# AP Physics C: Mechanics Ramps & Inclines

Section 3: Dynamics: Lecture 5 | 20:31 min

We’ve started to factor in real-world elements into our problems, and another very useful element is having an inclined ramp. Rather than a box sliding across the surface of a table, a box sliding up a ramp now has a retarding y-component as well as the x-component. Here we need to call upon what we learned in the beginning about breaking up a problem and solving for each dimension, and solving for the x- and y-components to find the total retarding force. Inclined planes are very common physics problems, so make sure you can do these frontwards, sideways, backwards, and blindfolded!

Dan Fullerton

Ramps & Inclines

Slide Duration:Table of Contents

7m 12s

- Intro0:00
- Objectives0:11
- What is Physics?0:27
- Why?0:50
- Physics Answers the 'Why' Question0:51
- Matter1:27
- Matter1:28
- Mass1:43
- Inertial Mass1:50
- Gravitational Mass2:13
- A Spacecraft's Mass3:03
- What is the Mass of the Spacecraft?3:05
- Energy3:37
- Energy3:38
- Work3:45
- Putting Energy and Work Together3:50
- Mass-Energy Equivalence4:15
- Relationship between Mass & Energy: E = mc²4:16
- Source of Energy on Earth4:47
- The Study of Everything5:00
- Physics is the Study of Everything5:01
- Mechanics5:29
- Topics Covered5:30
- Topics Not Covered6:07
- Next Steps6:44
- Three Things You'd Like to Learn About in Physics6:45

1h 51s

- Intro0:00
- Objectives0:10
- Vectors and Scalars1:06
- Scalars1:07
- Vectors1:27
- Vector Representations2:00
- Vector Representations2:01
- Graphical Vector Addition2:54
- Graphical Vector Addition2:55
- Graphical Vector Subtraction5:36
- Graphical Vector Subtraction5:37
- Vector Components7:12
- Vector Components7:13
- Angle of a Vector8:56
- tan θ9:04
- sin θ9:25
- cos θ9:46
- Vector Notation10:10
- Vector Notation 110:11
- Vector Notation 212:59
- Example I: Magnitude of the Horizontal & Vertical Component16:08
- Example II: Magnitude of the Plane's Eastward Velocity17:59
- Example III: Magnitude of Displacement19:33
- Example IV: Total Displacement from Starting Position21:51
- Example V: Find the Angle Theta Depicted by the Diagram26:35
- Vector Notation, cont.27:07
- Unit Vector Notation27:08
- Vector Component Notation27:25
- Vector Multiplication28:39
- Dot Product28:40
- Cross Product28:54
- Dot Product29:03
- Dot Product29:04
- Defining the Dot Product29:26
- Defining the Dot Product29:27
- Calculating the Dot Product29:42
- Unit Vector Notation29:43
- Vector Component Notation30:58
- Example VI: Calculating a Dot Product31:45
- Example VI: Part 1 - Find the Dot Product of the Following Vectors31:46
- Example VI: Part 2 - What is the Angle Between A and B?32:20
- Special Dot Products33:52
- Dot Product of Perpendicular Vectors33:53
- Dot Product of Parallel Vectors34:03
- Dot Product Properties34:51
- Commutative34:52
- Associative35:05
- Derivative of A * B35:24
- Example VII: Perpendicular Vectors35:47
- Cross Product36:42
- Cross Product of Two Vectors36:43
- Direction Using the Right-hand Rule37:32
- Cross Product of Parallel Vectors38:04
- Defining the Cross Product38:13
- Defining the Cross Product38:14
- Calculating the Cross Product Unit Vector Notation38:41
- Calculating the Cross Product Unit Vector Notation38:42
- Calculating the Cross Product Matrix Notation39:18
- Calculating the Cross Product Matrix Notation39:19
- Example VII: Find the Cross Product of the Following Vectors42:09
- Cross Product Properties45:16
- Cross Product Properties45:17
- Units46:41
- Fundamental Units46:42
- Derived units47:13
- Example IX: Dimensional Analysis47:21
- Calculus49:05
- Calculus49:06
- Differential Calculus49:49
- Differentiation & Derivative49:50
- Example X: Derivatives51:21
- Integral Calculus53:03
- Integration53:04
- Integral53:11
- Integration & Derivation are Inverse Functions53:16
- Determine the Original Function53:37
- Common Integrations54:45
- Common Integrations54:46
- Example XI: Integrals55:17
- Example XII: Calculus Applications58:32

