- Example 12: Displacement From v-t Graph28:14

36m 13s

- Intro0:00
- Objectives0:07
- Problem-Solving Toolbox0:42
- Graphs Are Not Always the Most Effective0:47
- Kinematic Equations Helps us Solve for Five Key Variables0:56
- Deriving the Kinematic Equations1:29
- Kinematic Equations7:40
- Problem Solving Steps8:13
- Label Your Horizontal or Vertical Motion8:20
- Choose a Direction as Positive8:24
- Create a Motion Analysis Table8:33
- Fill in Your Givens8:42
- Solve for Unknowns8:45
- Example 1: Horizontal Kinematics8:51
- Example 2: Vertical Kinematics11:13
- Example 3: 2 Step Problem13:25
- Example 4: Acceleration Problem16:44
- Example 5: Particle Diagrams17:56
- Example 6: Quadratic Solution20:13
- Free Fall24:24
- When the Only Force Acting on an Object is the Force of Gravity, the Motion is Free Fall24:27
- Air Resistance24:51
- Drop a Ball24:56
- Remove the Air from the Room25:02
- Analyze the Motion of Objects by Neglecting Air Resistance25:06
- Acceleration Due to Gravity25:22
- g = 9.8 m/s225:25
- Approximate g as 10 m/s2 on the AP Exam25:37
- G is Referred to as the Gravitational Field Strength25:48
- Objects Falling From Rest26:15
- Objects Starting from Rest Have an Initial velocity of 026:19
- Acceleration is +g26:34
- Example 7: Falling Objects26:47
- Objects Launched Upward27:59
- Acceleration is -g28:04
- At Highest Point, the Object has a Velocity of 028:19
- Symmetry of Motion28:27
- Example 8: Ball Thrown Upward28:47
- Example 9: Height of a Jump29:23
- Example 10: Ball Thrown Downward33:08
- Example 11: Maximum Height34:16

20m 32s

- Intro0:00
- Objectives0:06
- What is a Projectile?0:26
- An Object That is Acted Upon Only By Gravity0:29
- Typically Launched at an Angle0:43
- Path of a Projectile1:03
- Projectiles Launched at an Angle Move in Parabolic Arcs1:06
- Symmetric and Parabolic1:32
- Horizontal Range and Max Height1:49
- Independence of Motion2:17
- Vertical2:49
- Horizontal2:52
- Example 1: Horizontal Launch3:49
- Example 2: Parabolic Path7:41
- Angled Projectiles8:30
- Must First Break Up the Object's Initial Velocity Into x- and y- Components of Initial Velocity8:32
- An Object Will Travel the Maximum Horizontal Distance with a Launch Angle of 45 Degrees8:43
- Example 3: Human Cannonball8:55
- Example 4: Motion Graphs12:55
- Example 5: Launch From a Height15:33
- Example 6: Acceleration of a Projectile19:56

10m 52s

- Intro0:00
- Objectives0:06
- Reference Frames0:18
- Motion of an Observer0:21
- No Way to Distinguish Between Motion at Rest and Motion at a Constant Velocity0:44
- Motion is Relative1:35
- Example 11:39
- Example 22:09
- Calculating Relative Velocities2:31
- Example 12:43
- Example 22:48
- Example 32:52
- Example 14:58
- Example 2: Airspeed6:19
- Example 3: 2-D Relative Motion7:39
- Example 4: Relative Velocity with Direction9:40

10m 16s

- Intro0:00
- Objective0:05
- Newton's 1st Law of Motion0:16
- An Object At Rest Will Remain At Rest0:21
- An Object In Motion Will Remain in Motion0:26
- Net Force0:39
- Also Known As the Law of Inertia0:46
- Force1:02
- Push or Pull1:04
- Newtons1:08
- Contact and Field Forces1:31
- Contact Forces1:50
- Field Forces2:11
- What is a Net Force?2:30
- Vector Sum of All the Forces Acting on an Object2:33
- Translational Equilibrium2:37
- Unbalanced Force Is a Net Force2:46
- What Does It Mean?3:49
- An Object Will Continue in Its Current State of Motion Unless an Unbalanced Force Acts Upon It3:50
- Example of Newton's First Law4:20
- Objects in Motion5:05
- Will Remain in Motion At Constant Velocity5:06
- Hard to Find a Frictionless Environment on Earth5:10
- Static Equilibrium5:40
- Net Force on an Object is 05:44
- Inertia6:21
- Tendency of an Object to Resist a Change in Velocity6:23
- Inertial Mass6:35
- Gravitational Mass6:40
- Example 1: Inertia7:10
- Example 2: Inertia7:37
- Example 3: Translational Equilibrium8:03
- Example 4: Net Force8:40

34m 55s

- Intro0:00
- Objective0:07
- Free Body Diagrams0:37
- Tools Used to Analyze Physical Situations0:40
- Show All the Forces Acting on a Single Object0:45
- Drawing FBDs0:58
- Draw Object of Interest as a Dot1:00
- Sketch a Coordinate System1:10
- Example 1: Falling Elephant1:18
- Example 2: Falling Elephant with Air Resistance2:07
- Example 3: Soda on Table3:00
- Example 4: Box in Equilibrium4:25
- Example 5: Block on a Ramp5:01
- Pseudo-FBDs5:53
- Draw When Forces Don't Line Up with Axes5:56
- Break Forces That Don’t Line Up with Axes into Components That Do6:00
- Example 6: Objects on a Ramp6:32
- Example 7: Car on a Banked Turn10:23
- Newton's 2nd Law of Motion12:56
- The Acceleration of an Object is in the Direction of the Directly Proportional to the Net Force Applied13:06
- Newton's 1st Two Laws Compared13:45
- Newton's 1st Law13:51
- Newton's 2nd Law14:10
- Applying Newton's 2nd Law14:50
- Example 8: Applying Newton's 2nd Law15:23
- Example 9: Stopping a Baseball16:52
- Example 10: Block on a Surface19:51
- Example 11: Concurrent Forces21:16
- Mass vs. Weight22:28
- Mass22:29
- Weight22:47
- Example 12: Mass vs. Weight23:16
- Translational Equilibrium24:47
- Occurs When There Is No Net Force on an Object24:49
- Equilibrant24:57
- Example 13: Translational Equilibrium25:29
- Example 14: Translational Equilibrium26:56
- Example 15: Determining Acceleration28:05
- Example 16: Suspended Mass31:03

5m 58s

- Intro0:00
- Objectives0:06
- Newton's 3rd Law of Motion0:20
- All Forces Come in Pairs0:24
- Examples1:22
- Action-Reaction Pairs2:07
- Girl Kicking Soccer Ball2:11
- Rocket Ship in Space2:29
- Gravity on You2:53
- Example 1: Force of Gravity3:34
- Example 2: Sailboat4:00
- Example 3: Hammer and Nail4:49
- Example 4: Net Force5:06

17m 49s

- Intro0:00
- Objectives0:06
- Examples0:23
- Friction Opposes Motion0:24
- Kinetic Friction0:27
- Static Friction0:36
- Magnitude of Frictional Force Is Determined By Two Things0:41
- Coefficient Friction2:27
- Ratio of the Frictional Force and the Normal Force2:28
- Chart of Different Values of Friction2:48
- Kinetic or Static?3:31
- Example 1: Car Sliding4:18
- Example 2: Block on Incline5:03
- Calculating the Force of Friction5:48
- Depends Only Upon the Nature of the Surfaces in Contact and the Magnitude of the Force5:50
- Terminal Velocity6:14
- Air Resistance6:18
- Terminal Velocity of the Falling Object6:33
- Example 3: Finding the Frictional Force7:36
- Example 4: Box on Wood Surface9:13
- Example 5: Static vs. Kinetic Friction11:49
- Example 6: Drag Force on Airplane12:15
- Example 7: Pulling a Sled13:21

35m 27s

- Intro0:00
- Objectives0:08
- Free Body Diagrams0:49
- Drawing FBDs1:09
- Draw Object of Interest as a Dot1:12
- Sketch a Coordinate System1:18
- Example 1: FBD of Block on Ramp1:39
- Pseudo-FBDs1:59
- Draw Object of Interest as a Dot2:00
- Break Up the Forces2:07
- Box on a Ramp2:12
- Example 2: Box at Rest4:28
- Example 3: Box Held by Force5:00
- What is an Atwood Machine?6:46
- Two Objects are Connected by a Light String Over a Mass-less Pulley6:49
- Properties of Atwood Machines7:13
- Ideal Pulleys are Frictionless and Mass-less7:16
- Tension is Constant in a Light String Passing Over an Ideal Pulley7:23
- Solving Atwood Machine Problems8:02
- Alternate Solution12:07
- Analyze the System as a Whole12:12
- Elevators14:24
- Scales Read the Force They Exert on an Object Placed Upon Them14:42
- Can be Used to Analyze Using Newton's 2nd Law and Free body Diagrams15:23
- Example 4: Elevator Accelerates Upward15:36
- Example 5: Truck on a Hill18:30
- Example 6: Force Up a Ramp19:28
- Example 7: Acceleration Down a Ramp21:56
- Example 8: Basic Atwood Machine24:05
- Example 9: Masses and Pulley on a Table26:47
- Example 10: Mass and Pulley on a Ramp29:15
- Example 11: Elevator Accelerating Downward33:00

26m 6s

- Intro0:00
- Objectives0:06
- Momentum0:31
- Example0:35
- Momentum measures How Hard It Is to Stop a Moving Object0:47
- Vector Quantity0:58
- Example 1: Comparing Momenta1:48
- Example 2: Calculating Momentum3:08
- Example 3: Changing Momentum3:50
- Impulse5:02
- Change In Momentum5:05
- Example 4: Impulse5:26
- Example 5: Impulse-Momentum6:41
- Deriving the Impulse-Momentum Theorem9:04
- Impulse-Momentum Theorem12:02
- Example 6: Impulse-Momentum Theorem12:15
- Non-Constant Forces13:55
- Impulse or Change in Momentum13:56
- Determine the Impulse by Calculating the Area of the Triangle Under the Curve14:07
- Center of Mass14:56
- Real Objects Are More Complex Than Theoretical Particles14:59
- Treat Entire Object as if Its Entire Mass Were Contained at the Object's Center of Mass15:09
- To Calculate the Center of Mass15:17
- Example 7: Force on a Moving Object15:49
- Example 8: Motorcycle Accident17:49
- Example 9: Auto Collision19:32
- Example 10: Center of Mass (1D)21:29
- Example 11: Center of Mass (2D)23:28

21m 59s

- Intro0:00
- Objectives0:09
- Conservation of Momentum0:18
- Linear Momentum is Conserved in an Isolated System0:21
- Useful for Analyzing Collisions and Explosions0:27
- Momentum Tables0:58
- Identify Objects in the System1:05
- Determine the Momenta of the Objects Before and After the Event1:10
- Add All the Momenta From Before the Event and Set Them Equal to Momenta After the Event1:15
- Solve Your Resulting Equation for Unknowns1:20
- Types of Collisions1:31
- Elastic Collision1:36
- Inelastic Collision1:56
- Example 1: Conservation of Momentum (1D)2:02
- Example 2: Inelastic Collision5:12
- Example 3: Recoil Velocity7:16
- Example 4: Conservation of Momentum (2D)9:29
- Example 5: Atomic Collision16:02

7m 18s

- Intro0:00
- Objectives0:07
- Uniform Circular Motion0:20
- Circumference0:32
- Average Speed Formula Still Applies0:46
- Frequency1:03
- Number of Revolutions or Cycles Which Occur Each Second1:04
- Hertz1:24
- Formula for Frequency1:28
- Period1:36
- Time It Takes for One Complete Revolution or Cycle1:37
- Frequency and Period1:54
- Example 1: Car on a Track2:08
- Example 2: Race Car3:55
- Example 3: Toy Train4:45
- Example 4: Round-A-Bout5:39

26m 37s

- Intro0:00
- Objectives0:08
- Uniform Circular Motion0:38
- Direction of ac1:41
- Magnitude of ac3:50
- Centripetal Force4:08
- For an Object to Accelerate, There Must Be a Net Force4:18
- Centripetal Force4:26
- Calculating Centripetal Force6:14
- Example 1: Acceleration7:31
- Example 2: Direction of ac8:53
- Example 3: Loss of Centripetal Force9:19
- Example 4: Velocity and Centripetal Force10:08
- Example 5: Demon Drop10:55
- Example 6: Centripetal Acceleration vs. Speed14:11
- Example 7: Calculating ac15:03
- Example 8: Running Back15:45
- Example 9: Car at an Intersection17:15
- Example 10: Bucket in Horizontal Circle18:40
- Example 11: Bucket in Vertical Circle19:20
- Example 12: Frictionless Banked Curve21:55

32m 56s

- Intro0:00
- Objectives0:08
- Universal Gravitation0:29
- The Bigger the Mass the Closer the Attraction0:48
- Formula for Gravitational Force1:16
- Calculating g2:43
- Mass of Earth2:51
- Radius of Earth2:55
- Inverse Square Relationship4:32
- Problem Solving Hints7:21
- Substitute Values in For Variables at the End of the Problem Only7:26
- Estimate the Order of Magnitude of the Answer Before Using Your Calculator7:38
- Make Sure Your Answer Makes Sense7:55
- Example 1: Asteroids8:20
- Example 2: Meteor and the Earth10:17
- Example 3: Satellite13:13
- Gravitational Fields13:50
- Gravity is a Non-Contact Force13:54
- Closer Objects14:14
- Denser Force Vectors14:19
- Gravitational Field Strength15:09
- Example 4: Astronaut16:19
- Gravitational Potential Energy18:07
- Two Masses Separated by Distance Exhibit an Attractive Force18:11
- Formula for Gravitational Field19:21
- How Do Orbits Work?19:36
- Example5: Gravitational Field Strength for Space Shuttle in Orbit21:35
- Example 6: Earth's Orbit25:13
- Example 7: Bowling Balls27:25
- Example 8: Freely Falling Object28:07
- Example 9: Finding g28:40
- Example 10: Space Vehicle on Mars29:10
- Example 11: Fg vs. Mass Graph30:24
- Example 12: Mass on Mars31:14
- Example 13: Two Satellites31:51

15m 33s

- Intro0:00
- Objectives0:07
- Radians and Degrees0:26
- In Degrees, Once Around a Circle is 360 Degrees0:29
- In Radians, Once Around a Circle is 2π0:34
- Example 1: Degrees to Radians0:57
- Example 2: Radians to Degrees1:31
- Linear vs. Angular Displacement2:00
- Linear Position2:05
- Angular Position2:10
- Linear vs. Angular Velocity2:35
- Linear Speed2:39
- Angular Speed2:42
- Direction of Angular Velocity3:05
- Converting Linear to Angular Velocity4:22
- Example 3: Angular Velocity Example4:41
- Linear vs. Angular Acceleration5:36
- Example 4: Angular Acceleration6:15
- Kinematic Variable Parallels7:47
- Displacement7:52
- Velocity8:10
- Acceleration8:16
- Time8:22
- Kinematic Variable Translations8:30
- Displacement8:34
- Velocity8:42
- Acceleration8:50
- Time0:00
- Kinematic Equation Parallels9:09
- Kinematic Equations9:12
- Delta9:33
- Final Velocity Squared and Angular Velocity Squared9:54
- Example 5: Medieval Flail10:24
- Example 6: CD Player10:57
- Example 7: Carousel12:13
- Example 8: Circular Saw13:35

11m 21s

- Intro0:00
- Objectives0:05
- Torque0:18
- Force That Causes an Object to Turn0:22
- Must be Perpendicular to the Displacement to Cause a Rotation0:27
- Lever Arm: The Stronger the Force, The More Torque0:45
- Direction of the Torque Vector1:53
- Perpendicular to the Position Vector and the Force Vector1:54
- Right-Hand Rule2:08
- Newton's 2nd Law: Translational vs. Rotational2:46
- Equilibrium3:58
- Static Equilibrium4:01
- Dynamic Equilibrium4:09
- Rotational Equilibrium4:22
- Example 1: Pirate Captain4:32
- Example 2: Auto Mechanic5:25
- Example 3: Sign Post6:44
- Example 4: See-Saw9:01

36m 6s

- Intro0:00
- Objectives0:08
- Types of Inertia0:39
- Inertial Mass (Translational Inertia)0:42
- Moment of Inertia (Rotational Inertia)0:53
- Moment of Inertia for Common Objects1:48
- Example 1: Calculating Moment of Inertia2:53
- Newton's 2nd Law - Revisited5:09
- Acceleration of an Object5:15
- Angular Acceleration of an Object5:24
- Example 2: Rotating Top5:47
- Example 3: Spinning Disc7:54
- Angular Momentum9:41
- Linear Momentum9:43
- Angular Momentum10:00
- Calculating Angular Momentum10:51
- Direction of the Angular Momentum Vector11:26
- Total Angular Momentum12:29
- Example 4: Angular Momentum of Particles14:15
- Example 5: Rotating Pedestal16:51
- Example 6: Rotating Discs18:39
- Angular Momentum and Heavenly Bodies20:13
- Types of Kinetic Energy23:41
- Objects Traveling with a Translational Velocity23:45
- Objects Traveling with Angular Velocity24:00
- Translational vs. Rotational Variables24:33
- Example 7: Kinetic Energy of a Basketball25:45
- Example 8: Playground Round-A-Bout28:17
- Example 9: The Ice Skater30:54
- Example 10: The Bowler33:15

31m 20s

- Intro0:00
- Objectives0:09
- What Is Work?0:31
- Power Output0:35
- Transfer Energy0:39
- Work is the Process of Moving an Object by Applying a Force0:46
- Examples of Work0:56
- Calculating Work2:16
- Only the Force in the Direction of the Displacement Counts2:33
- Formula for Work2:48
- Example 1: Moving a Refrigerator3:16
- Example 2: Liberating a Car3:59
- Example 3: Crate on a Ramp5:20
- Example 4: Lifting a Box7:11
- Example 5: Pulling a Wagon8:38
- Force vs. Displacement Graphs9:33
- The Area Under a Force vs. Displacement Graph is the Work Done by the Force9:37
- Find the Work Done9:49
- Example 6: Work From a Varying Force11:00
- Hooke's Law12:42
- The More You Stretch or Compress a Spring, The Greater the Force of the Spring12:46
- The Spring's Force is Opposite the Direction of Its Displacement from Equilibrium13:00
- Determining the Spring Constant14:21
- Work Done in Compressing the Spring15:27
- Example 7: Finding Spring Constant16:21
- Example 8: Calculating Spring Constant17:58
- Power18:43
- Work18:46
- Power18:50
- Example 9: Moving a Sofa19:26
- Calculating Power20:41
- Example 10: Motors Delivering Power21:27
- Example 11: Force on a Cyclist22:40
- Example 12: Work on a Spinning Mass23:52
- Example 13: Work Done by Friction25:05
- Example 14: Units of Power28:38
- Example 15: Frictional Force on a Sled29:43

20m 15s

- Intro0:00
- Objectives0:07
- What is Energy?0:24
- The Ability or Capacity to do Work0:26
- The Ability or Capacity to Move an Object0:34
- Types of Energy0:39
- Energy Transformations2:07
- Transfer Energy by Doing Work2:12
- Work-Energy Theorem2:20
- Units of Energy2:51
- Kinetic Energy3:08
- Energy of Motion3:13
- Ability or Capacity of a Moving Object to Move Another Object3:17
- A Single Object Can Only Have Kinetic Energy3:46
- Example 1: Kinetic Energy of a Motorcycle5:08
- Potential Energy5:59
- Energy An Object Possesses6:10
- Gravitational Potential Energy7:21
- Elastic Potential Energy9:58
- Internal Energy10:16
- Includes the Kinetic Energy of the Objects That Make Up the System and the Potential Energy of the Configuration10:20
- Calculating Gravitational Potential Energy in a Constant Gravitational Field10:57
- Sources of Energy on Earth12:41
- Example 2: Potential Energy13:41
- Example 3: Energy of a System14:40
- Example 4: Kinetic and Potential Energy15:36
- Example 5: Pendulum16:55