23m 47s

- Intro0:00
- Objectives0:10
- Position / Displacement0:39
- Object's Position0:40
- Position Vector0:45
- Displacement0:56
- Position & Displacement are Vectors1:05
- Position & Displacement in 1 Dimension1:11
- Example I: Distance & Displacement1:21
- Average Speed2:14
- Average Speed2:15
- Average Speed is Scalar2:27
- Average Velocity2:39
- Average Velocity2:40
- Average Velocity is a Vector2:57
- Example II: Speed vs. Velocity3:16
- Example II: Deer's Average Speed3:17
- Example II: Deer's Average Velocity3:48
- Example III: Chuck the Hungry Squirrel4:21
- Example III: Chuck's Distance Traveled4:22
- Example III: Chuck's Displacement4:43
- Example III: Chuck's Average Speed5:25
- Example III: Chuck's Average Velocity5:39
- Acceleration6:11
- Acceleration: Definition & Equation6:12
- Acceleration: Units6:19
- Relationship of Acceleration to Velocity6:52
- Example IV: Acceleration Problem7:05
- The Position Vector7:39
- The Position Vector7:40
- Average Velocity9:35
- Average Velocity9:36
- Instantaneous Velocity11:20
- Instantaneous Velocity11:21
- Instantaneous Velocity is the Derivative of Position with Respect to Time11:35
- Area Under the Velocity-time Graph12:08
- Acceleration12:36
- More on Acceleration12:37
- Average Acceleration13:11
- Velocity vs. Time Graph13:14
- Graph Transformations13:59
- Graphical Analysis of Motion14:00
- Velocity and acceleration in 2D14:35
- Velocity Vector in 2D14:39
- Acceleration Vector in 2D15:26
- Polynomial Derivatives16:10
- Polynomial Derivatives16:11
- Example V: Polynomial Kinematics16:31
- Example VI: Velocity Function17:54
- Example VI: Part A - Determine the Acceleration at t=1 Second17:55
- Example VI: Part B - Determine the Displacement between t=0 and t=5 Seconds18:33
- Example VII: Tortoise and Hare20:14
- Example VIII: d-t Graphs22:40

36m 47s

- Intro0:00
- Objectives0:09
- Special Case: Constant Acceleration0:31
- Constant Acceleration & Kinematic Equations0:32
- Deriving the Kinematic Equations1:28
- V = V₀ + at1:39
- ∆x = V₀t +(1/2)at²2:03
- V² = V₀² +2a∆x4:05
- Problem Solving Steps7:02
- Step 17:13
- Step 27:18
- Step 37:27
- Step 47:30
- Step 57:31
- Example IX: Horizontal Kinematics7:38
- Example X: Vertical Kinematics9:45
- Example XI: 2 Step Problem11:23
- Example XII: Acceleration Problem15:01
- Example XIII: Particle Diagrams15:57
- Example XIV: Particle Diagrams17:36
- Example XV: Quadratic Solution18:46
- Free Fall22:56
- Free Fall22:57
- Air Resistance23:24
- Air Resistance23:25
- Acceleration Due to Gravity23:48
- Acceleration Due to Gravity23:49
- Objects Falling From Rest24:18
- Objects Falling From Rest24:19
- Example XVI: Falling Objects24:55
- Objects Launched Upward26:01
- Objects Launched Upward26:02
- Example XVII: Ball Thrown Upward27:16
- Example XVIII: Height of a Jump27:48
- Example XIX: Ball Thrown Downward31:10
- Example XX: Maximum Height32:27
- Example XXI: Catch-Up Problem33:53
- Example XXII: Ranking Max Height35:52

30m 34s

- Intro0:00
- Objectives0:07
- What is a Projectile?0:28
- What is a Projectile?0:29
- Path of a Projectile0:58
- Path of a Projectile0:59
- Independence of Motion2:45
- Vertical & Horizontal Motion2:46
- Example I: Horizontal Launch3:14
- Example II: Parabolic Path7:20
- Angled Projectiles8:01
- Angled Projectiles8:02
- Example III: Human Cannonball10:05
- Example IV: Motion Graphs14:39
- Graphing Projectile Motion19:05
- Horizontal Equation19:06
- Vertical Equation19:46
- Example V: Arrow Fired from Tower21:28
- Example VI: Arrow Fired from Tower24:10
- Example VII: Launch from a Height24:40
- Example VIII: Acceleration of a Projectile29:49

30m 24s

- Intro0:00
- Objectives0:08
- Radians and Degrees0:32
- Degrees0:35
- Radians0:40
- Example I: Radians and Degrees1:08
- Example I: Part A - Convert 90 Degrees to Radians1:09
- Example I: Part B - Convert 6 Radians to Degrees2:08
- Linear vs. Angular Displacement2:38
- Linear Displacement2:39
- Angular Displacement2:52
- Linear vs. Angular Velocity3:18
- Linear Velocity3:19
- Angular Velocity3:25
- Direction of Angular Velocity4:36
- Direction of Angular Velocity4:37
- Converting Linear to Angular Velocity5:05
- Converting Linear to Angular Velocity5:06
- Example II: Earth's Angular Velocity6:12
- Linear vs. Angular Acceleration7:26
- Linear Acceleration7:27
- Angular Acceleration7:32
- Centripetal Acceleration8:05
- Expressing Position Vector in Terms of Unit Vectors8:06
- Velocity10:00
- Centripetal Acceleration11:14
- Magnitude of Centripetal Acceleration13:24
- Example III: Angular Velocity & Centripetal Acceleration14:02
- Example IV: Moon's Orbit15:03
- Reference Frames17:44
- Reference Frames17:45
- Laws of Physics18:00
- Motion at Rest vs. Motion at a Constant Velocity18:21
- Motion is Relative19:20
- Reference Frame: Sitting in a Lawn Chair19:21
- Reference Frame: Sitting on a Train19:56
- Calculating Relative Velocities20:19
- Calculating Relative Velocities20:20
- Example: Calculating Relative Velocities20:57
- Example V: Man on a Train23:19
- Example VI: Airspeed24:56
- Example VII: 2-D Relative Motion26:12
- Example VIII: Relative Velocity w/ Direction28:32