23m 20s

- Intro0:00
- Objectives0:08
- Law of Conservation of Energy0:22
- Energy Cannot Be Created or Destroyed.. It Can Only Be Changed0:27
- Mechanical Energy0:34
- Conservation Laws0:40
- Examples0:49
- Kinematics vs. Energy4:34
- Energy Approach4:56
- Kinematics Approach6:04
- The Pendulum8:07
- Example 1: Cart Compressing a Spring13:09
- Example 214:23
- Example 3: Car Skidding to a Stop16:15
- Example 4: Accelerating an Object17:27
- Example 5: Block on Ramp18:06
- Example 6: Energy Transfers19:21

58m 30s

- Intro0:00
- Objectives0:08
- What Is Simple Harmonic Motion?0:57
- Nature's Typical Reaction to a Disturbance1:00
- A Displacement Which Results in a Linear Restoring Force Results in SHM1:25
- Review of Springs1:43
- When a Force is Applied to a Spring, the Spring Applies a Restoring Force1:46
- When the Spring is in Equilibrium, It Is 'Unstrained'1:54
- Factors Affecting the Force of A Spring2:00
- Oscillations3:42
- Repeated Motions3:45
- Cycle 13:52
- Period3:58
- Frequency4:07
- Spring-Block Oscillator4:47
- Mass of the Block4:59
- Spring Constant5:05
- Example 1: Spring-Block Oscillator6:30
- Diagrams8:07
- Displacement8:42
- Velocity8:57
- Force9:36
- Acceleration10:09
- U10:24
- K10:47
- Example 2: Harmonic Oscillator Analysis16:22
- Circular Motion vs. SHM23:26
- Graphing SHM25:52
- Example 3: Position of an Oscillator28:31
- Vertical Spring-Block Oscillator31:13
- Example 4: Vertical Spring-Block Oscillator34:26
- Example 5: Bungee36:39
- The Pendulum43:55
- Mass Is Attached to a Light String That Swings Without Friction About the Vertical Equilibrium44:04
- Energy and the Simple Pendulum44:58
- Frequency and Period of a Pendulum48:25
- Period of an Ideal Pendulum48:31
- Assume Theta is Small48:54
- Example 6: The Pendulum50:15
- Example 7: Pendulum Clock53:38
- Example 8: Pendulum on the Moon55:14
- Example 9: Mass on a Spring56:01

19m 48s

- Intro0:00
- Objectives0:09
- Fluids0:27
- Fluid is Matter That Flows Under Pressure0:31
- Fluid Mechanics is the Study of Fluids0:44
- Density0:57
- Density is the Ratio of an Object's Mass to the Volume It Occupies0:58
- Less Dense Fluids1:06
- Less Dense Solids1:09
- Example 1: Density of Water1:27
- Example 2: Volume of Gold2:19
- Example 3: Floating3:06
- Buoyancy3:54
- Force Exerted by a Fluid on an Object, Opposing the Object's Weight3:56
- Buoyant Force Determined Using Archimedes Principle4:03
- Example 4: Buoyant Force5:12
- Example 5: Shark Tank5:56
- Example 6: Concrete Boat7:47
- Example 7: Apparent Mass10:08
- Example 8: Volume of a Submerged Cube13:21
- Example 9: Determining Density15:37

18m 7s

- Intro0:00
- Objectives0:09
- Pressure0:25
- Pressure is the Effect of a Force Acting Upon a Surface0:27
- Formula for Pressure0:41
- Force is Always Perpendicular to the Surface0:50
- Exerting Pressure1:03
- Fluids Exert Outward Pressure in All Directions on the Sides of Any Container Holding the Fluid1:36
- Earth's Atmosphere Exerts Pressure1:42
- Example 1: Pressure on Keyboard2:17
- Example 2: Sleepy Fisherman3:03
- Example 3: Scale on Planet Physica4:12
- Example 4: Ranking Pressures5:00
- Pressure on a Submerged Object6:45
- Pressure a Fluid Exerts on an Object Submerged in That Fluid6:46
- If There Is Atmosphere Above the Fluid7:03
- Example 5: Gauge Pressure Scuba Diving7:27
- Example 6: Absolute Pressure Scuba Diving8:13
- Pascal's Principle8:51
- Force Multiplication Using Pascal's Principle9:24
- Example 7: Barber's Chair11:38
- Example 8: Hydraulic Auto Lift13:26
- Example 9: Pressure on a Penny14:41
- Example 10: Depth in Fresh Water16:39
- Example 11: Absolute vs. Gauge Pressure17:23

7m

- Intro0:00
- Objectives0:08
- Conservation of Mass for Fluid Flow0:18
- Law of Conservation of Mass for Fluids0:21
- Volume Flow Rate Remains Constant Throughout the Pipe0:35
- Volume Flow Rate0:59
- Quantified In Terms Of Volume Flow Rate1:01
- Area of Pipe x Velocity of Fluid1:05
- Must Be Constant Throughout Pipe1:10
- Example 1: Tapered Pipe1:44
- Example 2: Garden Hose2:37
- Example 3: Oil Pipeline4:49
- Example 4: Roots of Continuity Equation6:16

20m

- Intro0:00
- Objectives0:08
- Bernoulli's Principle0:21
- Airplane Wings0:35
- Venturi Pump1:56
- Bernoulli's Equation3:32
- Example 1: Torricelli's Theorem4:38
- Example 2: Gauge Pressure7:26
- Example 3: Shower Pressure8:16
- Example 4: Water Fountain12:29
- Example 5: Elevated Cistern15:26

24m 17s

- Intro0:00
- Objectives0:12
- Thermal Physics0:42
- Explores the Internal Energy of Objects Due to the Motion of the Atoms and Molecules Comprising the Objects0:46
- Explores the Transfer of This Energy From Object to Object0:53
- Temperature1:00
- Thermal Energy Is Related to the Kinetic Energy of All the Particles Comprising the Object1:03
- The More Kinetic Energy of the Constituent Particles Have, The Greater the Object's Thermal Energy1:12
- Temperature and Phases of Matter1:44
- Solids1:48
- Liquids1:56
- Gases2:02
- Average Kinetic Energy and Temperature2:16
- Average Kinetic Energy2:24
- Boltzmann's Constant2:29
- Temperature Scales3:06
- Converting Temperatures4:37
- Heat5:03
- Transfer of Thermal Energy5:06
- Accomplished Through Collisions Which is Conduction5:13
- Methods of Heat Transfer5:52
- Conduction5:59
- Convection6:19
- Radiation6:31
- Quantifying Heat Transfer in Conduction6:37
- Rate of Heat Transfer is Measured in Watts6:42
- Thermal Conductivity7:12
- Example 1: Average Kinetic Energy7:35
- Example 2: Body Temperature8:22
- Example 3: Temperature of Space9:30
- Example 4: Temperature of the Sun10:44
- Example 5: Heat Transfer Through Window11:38
- Example 6: Heat Transfer Across a Rod12:40
- Thermal Expansion14:18
- When Objects Are Heated, They Tend to Expand14:19
- At Higher Temperatures, Objects Have Higher Average Kinetic Energies14:24
- At Higher Levels of Vibration, The Particles Are Not Bound As Tightly to Each Other14:30
- Linear Expansion15:11
- Amount a Material Expands is Characterized by the Material's Coefficient of Expansion15:14
- One-Dimensional Expansion -> Linear Coefficient of Expansion15:20
- Volumetric Expansion15:38
- Three-Dimensional Expansion -> Volumetric Coefficient of Expansion15:45
- Volumetric Coefficient of Expansion is Roughly Three Times the Linear Coefficient of Expansion16:03
- Coefficients of Thermal Expansion16:24
- Example 7: Contracting Railroad Tie16:59
- Example 8: Expansion of an Aluminum Rod18:37
- Example 9: Water Spilling Out of a Glass20:18
- Example 10: Average Kinetic Energy vs. Temperature22:18
- Example 11: Expansion of a Ring23:07

24m 15s

- Intro0:00
- Objectives0:10
- Ideal Gases0:25
- Gas Is Comprised of Many Particles Moving Randomly in a Container0:34
- Particles Are Far Apart From One Another0:46
- Particles Do Not Exert Forces Upon One Another Unless They Come In Contact in an Elastic Collision0:53
- Ideal Gas Law1:18
- Atoms, Molecules, and Moles2:56
- Protons2:59
- Neutrons3:15
- Electrons3:18
- Examples3:25
- Example 1: Counting Moles4:58
- Example 2: Moles of CO2 in a Bottle6:00
- Example 3: Pressurized CO26:54
- Example 4: Helium Balloon8:53
- Internal Energy of an Ideal Gas10:17
- The Average Kinetic Energy of the Particles of an Ideal Gas10:21
- Total Internal Energy of the Ideal Gas Can Be Found by Multiplying the Average Kinetic Energy of the Gas's Particles by the Numbers of Particles in the Gas10:32
- Example 5: Internal Energy of Oxygen12:00
- Example 6: Temperature of Argon12:41
- Root-Mean-Square Velocity13:40
- This is the Square Root of the Average Velocity Squared For All the Molecules in the System13:43
- Derived from the Maxwell-Boltzmann Distribution Function13:56
- Calculating vrms14:56
- Example 7: Average Velocity of a Gas18:32
- Example 8: Average Velocity of a Gas19:44
- Example 9: vrms of Molecules in Equilibrium20:59
- Example 10: Moles to Molecules22:25
- Example 11: Relating Temperature and Internal Energy23:22