23m 57s

- Intro0:00
- Objectives0:11
- Newton's 1st Law of Motion0:28
- Newton's 1st Law of Motion0:29
- Force1:16
- Definition of Force1:17
- Units of Force1:20
- How Much is a Newton?1:25
- Contact Forces1:47
- Field Forces2:32
- What is a Net Force?2:53
- What is a Net Force?2:54
- What Does It Mean?4:35
- What Does It Mean?4:36
- Objects at Rest4:52
- Objects at Rest4:53
- Objects in Motion5:12
- Objects in Motion5:13
- Equilibrium6:03
- Static Equilibrium6:04
- Mechanical Equilibrium6:22
- Translational Equilibrium6:38
- Inertia6:48
- Inertia6:49
- Inertial Mass6:58
- Gravitational Mass7:11
- Example I: Inertia7:40
- Example II: Inertia8:03
- Example III: Translational Equilibrium8:25
- Example IV: Net Force9:19
- Free Body Diagrams10:34
- Free Body Diagrams Overview10:35
- Falling Elephant: Free Body Diagram10:53
- Free Body Diagram Neglecting Air Resistance10:54
- Free Body Diagram Including Air Resistance11:22
- Soda on Table11:54
- Free Body Diagram for a Glass of Soda Sitting on a Table11:55
- Free Body Diagram for Box on Ramp13:38
- Free Body Diagram for Box on Ramp13:39
- Pseudo- Free Body Diagram15:26
- Example V: Translational Equilibrium18:35

23m 57s

- Intro0:00
- Objectives0:09
- Newton's 2nd Law of Motion0:36
- Newton's 2nd Law of Motion0:37
- Applying Newton's 2nd Law1:12
- Step 11:13
- Step 21:18
- Step 31:27
- Step 41:36
- Example I: Block on a Surface1:42
- Example II: Concurrent Forces2:42
- Mass vs. Weight4:09
- Mass4:10
- Weight4:28
- Example III: Mass vs. Weight4:45
- Example IV: Translational Equilibrium6:43
- Example V: Translational Equilibrium8:23
- Example VI: Determining Acceleration10:13
- Example VII: Stopping a Baseball12:38
- Example VIII: Steel Beams14:11
- Example IX: Tension Between Blocks17:03
- Example X: Banked Curves18:57
- Example XI: Tension in Cords24:03
- Example XII: Graphical Interpretation27:13
- Example XIII: Force from Velocity28:12
- Newton's 3rd Law29:16
- Newton's 3rd Law29:17
- Examples - Newton's 3rd Law30:01
- Examples - Newton's 3rd Law30:02
- Action-Reaction Pairs30:40
- Girl Kicking Soccer Ball30:41
- Rocket Ship in Space31:02
- Gravity on You31:23
- Example XIV: Force of Gravity32:11
- Example XV: Sailboat32:38
- Example XVI: Hammer and Nail33:18
- Example XVII: Net Force33:47

20m 41s

- Intro0:00
- Objectives0:06
- Coefficient of Friction0:21
- Coefficient of Friction0:22
- Approximate Coefficients of Friction0:44
- Kinetic or Static?1:21
- Sled Sliding Down a Snowy Hill1:22
- Refrigerator at Rest that You Want to Move1:32
- Car with Tires Rolling Freely1:49
- Car Skidding Across Pavement2:01
- Example I: Car Sliding2:21
- Example II: Block on Incline3:04
- Calculating the Force of Friction3:33
- Calculating the Force of Friction3:34
- Example III: Finding the Frictional Force4:02
- Example IV: Box on Wood Surface5:34
- Example V: Static vs. Kinetic Friction7:35
- Example VI: Drag Force on Airplane7:58
- Example VII: Pulling a Sled8:41
- Example VIII: AP-C 2007 FR113:23
- Example VIII: Part A13:24
- Example VIII: Part B14:40
- Example VIII: Part C15:19
- Example VIII: Part D17:08
- Example VIII: Part E18:24