22m 29s

- Intro0:00
- Objectives0:06
- Zeroth Law of Thermodynamics0:26
- First Law of Thermodynamics1:00
- The Change in the Internal Energy of a Closed System is Equal to the Heat Added to the System Plus the Work Done on the System1:04
- It is a Restatement of the Law of Conservation of Energy1:19
- Sign Conventions Are Important1:25
- Work Done on a Gas1:44
- Example 1: Adding Heat to a System3:25
- Example 2: Expanding a Gas4:07
- P-V Diagrams5:11
- Pressure-Volume Diagrams are Useful Tools for Visualizing Thermodynamic Processes of Gases5:13
- Use Ideal Gas Law to Determine Temperature of Gas5:25
- P-V Diagrams II5:55
- Volume Increases, Pressure Decreases6:00
- As Volume Expands, Gas Does Work6:19
- Temperature Rises as You Travel Up and Right on a PV Diagram6:29
- Example 3: PV Diagram Analysis6:40
- Types of PV Processes7:52
- Adiabatic8:03
- Isobaric8:19
- Isochoric8:28
- Isothermal8:35
- Adiabatic Processes8:47
- Heat Is not Transferred Into or Out of The System8:50
- Heat = 08:55
- Isobaric Processes9:19
- Pressure Remains Constant9:21
- PV Diagram Shows a Horizontal Line9:27
- Isochoric Processes9:51
- Volume Remains Constant9:52
- PV Diagram Shows a Vertical Line9:58
- Work Done on the Gas is Zero10:01
- Isothermal Processes10:27
- Temperature Remains Constant10:29
- Lines on a PV Diagram Are Isotherms10:31
- PV Remains Constant10:38
- Internal Energy of Gas Remains Constant10:40
- Example 4: Adiabatic Expansion10:46
- Example 5: Removing Heat11:25
- Example 6: Ranking Processes13:08
- Second Law of Thermodynamics13:59
- Heat Flows Naturally From a Warmer Object to a Colder Object14:02
- Heat Energy Cannot be Completely Transformed Into Mechanical Work14:11
- All Natural Systems Tend Toward a Higher Level of Disorder14:19
- Heat Engines14:52
- Heat Engines Convert Heat Into Mechanical Work14:56
- Efficiency of a Heat Engine is the Ratio of the Engine You Get Out to the Energy You Put In14:59
- Power in Heat Engines16:09
- Heat Engines and PV Diagrams17:38
- Carnot Engine17:54
- It Is a Theoretical Heat Engine That Operates at Maximum Possible Efficiency18:02
- It Uses Only Isothermal and Adiabatic Processes18:08
- Carnot's Theorem18:11
- Example 7: Carnot Engine18:49
- Example 8: Maximum Efficiency21:02
- Example 9: PV Processes21:51

38m 24s

- Intro0:00
- Objectives0:10
- Electric Charges0:34
- Matter is Made Up of Atoms0:37
- Protons Have a Charge of +10:45
- Electrons Have a Charge of -11:00
- Most Atoms Are Neutral1:04
- Ions1:15
- Fundamental Unit of Charge is the Coulomb1:29
- Like Charges Repel, While Opposites Attract1:50
- Example 1: Charge on an Object2:22
- Example 2: Charge of an Alpha Particle3:36
- Conductors and Insulators4:27
- Conductors Allow Electric Charges to Move Freely4:30
- Insulators Do Not Allow Electric Charges to Move Freely4:39
- Resistivity is a Material Property4:45
- Charging by Conduction5:05
- Materials May Be Charged by Contact, Known as Conduction5:07
- Conductors May Be Charged by Contact5:24
- Example 3: Charging by Conduction5:38
- The Electroscope6:44
- Charging by Induction8:00
- Example 4: Electrostatic Attraction9:23
- Coulomb's Law11:46
- Charged Objects Apply a Force Upon Each Other = Coulombic Force11:52
- Force of Attraction or Repulsion is Determined by the Amount of Charge and the Distance Between the Charges12:04
- Example 5: Determine Electrostatic Force13:09
- Example 6: Deflecting an Electron Beam15:35
- Electric Fields16:28
- The Property of Space That Allows a Charged Object to Feel a Force16:44
- Electric Field Strength Vector is the Amount of Electrostatic Force Observed by a Charge Per Unit of Charge17:01
- The Direction of the Electric Field Vector is the Direction a Positive Charge Would Feel a Force17:24
- Example 7: Field Between Metal Plates17:58
- Visualizing the Electric Field19:27
- Electric Field Lines Point Away from Positive Charges and Toward Negative Charges19:40
- Electric Field Lines Intersect Conductors at Right Angles to the Surface19:50
- Field Strength and Line Density Decreases as You Move Away From the Charges19:58
- Electric Field Lines20:09
- E Field Due to a Point Charge22:32
- Electric Fields Are Caused by Charges22:35
- Electric Field Due to a Point Charge Can Be Derived From the Definition of the Electric Field and Coulomb's Law22:38
- To Find the Electric Field Due to Multiple Charges23:09
- Comparing Electricity to Gravity23:56
- Force24:02
- Field Strength24:16
- Constant24:37
- Charge/ Mass Units25:01
- Example 8: E Field From 3 Point Charges25:07
- Example 9: Where is the E Field Zero?31:43
- Example 10: Gravity and Electricity36:38
- Example 11: Field Due to Point Charge37:34

35m 58s

- Intro0:00
- Objectives0:09
- Electric Potential Energy0:32
- When an Object Was Lifted Against Gravity By Applying a Force for Some Distance, Work Was Done0:35
- When a Charged Object is Moved Against an Electric Field by Applying a Force for Some Distance, Work is Done0:43
- Electric Potential Difference1:30
- Example 1: Charge From Work2:06
- Example 2: Electric Energy3:09
- The Electron-Volt4:02
- Electronvolt (eV)4:15
- 1eV is the Amount of Work Done in Moving an Elementary Charge Through a Potential Difference of 1 Volt4:28
- Example 3: Energy in eV5:33
- Equipotential Lines6:32
- Topographic Maps Show Lines of Equal Altitude, or Equal Gravitational Potential6:36
- Lines Connecting Points of Equal Electrical Potential are Known as Equipotential Lines6:57
- Drawing Equipotential Lines8:15
- Potential Due to a Point Charge10:46
- Calculate the Electric Field Vector Due to a Point Charge10:52
- Calculate the Potential Difference Due to a Point Charge11:05
- To Find the Potential Difference Due to Multiple Point Charges11:16
- Example 4: Potential Due to a Point Charge11:52
- Example 5: Potential Due to Point Charges13:04
- Parallel Plates16:34
- Configurations in Which Parallel Plates of Opposite Charge are Situated a Fixed Distance From Each Other16:37
- These Can Create a Capacitor16:45
- E Field Due to Parallel Plates17:14
- Electric Field Away From the Edges of Two Oppositely Charged Parallel Plates is Constant17:15
- Magnitude of the Electric Field Strength is Give By the Potential Difference Between the Plates Divided by the Plate Separation17:47
- Capacitors18:09
- Electric Device Used to Store Charge18:11
- Once the Plates Are Charged, They Are Disconnected18:30
- Device's Capacitance18:46
- Capacitors Store Energy19:28
- Charges Located on the Opposite Plates of a Capacitor Exert Forces on Each Other19:31
- Example 6: Capacitance20:28
- Example 7: Charge on a Capacitor22:03
- Designing Capacitors24:00
- Area of the Plates24:05
- Separation of the Plates24:09
- Insulating Material24:13
- Example 8: Designing a Capacitor25:35
- Example 9: Calculating Capacitance27:39
- Example 10: Electron in Space29:47
- Example 11: Proton Energy Transfer30:35
- Example 12: Two Conducting Spheres32:50
- Example 13: Equipotential Lines for a Capacitor34:48

21m 14s

- Intro0:00
- Objectives0:06
- Electric Current0:19
- Path Through Current Flows0:21
- Current is the Amount of Charge Passing a Point Per Unit Time0:25
- Conventional Current is the Direction of Positive Charge Flow0:43
- Example 1: Current Through a Resistor1:19
- Example 2: Current Due to Elementary Charges1:47
- Example 3: Charge in a Light Bulb2:35
- Example 4: Flashlights3:03
- Conductivity and Resistivity4:41
- Conductivity is a Material's Ability to Conduct Electric Charge4:53
- Resistivity is a Material's Ability to Resist the Movement of Electric Charge5:11
- Resistance vs. Resistivity vs. Resistors5:35
- Resistivity Is a Material Property5:40
- Resistance Is a Functional Property of an Element in an Electric Circuit5:57
- A Resistor is a Circuit Element7:23
- Resistors7:45
- Example 5: Calculating Resistance8:17
- Example 6: Resistance Dependencies10:09
- Configuration of Resistors10:50
- When Placed in a Circuit, Resistors Can be Organized in Both Serial and Parallel Arrangements10:53
- May Be Useful to Determine an Equivalent Resistance Which Could Be Used to Replace a System or Resistors with a Single Equivalent Resistor10:58
- Resistors in Series11:15
- Resistors in Parallel12:35
- Example 7: Finding Equivalent Resistance15:01
- Example 8: Length and Resistance17:43
- Example 9: Comparing Resistors18:21
- Example 10: Comparing Wires19:12

10m 35s

- Intro0:00
- Objectives0:06
- Ohm's Law0:21
- Relates Resistance, Potential Difference, and Current Flow0:23
- Example 1: Resistance of a Wire1:22
- Example 2: Circuit Current1:58
- Example 3: Variable Resistor2:30
- Ohm's 'Law'?3:22
- Very Useful Empirical Relationship3:31
- Test if a Material is 'Ohmic'3:40
- Example 4: Ohmic Material3:58
- Electrical Power4:24
- Current Flowing Through a Circuit Causes a Transfer of Energy Into Different Types4:26
- Example: Light Bulb4:36
- Example: Television4:58
- Calculating Power5:09
- Electrical Energy5:14
- Charge Per Unit Time Is Current5:29
- Expand Using Ohm's Law5:48
- Example 5: Toaster7:43
- Example 6: Electric Iron8:19
- Example 7: Power of a Resistor9:19
- Example 8: Information Required to Determine Power in a Resistor9:55