32m 10s

- Intro0:00
- Objectives0:07
- Retarding Forces0:41
- Retarding Forces0:42
- The Skydiver1:30
- Drag Forces on a Free-falling Object1:31
- Velocity as a Function of Time5:31
- Velocity as a Function of Time5:32
- Velocity as a Function of Time, cont.12:27
- Acceleration12:28
- Velocity as a Function of Time, cont.15:16
- Graph: Acceleration vs. Time16:06
- Graph: Velocity vs. Time16:40
- Graph: Displacement vs. Time17:04
- Example I: AP-C 2005 FR117:43
- Example I: Part A17:44
- Example I: Part B19:17
- Example I: Part C20:17
- Example I: Part D21:09
- Example I: Part E22:42
- Example II: AP-C 2013 FR224:26
- Example II: Part A24:27
- Example II: Part B25:25
- Example II: Part C26:22
- Example II: Part D27:04
- Example II: Part E30:50

20m 31s

- Intro0:00
- Objectives0:06
- Drawing Free Body Diagrams for Ramps0:32
- Step 1: Choose the Object & Draw It as a Dot or Box0:33
- Step 2: Draw and Label all the External Forces0:39
- Step 3: Sketch a Coordinate System0:42
- Example: Object on a Ramp0:52
- Pseudo-Free Body Diagrams2:06
- Pseudo-Free Body Diagrams2:07
- Redraw Diagram with All Forces Parallel to Axes2:18
- Box on a Ramp4:08
- Free Body Diagram for Box on a Ramp4:09
- Pseudo-Free Body Diagram for Box on a Ramp4:54
- Example I: Box at Rest6:13
- Example II: Box Held By Force6:35
- Example III: Truck on a Hill8:46
- Example IV: Force Up a Ramp9:29
- Example V: Acceleration Down a Ramp12:01
- Example VI: Able of Repose13:59
- Example VII: Sledding17:03

24m 58s

- Intro0:00
- Objectives0:07
- What is an Atwood Machine?0:25
- What is an Atwood Machine?0:26
- Properties of Atwood Machines1:03
- Ideal Pulleys are Frictionless and Massless1:04
- Tension is Constant1:14
- Setup for Atwood Machines1:26
- Setup for Atwood Machines1:27
- Solving Atwood Machine Problems1:52
- Solving Atwood Machine Problems1:53
- Alternate Solution5:24
- Analyze the System as a Whole5:25
- Example I: Basic Atwood Machine7:31
- Example II: Moving Masses9:59
- Example III: Masses and Pulley on a Table13:32
- Example IV: Mass and Pulley on a Ramp15:47
- Example V: Ranking Atwood Machines19:50

37m 34s

- Intro0:00
- Objectives0:07
- What is Work?0:36
- What is Work?0:37
- Units of Work1:09
- Work in One Dimension1:31
- Work in One Dimension1:32
- Examples of Work2:19
- Stuntman in a Jet Pack2:20
- A Girl Struggles to Push Her Stalled Car2:50
- A Child in a Ghost Costume Carries a Bag of Halloween Candy Across the Yard3:24
- Example I: Moving a Refrigerator4:03
- Example II: Liberating a Car4:53
- Example III: Lifting Box5:30
- Example IV: Pulling a Wagon6:13
- Example V: Ranking Work on Carts7:13
- Non-Constant Forces12:21
- Non-Constant Forces12:22
- Force vs. Displacement Graphs13:49
- Force vs. Displacement Graphs13:50
- Hooke's Law14:41
- Hooke's Law14:42
- Determining the Spring Constant15:38
- Slope of the Graph Gives the Spring Constant, k15:39
- Work Done in Compressing the Spring16:34
- Find the Work Done in Compressing the String16:35
- Example VI: Finding Spring Constant17:21
- Example VII: Calculating Spring Constant19:48
- Example VIII: Hooke's Law20:30
- Example IX: Non-Linear Spring22:18
- Work in Multiple Dimensions23:52
- Work in Multiple Dimensions23:53
- Work-Energy Theorem25:25
- Work-Energy Theorem25:26
- Example X: Work-Energy Theorem28:35
- Example XI: Work Done on Moving Carts30:46
- Example XII: Velocity from an F-d Graph35:01

28m 4s

- Intro0:00
- Objectives0:08
- Energy Transformations0:31
- Energy Transformations0:32
- Work-Energy Theorem0:57
- Kinetic Energy1:12
- Kinetic Energy: Definition1:13
- Kinetic Energy: Equation1:55
- Example I: Frog-O-Cycle2:07
- Potential Energy2:46
- Types of Potential Energy2:47
- A Potential Energy Requires an Interaction between Objects3:29
- Internal energy3:50
- Internal Energy3:51
- Types of Energy4:37
- Types of Potential & Kinetic Energy4:38
- Gravitational Potential Energy5:42
- Gravitational Potential Energy5:43
- Example II: Potential Energy7:27
- Example III: Kinetic and Potential Energy8:16
- Example IV: Pendulum9:09
- Conservative Forces11:37
- Conservative Forces Overview11:38
- Type of Conservative Forces12:42
- Types of Non-conservative Forces13:02
- Work Done by Conservative Forces13:28
- Work Done by Conservative Forces13:29
- Newton's Law of Universal Gravitation14:18
- Gravitational Force of Attraction between Any Two Objects with Mass14:19
- Gravitational Potential Energy15:27
- Gravitational Potential Energy15:28
- Elastic Potential Energy17:36
- Elastic Potential Energy17:37
- Force from Potential Energy18:51
- Force from Potential Energy18:52
- Gravitational Force from the Gravitational Potential Energy20:46
- Gravitational Force from the Gravitational Potential Energy20:47
- Hooke's Law from Potential Energy22:04
- Hooke's Law from Potential Energy22:05
- Summary23:16
- Summary23:17
- Example V: Kinetic Energy of a Mass24:40
- Example VI: Force from Potential Energy25:48
- Example VII: Work on a Spinning Disc26:54

54m 56s

- Intro0:00
- Objectives0:09
- Conservation of Mechanical Energy0:32
- Consider a Single Conservative Force Doing Work on a Closed System0:33
- Non-Conservative Forces1:40
- Non-Conservative Forces1:41
- Work Done by a Non-conservative Force1:47
- Formula: Total Energy1:54
- Formula: Total Mechanical Energy2:04
- Example I: Falling Mass2:15
- Example II: Law of Conservation of Energy4:07
- Example III: The Pendulum6:34
- Example IV: Cart Compressing a Spring10:12
- Example V: Cart Compressing a Spring11:12
- Example V: Part A - Potential Energy Stored in the Compressed Spring11:13
- Example V: Part B - Maximum Vertical Height12:01
- Example VI: Car Skidding to a Stop13:05
- Example VII: Block on Ramp14:22
- Example VIII: Energy Transfers16:15
- Example IX: Roller Coaster20:04
- Example X: Bungee Jumper23:32
- Example X: Part A - Speed of the Jumper at a Height of 15 Meters Above the Ground24:48
- Example X: Part B - Speed of the Jumper at a Height of 30 Meters Above the Ground26:53
- Example X: Part C - How Close Does the Jumper Get to the Ground?28:28
- Example XI: AP-C 2002 FR330:28
- Example XI: Part A30:59
- Example XI: Part B31:54
- Example XI: Part C32:50
- Example XI: Part D & E33:52
- Example XII: AP-C 2007 FR335:24
- Example XII: Part A35:52
- Example XII: Part B36:27
- Example XII: Part C37:48
- Example XII: Part D39:32
- Example XIII: AP-C 2010 FR141:07
- Example XIII: Part A41:34
- Example XIII: Part B43:05
- Example XIII: Part C45:24
- Example XIII: Part D47:18
- Example XIV: AP-C 2013 FR148:25
- Example XIV: Part A48:50
- Example XIV: Part B49:31
- Example XIV: Part C51:27
- Example XIV: Part D52:46
- Example XIV: Part E53:25

16m 44s

- Intro0:00
- Objectives0:06
- Defining Power0:20
- Definition of Power0:21
- Units of Power0:27
- Average Power0:43
- Instantaneous Power1:03
- Instantaneous Power1:04
- Example I: Horizontal Box2:07
- Example II: Accelerating Truck4:48
- Example III: Motors Delivering Power6:00
- Example IV: Power Up a Ramp7:00
- Example V: Power from Position Function8:51
- Example VI: Motorcycle Stopping10:48
- Example VII: AP-C 2003 FR111:52
- Example VII: Part A11:53
- Example VII: Part B12:50
- Example VII: Part C14:36
- Example VII: Part D15:52

13m 9s

- Intro0:00
- Objectives0:07
- Momentum0:39
- Definition of Momentum0:40
- Total Momentum1:00
- Formula for Momentum1:05
- Units of Momentum1:11
- Example I: Changing Momentum1:18
- Impulse2:27
- Impulse2:28
- Example II: Impulse2:41
- Relationship Between Force and ∆p (Impulse)3:36
- Relationship Between Force and ∆p (Impulse)3:37
- Example III: Force from Momentum4:37
- Impulse-Momentum Theorem5:14
- Impulse-Momentum Theorem5:15
- Example IV: Impulse-Momentum6:26
- Example V: Water Gun & Horizontal Force7:56
- Impulse from F-t Graphs8:53
- Impulse from F-t Graphs8:54
- Example VI: Non-constant Forces9:16
- Example VII: F-t Graph10:01
- Example VIII: Impulse from Force11:19

46m 30s

- Intro0:00
- Objectives0:08
- Conservation of Linear Momentum0:28
- In an Isolated System0:29
- In Any Closed System0:37
- Direct Outcome of Newton's 3rd Law of Motion0:47
- Collisions and Explosions1:07
- Collisions and Explosions1:08
- The Law of Conservation of Linear Momentum1:25
- Solving Momentum Problems1:35
- Solving Momentum Problems1:36
- Types of Collisions2:08
- Elastic Collision2:09
- Inelastic Collision2:34
- Example I: Traffic Collision3:00
- Example II: Collision of Two Moving Objects6:55
- Example III: Recoil Velocity9:47
- Example IV: Atomic Collision12:12
- Example V: Collision in Multiple Dimensions18:11
- Example VI: AP-C 2001 FR125:16
- Example VI: Part A25:33
- Example VI: Part B26:44
- Example VI: Part C28:17
- Example VI: Part D28:58
- Example VII: AP-C 2002 FR130:10
- Example VII: Part A30:20
- Example VII: Part B32:14
- Example VII: Part C34:25
- Example VII: Part D36:17
- Example VIII: AP-C 2014 FR138:55
- Example VIII: Part A39:28
- Example VIII: Part B41:00
- Example VIII: Part C42:57
- Example VIII: Part D44:20