8m 44s

- Intro0:00
- Objectives0:08
- Electrical Circuits0:21
- A Closed-Loop Path Through Which Current Can Flow0:22
- Can Be Made Up of Most Any Materials, But Typically Comprised of Electrical Devices0:27
- Circuit Schematics1:09
- Symbols Represent Circuit Elements1:30
- Lines Represent Wires1:33
- Sources for Potential Difference: Voltaic Cells, Batteries, Power Supplies1:36
- Complete Conducting Paths2:43
- Voltmeters3:20
- Measure the Potential Difference Between Two Points in a Circuit3:21
- Connected in Parallel with the Element to be Measured3:25
- Have Very High Resistance3:59
- Ammeters4:19
- Measure the Current Flowing Through an Element of a Circuit4:20
- Connected in Series with the Circuit4:25
- Have Very Low Resistance4:45
- Example 1: Ammeter and Voltmeter Placement4:56
- Example 2: Analyzing R6:27
- Example 3: Voltmeter Placement7:12
- Example 4: Behavior or Electrical Meters7:31

48m 58s

- Intro0:00
- Objectives0:07
- Series Circuits0:27
- Series Circuits Have Only a Single Current Path0:29
- Removal of any Circuit Element Causes an Open Circuit0:31
- Kirchhoff's Laws1:36
- Tools Utilized in Analyzing Circuits1:42
- Kirchhoff's Current Law States1:47
- Junction Rule2:00
- Kirchhoff's Voltage Law States2:05
- Loop Rule2:18
- Example 1: Voltage Across a Resistor2:23
- Example 2: Current at a Node3:45
- Basic Series Circuit Analysis4:53
- Example 3: Current in a Series Circuit9:21
- Example 4: Energy Expenditure in a Series Circuit10:14
- Example 5: Analysis of a Series Circuit12:07
- Example 6: Voltmeter In a Series Circuit14:57
- Parallel Circuits17:11
- Parallel Circuits Have Multiple Current Paths17:13
- Removal of a Circuit Element May Allow Other Branches of the Circuit to Continue Operating17:15
- Basic Parallel Circuit Analysis18:19
- Example 7: Parallel Circuit Analysis21:05
- Example 8: Equivalent Resistance22:39
- Example 9: Four Parallel Resistors23:16
- Example 10: Ammeter in a Parallel Circuit26:27
- Combination Series-Parallel Circuits28:50
- Look For Portions of the Circuit With Parallel Elements28:56
- Work Back to Original Circuit29:09
- Analysis of a Combination Circuit29:20
- Internal Resistance34:11
- In Reality, Voltage Sources Have Some Amount of 'Internal Resistance'34:16
- Terminal Voltage of the Voltage Source is Reduced Slightly34:25
- Example 11: Two Voltage Sources35:16
- Example 12: Internal Resistance42:46
- Example 13: Complex Circuit with Meters45:22
- Example 14: Parallel Equivalent Resistance48:24

24m 47s

- Intro0:00
- Objectives0:08
- Capacitors in Parallel0:34
- Capacitors Store Charge on Their Plates0:37
- Capacitors In Parallel Can Be Replaced with an Equivalent Capacitor0:46
- Capacitors in Series2:42
- Charge on Capacitors Must Be the Same2:44
- Capacitor In Series Can Be Replaced With an Equivalent Capacitor2:47
- RC Circuits5:40
- Comprised of a Source of Potential Difference, a Resistor Network, and One or More Capacitors5:42
- Uncharged Capacitors Act Like Wires6:04
- Charged Capacitors Act Like Opens6:12
- Charging an RC Circuit6:23
- Discharging an RC Circuit11:36
- Example 1: RC Analysis14:50
- Example 2: More RC Analysis18:26
- Example 3: Equivalent Capacitance21:19
- Example 4: More Equivalent Capacitance22:48

19m 48s

- Intro0:00
- Objectives0:07
- Magnetism0:32
- A Force Caused by Moving Charges0:34
- Magnetic Domains Are Clusters of Atoms with Electrons Spinning in the Same Direction0:51
- Example 1: Types of Fields1:23
- Magnetic Field Lines2:25
- Make Closed Loops and Run From North to South Outside the Magnet2:26
- Magnetic Flux2:42
- Show the Direction the North Pole of a Magnet Would Tend to Point If Placed in the Field2:54
- Example 2: Lines of Magnetic Force3:49
- Example 3: Forces Between Bar Magnets4:39
- The Compass5:28
- The Earth is a Giant Magnet5:31
- The Earth's Magnetic North pole is Located Near the Geographic South Pole, and Vice Versa5:33
- A Compass Lines Up with the Net Magnetic Field6:07
- Example 3: Compass in Magnetic Field6:41
- Example 4: Compass Near a Bar Magnet7:14
- Magnetic Permeability7:59
- The Ratio of the Magnetic Field Strength Induced in a Material to the Magnetic Field Strength of the Inducing Field8:02
- Free Space8:13
- Highly Magnetic Materials Have Higher Values of Magnetic Permeability8:34
- Magnetic Dipole Moment8:41
- The Force That a Magnet Can Exert on Moving Charges8:46
- Relative Strength of a Magnet8:54
- Forces on Moving Charges9:10
- Moving Charges Create Magnetic Fields9:11
- Magnetic Fields Exert Forces on Moving Charges9:17
- Direction of the Magnetic Force9:57
- Direction is Given by the Right-Hand Rule10:05
- Right-Hand Rule10:09
- Mass Spectrometer10:52
- Magnetic Fields Accelerate Moving Charges So That They Travel in a Circle10:58
- Used to Determine the Mass of an Unknown Particle11:04
- Velocity Selector12:44
- Mass Spectrometer with an Electric Field Added12:47
- Example 5: Force on an Electron14:13
- Example 6: Velocity of a Charged Particle15:25
- Example 7: Direction of the Magnetic Force16:52
- Example 8: Direction of Magnetic Force on Moving Charges17:43
- Example 9: Electron Released From Rest in Magnetic Field18:53

21m 29s

- Intro0:00
- Objectives0:09
- Force on a Current-Carrying Wire0:30
- A Current-Carrying Wire in a Magnetic Field May Experience a Magnetic Force0:33
- Direction Given by the Right-Hand Rule1:11
- Example 1: Force on a Current-Carrying Wire1:38
- Example 2: Equilibrium on a Submerged Wire2:33
- Example 3: Torque on a Loop of Wire5:55
- Magnetic Field Due to a Current-Carrying Wire8:49
- Moving Charges Create Magnetic Fields8:53
- Wires Carry Moving Charges8:56
- Direction Given by the Right-Hand Rule9:21
- Example 4: Magnetic Field Due to a Wire10:56
- Magnetic Field Due to a Solenoid12:12
- Solenoid is a Coil of Wire12:19
- Direction Given by the Right-Hand Rule12:47
- Forces on 2 Parallel Wires13:34
- Current Flowing in the Same Direction14:52
- Current Flowing in Opposite Directions14:57
- Example 5: Magnetic Field Due to Wires15:19
- Example 6: Strength of an Electromagnet18:35
- Example 7: Force on a Wire19:30
- Example 8: Force Between Parallel Wires20:47

17m 26s

- Intro0:00
- Objectives0:09
- Induced EMF0:42
- Charges Flowing Through a Wire Create Magnetic Fields0:45
- Changing Magnetic Fields Cause Charges to Flow or 'Induce' a Current in a Process Known As Electromagnetic Induction0:49
- Electro-Motive Force is the Potential Difference Created by a Changing Magnetic Field0:57
- Magnetic Flux is the Amount of Magnetic Fields Passing Through an Area1:17
- Finding the Magnetic Flux1:36
- Magnetic Field Strength1:39
- Angle Between the Magnetic Field Strength and the Normal to the Area1:51
- Calculating Induced EMF3:01
- The Magnitude of the Induced EMF is Equal to the Rate of Change of the Magnetic Flux3:04
- Induced EMF in a Rectangular Loop of Wire4:03
- Lenz's Law5:17
- Electric Generators and Motors9:28
- Generate an Induced EMF By Turning a Coil of Wire in a magnetic Field9:31
- Generators Use Mechanical Energy to Turn the Coil of Wire9:39
- Electric Motor Operates Using Same Principle10:30
- Example 1: Finding Magnetic Flux10:43
- Example 2: Finding Induced EMF11:54
- Example 3: Changing Magnetic Field13:52
- Example 4: Current Induced in a Rectangular Loop of Wire15:23

26m 41s

- Intro0:00
- Objectives0:09
- Waves0:32
- Pulse1:00
- A Pulse is a Single Disturbance Which Carries Energy Through a Medium or Space1:05
- A Wave is a Series of Pulses1:18
- When a Pulse Reaches a Hard Boundary1:37
- When a Pulse Reaches a Soft or Flexible Boundary2:04
- Types of Waves2:44
- Mechanical Waves2:56
- Electromagnetic Waves3:14
- Types of Wave Motion3:38
- Longitudinal Waves3:39
- Transverse Waves4:18
- Anatomy of a Transverse Wave5:18
- Example 1: Waves Requiring a Medium6:59
- Example 2: Direction of Displacement7:36
- Example 3: Bell in a Vacuum Jar8:47
- Anatomy of a Longitudinal Wave9:22
- Example 4: Tuning Fork9:57
- Example 5: Amplitude of a Sound Wave10:24
- Frequency and Period10:47
- Example 6: Period of an EM Wave11:23
- Example 7: Frequency and Period12:01
- The Wave Equation12:32
- Velocity of a Wave is a Function of the Type of Wave and the Medium It Travels Through12:36
- Speed of a Wave is Related to Its Frequency and Wavelength12:41
- Example 8: Wavelength Using the Wave Equation13:54
- Example 9: Period of an EM Wave14:35
- Example 10: Blue Whale Waves16:03
- Sound Waves17:29
- Sound is a Mechanical Wave Observed by Detecting Vibrations in the Inner Ear17:33
- Particles of Sound Wave Vibrate Parallel With the Direction of the Wave's Velocity17:56
- Example 11: Distance from Speakers18:24
- Resonance19:45
- An Object with the Same 'Natural Frequency' May Begin to Vibrate at This Frequency19:55
- Classic Example20:01
- Example 12: Vibrating Car20:32
- Example 13: Sonar Signal21:28
- Example 14: Waves Across Media24:06
- Example 15: Wavelength of Middle C25:24