28m 26s

- Intro0:00
- Objectives0:07
- Center of Mass0:45
- Center of Mass0:46
- Finding Center of Mass by Inspection1:25
- For Uniform Density Objects1:26
- For Objects with Multiple Parts1:36
- For Irregular Objects1:44
- Example I: Center of Mass by Inspection2:06
- Calculating Center of Mass for Systems of Particles2:25
- Calculating Center of Mass for Systems of Particles2:26
- Example II: Center of Mass (1D)3:15
- Example III: Center of Mass of Continuous System4:29
- Example IV: Center of Mass (2D)6:00
- Finding Center of Mass by Integration7:38
- Finding Center of Mass by Integration7:39
- Example V: Center of Mass of a Uniform Rod8:10
- Example VI: Center of Mass of a Non-Uniform Rod11:40
- Center of Mass Relationships14:44
- Center of Mass Relationships14:45
- Center of Gravity17:36
- Center of Gravity17:37
- Uniform Gravitational Field vs. Non-uniform Gravitational Field17:53
- Example VII: AP-C 2004 FR118:26
- Example VII: Part A18:45
- Example VII: Part B19:38
- Example VII: Part C21:03
- Example VII: Part D22:04
- Example VII: Part E24:52

21m 36s

- Intro0:00
- Objectives0:08
- Uniform Circular Motion0:42
- Distance Around the Circle for Objects Traveling in a Circular Path at Constant Speed0:51
- Average Speed for Objects Traveling in a Circular Path at Constant Speed1:15
- Frequency1:42
- Definition of Frequency1:43
- Symbol of Frequency1:46
- Units of Frequency1:49
- Period2:04
- Period2:05
- Frequency and Period2:19
- Frequency and Period2:20
- Example I: Race Car2:32
- Example II: Toy Train3:22
- Example III: Round-A-Bout4:07
- Example III: Part A - Period of the Motion4:08
- Example III: Part B- Frequency of the Motion4:43
- Example III: Part C- Speed at Which Alan Revolves4:58
- Uniform Circular Motion5:28
- Is an Object Undergoing Uniform Circular Motion Accelerating?5:29
- Direction of Centripetal Acceleration6:21
- Direction of Centripetal Acceleration6:22
- Magnitude of Centripetal Acceleration8:23
- Magnitude of Centripetal Acceleration8:24
- Example IV: Car on a Track8:39
- Centripetal Force10:14
- Centripetal Force10:15
- Calculating Centripetal Force11:47
- Calculating Centripetal Force11:48
- Example V: Acceleration12:41
- Example VI: Direction of Centripetal Acceleration13:44
- Example VII: Loss of Centripetal Force14:03
- Example VIII: Bucket in Horizontal Circle14:44
- Example IX: Bucket in Vertical Circle15:24
- Example X: Demon Drop17:38
- Example X: Question 118:02
- Example X: Question 218:25
- Example X: Question 319:22
- Example X: Question 420:13

32m 52s

- Intro0:00
- Objectives0:07
- Radians and Degrees0:35
- Once Around a Circle: In Degrees0:36
- Once Around a Circle: In Radians0:48
- Measurement of Radian0:51
- Example I: Radian and Degrees1:08
- Example I: Convert 90° to Radians1:09
- Example I: Convert 6 Radians to Degree1:23
- Linear vs. Angular Displacement1:43
- Linear Displacement1:44
- Angular Displacement1:51
- Linear vs. Angular Velocity2:04
- Linear Velocity2:05
- Angular Velocity2:10
- Direction of Angular Velocity2:28
- Direction of Angular Velocity2:29
- Converting Linear to Angular Velocity2:58
- Converting Linear to Angular Velocity2:59
- Example II: Angular Velocity of Earth3:51
- Linear vs. Angular Acceleration4:35
- Linear Acceleration4:36
- Angular Acceleration4:42
- Example III: Angular Acceleration5:09
- Kinematic Variable Parallels6:30
- Kinematic Variable Parallels: Translational & Angular6:31
- Variable Translations7:00
- Variable Translations: Translational & Angular7:01
- Kinematic Equation Parallels7:38
- Kinematic Equation Parallels: Translational & Rotational7:39
- Example IV: Deriving Centripetal Acceleration8:29
- Example V: Angular Velocity13:24
- Example V: Part A13:25
- Example V: Part B14:15
- Example VI: Wheel in Motion14:39
- Example VII: AP-C 2003 FR316:23
- Example VII: Part A16:38
- Example VII: Part B17:34
- Example VII: Part C24:02
- Example VIII: AP-C 2014 FR225:35
- Example VIII: Part A25:47
- Example VIII: Part B26:28
- Example VIII: Part C27:48
- Example VIII: Part D28:26
- Example VIII: Part E29:16

24m

- Intro0:00
- Objectives0:07
- Types of Inertia0:34
- Inertial Mass0:35
- Moment of Inertia0:44
- Kinetic Energy of a Rotating Disc1:25
- Kinetic Energy of a Rotating Disc1:26
- Calculating Moment of Inertia (I)5:32
- Calculating Moment of Inertia (I)5:33
- Moment of Inertia for Common Objects5:49
- Moment of Inertia for Common Objects5:50
- Example I: Point Masses6:46
- Example II: Uniform Rod9:09
- Example III: Solid Cylinder13:07
- Parallel Axis Theorem (PAT)17:33
- Parallel Axis Theorem (PAT)17:34
- Example IV: Calculating I Using the Parallel Axis Theorem18:39
- Example V: Hollow Sphere20:18
- Example VI: Long Thin Rod20:55
- Example VII: Ranking Moment of Inertia21:50
- Example VIII: Adjusting Moment of Inertia22:39

26m 9s

- Intro0:00
- Objectives0:06
- Torque0:18
- Definition of Torque0:19
- Torque & Rotation0:26
- Lever Arm ( r )0:30
- Example: Wrench0:39
- Direction of the Torque Vector1:45
- Direction of the Torque Vector1:46
- Finding Direction Using the Right-hand Rule1:53
- Newton's 2nd Law: Translational vs. Rotational2:20
- Newton's 2nd Law: Translational vs. Rotational2:21
- Equilibrium3:17
- Static Equilibrium3:18
- Dynamic Equilibrium3:30
- Example I: See-Saw Problem3:46
- Example II: Beam Problem7:12
- Example III: Pulley with Mass10:34
- Example IV: Net Torque13:46
- Example V: Ranking Torque15:29
- Example VI: Ranking Angular Acceleration16:25
- Example VII: Café Sign17:19
- Example VIII: AP-C 2008 FR219:44
- Example VIII: Part A20:12
- Example VIII: Part B21:08
- Example VIII: Part C22:36
- Example VIII: Part D24:37

56m 58s

- Intro0:00
- Objectives0:08
- Conservation of Energy0:48
- Translational Kinetic Energy0:49
- Rotational Kinetic Energy0:54
- Total Kinetic Energy1:03
- Example I: Disc Rolling Down an Incline1:10
- Rotational Dynamics4:25
- Rotational Dynamics4:26
- Example II: Strings with Massive Pulleys4:37
- Example III: Rolling without Slipping9:13
- Example IV: Rolling with Slipping13:45
- Example V: Amusement Park Swing22:49
- Example VI: AP-C 2002 FR226:27
- Example VI: Part A26:48
- Example VI: Part B27:30
- Example VI: Part C29:51
- Example VI: Part D30:50
- Example VII: AP-C 2006 FR331:39
- Example VII: Part A31:49
- Example VII: Part B36:20
- Example VII: Part C37:14
- Example VII: Part D38:48
- Example VIII: AP-C 2010 FR239:40
- Example VIII: Part A39:46
- Example VIII: Part B40:44
- Example VIII: Part C44:31
- Example VIII: Part D46:44
- Example IX: AP-C 2013 FR348:27
- Example IX: Part A48:47
- Example IX: Part B50:33
- Example IX: Part C53:28
- Example IX: Part D54:15
- Example IX: Part E56:20

33m 2s

- Intro0:00
- Objectives0:09
- Linear Momentum0:44
- Definition of Linear Momentum0:45
- Total Angular Momentum0:52
- p = mv0:59
- Angular Momentum1:08
- Definition of Angular Momentum1:09
- Total Angular Momentum1:21
- A Mass with Velocity v Moving at Some Position r1:29
- Calculating Angular Momentum1:44
- Calculating Angular Momentum1:45
- Spin Angular Momentum4:17
- Spin Angular Momentum4:18
- Example I: Object in Circular Orbit4:51
- Example II: Angular Momentum of a Point Particle6:34
- Angular Momentum and Net Torque9:03
- Angular Momentum and Net Torque9:04
- Conservation of Angular Momentum11:53
- Conservation of Angular Momentum11:54
- Example III: Ice Skater Problem12:20
- Example IV: Combining Spinning Discs13:52
- Example V: Catching While Rotating15:13
- Example VI: Changes in Angular Momentum16:47
- Example VII: AP-C 2005 FR317:37
- Example VII: Part A18:12
- Example VII: Part B18:32
- Example VII: Part C19:53
- Example VII: Part D21:52
- Example VIII: AP-C 2014 FR324:23
- Example VIII: Part A24:31
- Example VIII: Part B25:33
- Example VIII: Part C26:58
- Example VIII: Part D28:24
- Example VIII: Part E30:42