20m 45s

- Intro0:00
- Objectives0:09
- Superposition0:30
- When More Than One Wave Travels Through the Same Location in the Same Medium0:32
- The Total Displacement is the Sum of All the Individual Displacements of the Waves0:46
- Example 1: Superposition of Pulses1:01
- Types of Interference2:02
- Constructive Interference2:05
- Destructive Interference2:18
- Example 2: Interference2:47
- Example 3: Shallow Water Waves3:27
- Standing Waves4:23
- When Waves of the Same Frequency and Amplitude Traveling in Opposite Directions Meet in the Same Medium4:26
- A Wave in Which Nodes Appear to be Standing Still and Antinodes Vibrate with Maximum Amplitude Above and Below the Axis4:35
- Standing Waves in String Instruments5:36
- Standing Waves in Open Tubes8:49
- Standing Waves in Closed Tubes9:57
- Interference From Multiple Sources11:43
- Constructive11:55
- Destructive12:14
- Beats12:49
- Two Sound Waves with Almost the Same Frequency Interfere to Create a Beat Pattern12:52
- A Frequency Difference of 1 to 4 Hz is Best for Human Detection of Beat Phenomena13:05
- Example 414:13
- Example 518:03
- Example 619:14
- Example 7: Superposition20:08

19m 2s

- Intro0:00
- Objective0:08
- Doppler Effect0:36
- The Shift In A Wave's Observed Frequency Due to Relative Motion Between the Source of the Wave and Observer0:39
- When Source and/or Observer Move Toward Each Other0:45
- When Source and/or Observer Move Away From Each Other0:52
- Practical Doppler Effect1:01
- Vehicle Traveling Past You1:05
- Applications Are Numerous and Widespread1:56
- Doppler Effect - Astronomy2:43
- Observed Frequencies Are Slightly Lower Than Scientists Would Predict2:50
- More Distant Celestial Objects Are Moving Away from the Earth Faster Than Nearer Objects3:22
- Example 1: Car Horn3:36
- Example 2: Moving Speaker4:13
- Diffraction5:35
- The Bending of Waves Around Obstacles5:37
- Most Apparent When Wavelength Is Same Order of Magnitude as the Obstacle/ Opening6:10
- Single-Slit Diffraction6:16
- Double-Slit Diffraction8:13
- Diffraction Grating11:07
- Sharper and Brighter Maxima11:46
- Useful for Determining Wavelengths Accurately12:07
- Example 3: Double Slit Pattern12:30
- Example 4: Determining Wavelength16:05
- Example 5: Radar Gun18:04
- Example 6: Red Shift18:29

11m 35s

- Intro0:00
- Objectives0:14
- Electromagnetic (EM) Waves0:31
- Light is an EM Wave0:43
- EM Waves Are Transverse Due to the Modulation of the Electric and Magnetic Fields Perpendicular to the Wave Velocity1:00
- Electromagnetic Wave Characteristics1:37
- The Product of an EM Wave's Frequency and Wavelength Must be Constant in a Vacuum1:43
- Polarization3:36
- Unpoloarized EM Waves Exhibit Modulation in All Directions3:47
- Polarized Light Consists of Light Vibrating in a Single Direction4:07
- Polarizers4:29
- Materials Which Act Like Filters to Only Allow Specific Polarizations of Light to Pass4:33
- Polarizers Typically Are Sheets of Material in Which Long Molecules Are Lined Up Like a Picket Fence5:10
- Polarizing Sunglasses5:22
- Reduce Reflections5:26
- Polarizing Sunglasses Have Vertical Polarizing Filters5:48
- Liquid Crystal Displays6:08
- LCDs Use Liquid Crystals in a Suspension That Align Themselves in a Specific Orientation When a Voltage is Applied6:13
- Cross-Orienting a Polarizer and a Matrix of Liquid Crystals so Light Can Be Modulated Pixel-by-Pixel6:26
- Example 1: Color of Light7:30
- Example 2: Analyzing an EM Wave8:49
- Example 3: Remote Control9:45
- Example 4: Comparing EM Waves10:32

24m 32s

- Intro0:00
- Objectives0:10
- Waves at Boundaries0:37
- Reflected0:43
- Transmitted0:45
- Absorbed0:48
- Law of Reflection0:58
- The Angle of Incidence is Equal to the Angle of Reflection1:00
- They Are Both Measured From a Line Perpendicular, or Normal, to the Reflecting Surface1:22
- Types of Reflection1:54
- Diffuse Reflection1:57
- Specular Reflection2:08
- Example 1: Specular Reflection2:24
- Mirrors3:20
- Light Rays From the Object Reach the Plane Mirror and Are Reflected to the Observer3:27
- Virtual Image3:33
- Magnitude of Image Distance4:05
- Plane Mirror Ray Tracing4:15
- Object Distance4:26
- Image Distance4:43
- Magnification of Image7:03
- Example 2: Plane Mirror Images7:28
- Example 3: Image in a Plane Mirror7:51
- Spherical Mirrors8:10
- Inner Surface of a Spherical Mirror8:19
- Outer Surface of a Spherical Mirror8:30
- Focal Point of a Spherical Mirror8:40
- Converging8:51
- Diverging9:00
- Concave (Converging) Spherical Mirrors9:09
- Light Rays Coming Into a Mirror Parallel to the Principal Axis9:14
- Light Rays Passing Through the Center of Curvature10:17
- Light Rays From the Object Passing Directly Through the Focal Point10:52
- Mirror Equation (Lens Equation)12:06
- Object and Image Distances Are Positive on the Reflecting Side of the Mirror12:13
- Formula12:19
- Concave Mirror with Object Inside f12:39
- Example 4: Concave Spherical Mirror14:21
- Example 5: Image From a Concave Mirror14:51
- Convex (Diverging) Spherical Mirrors16:29
- Light Rays Coming Into a Mirror Parallel to the Principal Axis16:37
- Light Rays Striking the Center of the Mirror16:50
- Light Rays Never Converge on the Reflective Side of a Convex Mirror16:54
- Convex Mirror Ray Tracing17:07
- Example 6: Diverging Rays19:12
- Example 7: Focal Length19:28
- Example 8: Reflected Sonar Wave19:53
- Example 9: Plane Mirror Image Distance20:20
- Example 10: Image From a Concave Mirror21:23
- Example 11: Converging Mirror Image Distance23:09

39m 42s

- Intro0:00
- Objectives0:09
- Refraction0:42
- When a Wave Reaches a Boundary Between Media, Part of the Wave is Reflected and Part of the Wave Enters the New Medium0:43
- Wavelength Must Change If the Wave's Speed Changes0:57
- Refraction is When This Causes The Wave to Bend as It Enters the New Medium1:12
- Marching Band Analogy1:22
- Index of Refraction2:37
- Measure of How Much Light Slows Down in a Material2:40
- Ratio of the Speed of an EM Wave in a Vacuum to the Speed of an EM Wave in Another Material is Known as Index of Refraction3:03
- Indices of Refraction3:21
- Dispersion4:01
- White Light is Refracted Twice in Prism4:23
- Index of Refraction of the Prism Material Varies Slightly with Respect to Frequency4:41
- Example 1: Determining n5:14
- Example 2: Light in Diamond and Crown Glass5:55
- Snell's Law6:24
- The Amount of a Light Wave Bends As It Enters a New Medium is Given by the Law of Refraction6:32
- Light Bends Toward the Normal as it Enters a Material With a Higher n7:08
- Light Bends Toward the Normal as it Enters a Material With a Lower n7:14
- Example 3: Angle of Refraction7:42
- Example 4: Changes with Refraction9:31
- Total Internal Reflection10:10
- When the Angle of Refraction Reaches 90 Degrees10:23
- Critical Angle10:34
- Total Internal Reflection10:51
- Applications of TIR12:13
- Example 5: Critical Angle of Water13:17
- Thin Lenses14:15
- Convex Lenses14:22
- Concave Lenses14:31
- Convex Lenses15:24
- Rays Parallel to the Principal Axis are Refracted Through the Far Focal Point of the Lens15:28
- A Ray Drawn From the Object Through the Center of the Lens Passes Through the Center of the Lens Unbent15:53
- Example 6: Converging Lens Image16:46
- Example 7: Image Distance of Convex Lens17:18
- Concave Lenses18:21
- Rays From the Object Parallel to the Principal Axis Are Refracted Away from the Principal Axis on a Line from the Near Focal Point Through the Point Where the Ray Intercepts the Center of the Lens18:25
- Concave Lenses Produce Upright, Virtual, Reduced Images20:30
- Example 8: Light Ray Thought a Lens20:36
- Systems of Optical Elements21:05
- Find the Image of the First Optical Elements and Utilize It as the Object of the Second Optical Element21:16
- Example 9: Lens and Mirrors21:35
- Thin Film Interference27:22
- When Light is Incident Upon a Thin Film, Some Light is Reflected and Some is Transmitted Into the Film27:25
- If the Transmitted Light is Again Reflected, It Travels Back Out of the Film and Can Interfere27:31
- Phase Change for Every Reflection from Low-Index to High-Index28:09
- Example 10: Thin Film Interference28:41
- Example 11: Wavelength in Diamond32:07
- Example 12: Light Incident on Crown Glass33:57
- Example 13: Real Image from Convex Lens34:44
- Example 14: Diverging Lens35:45
- Example 15: Creating Enlarged, Real Images36:22
- Example 16: Image from a Converging Lens36:48
- Example 17: Converging Lens System37:50

23m 47s

- Intro0:00
- Objectives0:11
- Duality of Light0:37
- Photons0:47
- Dual Nature0:53
- Wave Evidence1:00
- Particle Evidence1:10
- Blackbody Radiation & the UV Catastrophe1:20
- Very Hot Objects Emitted Radiation in a Specific Spectrum of Frequencies and Intensities1:25
- Color Objects Emitted More Intensity at Higher Wavelengths1:45
- Quantization of Emitted Radiation1:56
- Photoelectric Effect2:38
- EM Radiation Striking a Piece of Metal May Emit Electrons2:41
- Not All EM Radiation Created Photoelectrons2:49
- Photons of Light3:23
- Photon Has Zero Mass, Zero Charge3:32
- Energy of a Photon is Quantized3:36
- Energy of a Photon is Related to its Frequency3:41
- Creation of Photoelectrons4:17
- Electrons in Metals Were Held in 'Energy Walls'4:20
- Work Function4:32
- Cutoff Frequency4:54
- Kinetic Energy of Photoelectrons5:14
- Electron in a Metal Absorbs a Photon with Energy Greater Than the Metal's Work Function5:16
- Electron is Emitted as a Photoelectron5:24
- Any Absorbed Energy Beyond That Required to Free the Electron is the KE of the Photoelectron5:28
- Photoelectric Effect in a Circuit6:37
- Compton Effect8:28
- Less of Energy and Momentum8:49
- Lost by X-Ray Equals Energy and Gained by Photoelectron8:52
- Compton Wavelength9:09
- Major Conclusions9:36
- De Broglie Wavelength10:44
- Smaller the Particle, the More Apparent the Wave Properties11:03
- Wavelength of a Moving Particle is Known as Its de Broglie Wavelength11:07
- Davisson-Germer Experiment11:29
- Verifies Wave Nature of Moving Particles11:30
- Shoot Electrons at Double Slit11:34
- Example 111:46
- Example 213:07
- Example 313:48
- Example 4A15:33
- Example 4B18:47
- Example 5: Wave Nature of Light19:54
- Example 6: Moving Electrons20:43
- Example 7: Wavelength of an Electron21:11
- Example 8: Wrecking Ball22:50

14m 21s

- Intro0:00
- Objectives0:09
- Rutherford's Gold Foil Experiment0:35
- Most of the Particles Go Through Undeflected1:12
- Some Alpha Particles Are Deflected Large Amounts1:15
- Atoms Have a Small, Massive, Positive Nucleus1:20
- Electrons Orbit the Nucleus1:23
- Most of the Atom is Empty Space1:26
- Problems with Rutherford's Model1:31
- Charges Moving in a Circle Accelerate, Therefore Classical Physics Predicts They Should Release Photons1:39
- Lose Energy When They Release Photons1:46
- Orbits Should Decay and They Should Be Unstable1:50
- Bohr Model of the Atom2:09
- Electrons Don't Lose Energy as They Accelerate2:20
- Each Atom Allows Only a Limited Number of Specific Orbits at Each Energy Level2:35
- Electrons Must Absorb or Emit a Photon of Energy to Change Energy Levels2:40
- Energy Level Diagrams3:29
- n=1 is the Lowest Energy State3:34
- Negative Energy Levels Indicate Electron is Bound to Nucleus of the Atom4:03
- When Electron Reaches 0 eV It Is No Longer Bound4:20
- Electron Cloud Model (Probability Model)4:46
- Electron Only Has A Probability of Being Located in Certain Regions Surrounding the Nucleus4:53
- Electron Orbitals Are Probability Regions4:58
- Atomic Spectra5:16
- Atoms Can Only Emit Certain Frequencies of Photons5:19
- Electrons Can Only Absorb Photons With Energy Equal to the Difference in Energy Levels5:34
- This Leads to Unique Atomic Spectra of Emitted and Absorbed Radiation for Each Element5:37
- Incandescence Emits a Continuous Energy5:43
- If All Colors of Light Are Incident Upon a Cold Gas, The Gas Only Absorbs Frequencies Corresponding to Photon Energies Equal to the Difference Between the Gas's Atomic Energy Levels6:16
- Continuous Spectrum6:42
- Absorption Spectrum6:50
- Emission Spectrum7:08
- X-Rays7:36
- The Photoelectric Effect in Reverse7:38
- Electrons Are Accelerated Through a Large Potential Difference and Collide with a Molybdenum or Platinum Plate7:53
- Example 1: Electron in Hydrogen Atom8:24
- Example 2: EM Emission in Hydrogen10:05
- Example 3: Photon Frequencies11:30
- Example 4: Bright-Line Spectrum12:24
- Example 5: Gas Analysis13:08

15m 47s

- Intro0:00
- Objectives0:08
- The Nucleus0:33
- Protons Have a Charge or +1 e0:39
- Neutrons Are Neutral (0 Charge)0:42
- Held Together by the Strong Nuclear Force0:43
- Example 1: Deconstructing an Atom1:20
- Mass-Energy Equivalence2:06
- Mass is a Measure of How Much Energy an Object Contains2:16
- Universal Conservation of Laws2:31
- Nuclear Binding Energy2:53
- A Strong Nuclear Force Holds Nucleons Together3:04
- Mass of the Individual Constituents is Greater Than the Mass of the Combined Nucleus3:19
- Binding Energy of the Nucleus3:32
- Mass Defect3:37
- Nuclear Decay4:30
- Alpha Decay4:42
- Beta Decay5:09
- Gamma Decay5:46
- Fission6:40
- The Splitting of a Nucleus Into Two or More Nuclei6:42
- For Larger Nuclei, the Mass of Original Nucleus is Greater Than the Sum of the Mass of the Products When Split6:47
- Fusion8:14
- The Process of Combining Two Or More Smaller Nuclei Into a Larger Nucleus8:15
- This Fuels Our Sun and Stars8:28
- Basis of Hydrogen Bomb8:31
- Forces in the Universe9:00
- Strong Nuclear Force9:06
- Electromagnetic Force9:13
- Weak Nuclear Force9:22
- Gravitational Force9:27
- Example 2: Deuterium Nucleus9:39
- Example 3: Particle Accelerator10:24
- Example 4: Tritium Formation12:03
- Example 5: Beta Decay13:02
- Example 6: Gamma Decay14:15
- Example 7: Annihilation14:39

38m 1s

- Intro0:00
- Problem 11:33
- Problem 21:57
- Problem 32:50
- Problem 43:46
- Problem 54:13
- Problem 64:41
- Problem 76:12
- Problem 86:49
- Problem 97:49
- Problem 109:31
- Problem 1110:08
- Problem 1211:03
- Problem 1311:30
- Problem 1412:28
- Problem 1514:04
- Problem 1615:05
- Problem 1715:55
- Problem 1817:06
- Problem 1918:43
- Problem 2019:58
- Problem 2122:03
- Problem 2222:49
- Problem 2323:28
- Problem 2424:04
- Problem 2525:07
- Problem 2626:46
- Problem 2728:03
- Problem 2828:49
- Problem 2930:20
- Problem 3031:10
- Problem 3133:03
- Problem 3233:46
- Problem 3334:47
- Problem 3436:07
- Problem 3536:44

37m 49s

- Intro0:00
- Problem 360:18
- Problem 370:42
- Problem 382:13
- Problem 394:10
- Problem 404:47
- Problem 415:52
- Problem 427:22
- Problem 438:16
- Problem 449:11
- Problem 459:42
- Problem 4610:56
- Problem 4712:03
- Problem 4813:58
- Problem 4914:49
- Problem 5015:36
- Problem 5115:51
- Problem 5217:18
- Problem 5317:59
- Problem 5419:10
- Problem 5521:27
- Problem 5622:40
- Problem 5723:19
- Problem 5823:50
- Problem 5925:35
- Problem 6026:45
- Problem 6127:57
- Problem 6228:32
- Problem 6329:52
- Problem 6430:27
- Problem 6531:27
- Problem 6632:22
- Problem 6733:18
- Problem 6835:21
- Problem 6936:27
- Problem 7036:46

16m 53s

- Intro0:00
- Question 10:23
- Question 28:55

9m 20s

- Intro0:00
- Question 30:14
- Question 44:34

18m 12s

- Intro0:00
- Question 50:15
- Question 63:29
- Question 76:18
- Question 812:53

3m 53s

- Intro0:00
- Question 10:38
- Question 20:51
- Question 31:09
- Question 41:24
- Question 51:49
- Question 62:11
- Question 72:27
- Question 82:49
- Question 93:03
- Question 103:23

7m 6s

- Intro0:00
- Question 10:13
- Question 20:50
- Question 31:56
- Question 42:24
- Question 53:32
- Question 64:01
- Question 75:36
- Question 86:36

6m 48s

- Intro0:00
- Question 10:13
- Question 22:01
- Question 33:06
- Question 43:41
- Question 54:30
- Question 65:52

8m 16s

- Intro0:00
- Question 10:19
- Question 22:19
- Question 33:16
- Question 44:36
- Question 56:43

7m 56s

- Intro0:00
- Question 1-40:12
- Question 52:36
- Question 63:11
- Question 74:44
- Question 86:16

4m 17s

- Intro0:00
- Question 10:13
- Question 20:45
- Question 31:25
- Question 42:00
- Question 52:32
- Question 63:38

4m 34s

- Intro0:00
- Question 10:15
- Question 21:02
- Question 31:50
- Question 42:04
- Question 52:26
- Question 62:54
- Question 73:11
- Question 83:29
- Question 93:47
- Question 104:02

5m 40s

- Intro0:00
- Question 10:16
- Question 20:55
- Question 31:50
- Question 42:40
- Question 53:33
- Question 63:56
- Question 74:29

3m 44s

- Intro0:00
- Question 10:17
- Question 20:44
- Question 31:14
- Question 41:51
- Question 52:11
- Question 62:29
- Question 72:53

6m 37s

- Intro0:00
- Question 10:13
- Question 20:47
- Question 31:25
- Question 42:26
- Question 53:43
- Question 64:41
- Question 75:13
- Question 85:50

6m 13s

- Intro0:00
- Question 10:18
- Question 21:01
- Question 32:50
- Question 43:11
- Question 55:08

5m 17s

- Intro0:00
- Question 10:21
- Question 21:01
- Question 31:50
- Question 42:33
- Question 53:10
- Question 63:31
- Question 73:56
- Question 84:33

6m 33s

- Intro0:00
- Question 10:19
- Question 21:05
- Question 32:09
- Question 42:53
- Question 53:17
- Question 64:00
- Question 74:41
- Question 85:20

9m 29s

- Intro0:00
- Question 10:19
- Question 22:17
- Question 33:25
- Question 43:56
- Question 54:28
- Question 65:04
- Question 76:18
- Question 86:57
- Question 97:47

9m 33s

- Intro0:00
- Question 10:15
- Question 22:08
- Question 34:03
- Question 44:10
- Question 56:08
- Question 66:55
- Question 78:26

6m 2s

- Intro0:00
- Question 10:13
- Question 20:29
- Question 30:55
- Question 41:36
- Question 52:18
- Question 63:22
- Question 74:01
- Question 84:18
- Question 94:49

7m 59s

- Intro0:00
- Question 10:13
- Question 42:26
- Question 53:37
- Question 64:39
- Question 75:28
- Question 85:51

8m 47s

- Intro0:00
- Question 10:18
- Question 21:27
- Question 31:44
- Question 42:33
- Question 52:44
- Question 63:33
- Question 74:41
- Question 85:19
- Question 95:37
- Question 107:12
- Question 117:40

7m 6s

- Intro0:00
- Question 10:10
- Question 21:03
- Question 31:32
- Question 42:12
- Question 53:01
- Question 63:49
- Question 74:24
- Question 84:50
- Question 95:32
- Question 105:55
- Question 116:26

4m 13s

- Intro0:00
- Question 10:14
- Question 20:47
- Question 31:25
- Question 42:25
- Question 53:01

4m 11s

- Intro0:00
- Question 10:19
- Question 20:51
- Question 31:30
- Question 42:19
- Question 53:12

5m 12s

- Intro0:00
- Question 10:14
- Question 20:42
- Question 31:08
- Question 41:43
- Question 52:22
- Question 62:49
- Question 73:14
- Question 84:02

6m 54s

- Intro0:00
- Question 10:13
- Question 20:42
- Question 32:01
- Question 43:02
- Question 53:52
- Question 64:15
- Question 74:37
- Question 84:59
- Question 95:50

5m 15s

- Intro0:00
- Question 10:12
- Question 20:53
- Question 31:44
- Question 42:31
- Question 53:21
- Question 64:06

4m 27s

- Intro0:00
- Question 10:12
- Question 20:33
- Question 30:59
- Question 41:32
- Question 51:56
- Question 62:50
- Question 73:19
- Question 83:50

6m 36s

- Intro0:00
- Question 10:12
- Question 22:16
- Question 32:33
- Question 42:42
- Question 53:18
- Question 65:51
- Question 76:00

3m 43s

- Intro0:00
- Question 10:16
- Question 20:31
- Question 30:56
- Question 41:19
- Question 51:35
- Question 62:36
- Question 73:03

4m 21s

- Intro0:00
- Question 10:13
- Question 20:36
- Question 30:47
- Question 41:13
- Question 51:27
- Question 61:39
- Question 71:54
- Question 82:22
- Question 92:51
- Question 103:32

5m 33s

- Intro0:00
- Question 10:23
- Question 21:04
- Question 32:01
- Question 42:50
- Question 53:12
- Question 63:57
- Question 74:16
- Question 84:42
- Question 94:56

3m 52s

- Intro0:00
- Question 10:13
- Question 20:40
- Question 31:04
- Question 41:17
- Question 51:39
- Question 62:07
- Question 72:41
- Question 83:09

3m 48s

- Intro0:00
- Question 10:12
- Question 20:50
- Question 31:29
- Question 41:46
- Question 53:08

2m 49s

- Intro0:00
- Question 10:29
- Question 51:03
- Question 61:24
- Question 72:01

2m 34s

- Intro0:00
- Question 10:16
- Question 20:31
- Question 30:50
- Question 41:05
- Question 51:37
- Question 62:04

7m 6s

- Intro0:00
- Question 10:24
- Question 20:39
- Question 31:05
- Question 41:51
- Question 52:03
- Question 62:58
- Question 73:14
- Question 83:52
- Question 94:30
- Question 105:04
- Question 116:01
- Question 126:16

5m 30s

- Intro0:00
- Question 10:15
- Question 20:34
- Question 30:53
- Question 41:54
- Question 52:16
- Question 62:27
- Question 72:42
- Question 82:59
- Question 93:45
- Question 104:13
- Question 114:33

8m 13s

- Intro0:00
- Question 10:25
- Question 21:18
- Question 31:43
- Question 42:08
- Question 53:17
- Question 63:54
- Question 74:40
- Question 85:15
- Question 95:54
- Question 106:41
- Question 117:14

8m 15s

- Intro0:00
- Question 10:19
- Question 21:02
- Question 31:37
- Question 42:17
- Question 52:55
- Question 63:32
- Question 74:13
- Question 85:04
- Question 95:29
- Question 105:58
- Question 116:48
- Question 127:39

For more information, please see full course syllabus of AP Physics 1 & 2

1 answer

Last reply by: Professor Dan Fullerton

Sun Jan 8, 2017 11:32 AM

Post by Khalid Khan on January 8, 2017

Why do we not use kinetic energy when we calculate total energy in example 2?

1 answer

Last reply by: Professor Dan Fullerton

Sun Jan 8, 2017 11:20 AM

Post by Khalid Khan on January 8, 2017

Can you please explain where you got pi and the square root of m/k for the period and frequency formulas? We're learning this in class, and we haven't gotten to these formulas yet, so I am just curious.

1 answer

Last reply by: Professor Dan Fullerton

Thu Jun 30, 2016 9:22 AM

Post by Peter Ke on June 29, 2016

For example 6, when you say equilibrium position do you mean by when the pendulum faces directly down. If so doesn't it mean that the KE = maximum while PE = 0, so v=sqrt(2gh) does not apply? I think I am confuse please explain.

Thank you!

3 answers

Last reply by: Professor Dan Fullerton

Sat Apr 30, 2016 12:49 PM

Post by Shikha Bansal on April 29, 2016

For example 2b)the total energy was equal to the spring potential energy only, but for 2d) it was equal to the spring potential and the kinetic energy. Is it because .5 meters is the max it can go (since velocity is zero there)? If so, how did you know ,5 m is the maximum displacement?

Also, for 2c) wasn't the 5 Joules of total energy for the situation where the displacement was .5 meters? How come you used it when the displacement was 0 meters (aka equilibrium position)?

Furthermore, for 2c) I get that the kinetic energy is max at the equilibrium position, but shouldn't the spring potential energy equal 0? So why did u write that kinetic energy was equal to the spring potential energy?

Thanks for all the help!

1 answer

Last reply by: Professor Dan Fullerton

Thu Mar 31, 2016 3:38 PM

Post by Zhe Tian on March 28, 2016

Just a technical question but are angular velocity and angular frequency the same?

4 answers

Last reply by: Professor Dan Fullerton

Tue Aug 11, 2015 8:54 PM

Post by Anh Dang on August 10, 2015

In Circular Motion vs SHM, I don't get why you use sin for the equilibrium position and cosine for the max displacement. Also, why do you use the y coordinates for sin and not x?

2 answers

Last reply by: Jason Wilson

Tue Dec 9, 2014 5:32 PM

Post by Jason Wilson on December 6, 2014

Example 3: I may be simply typing incorrectly on the calculator or possibly missing an entire step. The inverse cos -1(.1/.2) all over 2pi: is coming back on my calc as 60/6.28 = 9.55 what am I missing...I am tired I am cramming right now. :)

3 answers

Last reply by: Professor Dan Fullerton

Sat Aug 30, 2014 8:39 PM

Post by Jungle Jones on August 30, 2014

In example 2, Hooke's Law says that F=-kx, but you just used F=kx to find the spring constant. I understood that the negative sign symbolizes that it is a restoring force, but can you explain why you didn't use the negative sign here?

And do never use the negative sign when doing calculations involving the law?

1 answer

Last reply by: Professor Dan Fullerton

Sat Aug 30, 2014 8:38 PM

Post by Jungle Jones on August 30, 2014

In example 1, I did omega = sqrt(k/m) and got 20, but I got the units of 1/(s^2).

k = 2000 N/m

m = 5 kg

N = kg m/(s^2)

so N/m -> kg/(s^2)

and that divided by 5 kg becomes 1/(s^2)

But it should be just 1/s, so what did I do wrong?

4 answers

Last reply by: Professor Dan Fullerton

Tue Jul 15, 2014 2:40 PM

Post by Jamal Tischler on July 15, 2014

I tried to calculate the spring oscilation period. I used the conservation of energy and kinematics equations for the average acceleration. 1/2kA^2=1/2mv^2 =>v^2=kA^2/m.

v^2=2aA+v0^2=2aA =>kA^2/m=2aA => a= kA/2m.

v=a*t. sqrt(kA^2/m)=kA/2m*t => t= 2 sqrt(m/k). This only the motion from the amplitude to the x=0 position. The farward 3 parts are the same because the kinetic energy is constantly transformed into elastic potential.

T=4*t=8 sqrt(m/k)

The formula said T=2*pi sqrt(m/k). pi doesnt equal 4.

Can you please explain this better ?

1 answer

Last reply by: Professor Dan Fullerton

Thu Mar 13, 2014 9:59 AM

Post by Lin Jiang on March 13, 2014

For example 5, why we needn't to find the equilibrium position. 1/2KX^2, I think x should be how far it pull from equilibrium.

0 answers

Post by Professor Dan Fullerton on February 17, 2014

I use an energy analysis, realizing that at the extremes, the kinetic energy is zero (for an instant the block is still), and all its energy is potential. So the potential energy in a spring is 0.5kx^2. When it's at equilibrium, however, there is no stretch in the spring, so PEs=0, and all the energy must be kinetic due to conservation of energy. So 0.5kx^2=0.5mv^2. Solve for the velocity!

0 answers

Post by sadia mussa on February 17, 2014

how do you get the formula for speed at equilibrium position as well as finding the last question for speed in the example for harmonic oscillator analysis because I don't seem to quite understand it, thanks

1 answer

Last reply by: Professor Dan Fullerton

Mon Dec 9, 2013 9:12 AM

Post by Constance Kang on December 9, 2013

in example 1, since w= rot(m/k) then if i do rot (5/2000) instead of 2pi f, how come i got a different answer ?

3 answers

Last reply by: Professor Dan Fullerton

Tue Apr 30, 2013 7:24 AM

Post by Saki Amagai on April 29, 2013

For example 6, it says "find the tension in the string at the equilibrium position". I think that the net force must equal zero at the equilibrium position; since in the previous slides, it mentioned that force and acceleration all equal zero at the point... Shouldn't "T = mg" and not "T - mg = mv^2/r"?