1h 1m 12s

- Intro0:00
- Objectives0:08
- Simple Harmonic Motion0:45
- Simple Harmonic Motion0:46
- Circular Motion vs. Simple Harmonic Motion (SHM)1:39
- Circular Motion vs. Simple Harmonic Motion (SHM)1:40
- Position, Velocity, & Acceleration4:55
- Position4:56
- Velocity5:12
- Acceleration5:49
- Frequency and Period6:37
- Frequency6:42
- Period6:49
- Angular Frequency7:05
- Angular Frequency7:06
- Example I: Oscillating System7:37
- Example I: Determine the Object's Angular Frequency7:38
- Example I: What is the Object's Position at Time t = 10s?8:16
- Example I: At What Time is the Object at x = 0.1m?9:10
- Mass on a Spring10:17
- Mass on a Spring10:18
- Example II: Analysis of Spring-Block System11:34
- Example III: Spring-Block ranking12:53
- General Form of Simple Harmonic Motion14:41
- General Form of Simple Harmonic Motion14:42
- Graphing Simple Harmonic Motion (SHM)15:22
- Graphing Simple Harmonic Motion (SHM)15:23
- Energy of Simple Harmonic Motion (SHM)15:49
- Energy of Simple Harmonic Motion (SHM)15:50
- Horizontal Spring Oscillator19:24
- Horizontal Spring Oscillator19:25
- Vertical Spring Oscillator20:58
- Vertical Spring Oscillator20:59
- Springs in Series23:30
- Springs in Series23:31
- Springs in Parallel26:08
- Springs in Parallel26:09
- The Pendulum26:59
- The Pendulum27:00
- Energy and the Simple Pendulum27:46
- Energy and the Simple Pendulum27:47
- Frequency and Period of a Pendulum30:16
- Frequency and Period of a Pendulum30:17
- Example IV: Deriving Period of a Simple Pendulum31:42
- Example V: Deriving Period of a Physical Pendulum35:20
- Example VI: Summary of Spring-Block System38:16
- Example VII: Harmonic Oscillator Analysis44:14
- Example VII: Spring Constant44:24
- Example VII: Total Energy44:45
- Example VII: Speed at the Equilibrium Position45:05
- Example VII: Speed at x = 0.30 Meters45:37
- Example VII: Speed at x = -0.40 Meter46:46
- Example VII: Acceleration at the Equilibrium Position47:21
- Example VII: Magnitude of Acceleration at x = 0.50 Meters47:35
- Example VII: Net Force at the Equilibrium Position48:04
- Example VII: Net Force at x = 0.25 Meter48:20
- Example VII: Where does Kinetic Energy = Potential Energy?48:33
- Example VIII: Ranking Spring Systems49:35
- Example IX: Vertical Spring Block Oscillator51:45
- Example X: Ranking Period of Pendulum53:50
- Example XI: AP-C 2009 FR254:50
- Example XI: Part A54:58
- Example XI: Part B57:57
- Example XI: Part C59:11
- Example XII: AP-C 2010 FR31:00:18
- Example XII: Part A1:00:49
- Example XII: Part B1:02:47
- Example XII: Part C1:04:30
- Example XII: Part D1:05:53
- Example XII: Part E1:08:13

34m 59s

- Intro0:00
- Objectives0:07
- Newton's Law of Universal Gravitation0:45
- Newton's Law of Universal Gravitation0:46
- Example I: Gravitational Force Between Earth and Sun2:24
- Example II: Two Satellites3:39
- Gravitational Field Strength4:23
- Gravitational Field Strength4:24
- Example III: Weight on Another Planet6:22
- Example IV: Gravitational Field of a Hollow Shell7:31
- Example V: Gravitational Field Inside a Solid Sphere8:33
- Velocity in Circular Orbit12:05
- Velocity in Circular Orbit12:06
- Period and Frequency for Circular Orbits13:56
- Period and Frequency for Circular Orbits13:57
- Mechanical Energy for Circular Orbits16:11
- Mechanical Energy for Circular Orbits16:12
- Escape Velocity17:48
- Escape Velocity17:49
- Kepler's 1st Law of Planetary Motion19:41
- Keller's 1st Law of Planetary Motion19:42
- Kepler's 2nd Law of Planetary Motion20:05
- Keller's 2nd Law of Planetary Motion20:06
- Kepler's 3rd Law of Planetary Motion20:57
- Ratio of the Squares of the Periods of Two Planets20:58
- Ratio of the Squares of the Periods to the Cubes of Their Semi-major Axes21:41
- Total Mechanical Energy for an Elliptical Orbit21:57
- Total Mechanical Energy for an Elliptical Orbit21:58
- Velocity and Radius for an Elliptical Orbit22:35
- Velocity and Radius for an Elliptical Orbit22:36
- Example VI: Rocket Launched Vertically24:26
- Example VII: AP-C 2007 FR228:16
- Example VII: Part A28:35
- Example VII: Part B29:51
- Example VII: Part C31:14
- Example VII: Part D32:23
- Example VII: Part E33:16

28m 11s

- Intro0:00
- Problem 10:30
- Problem 20:51
- Problem 31:25
- Problem 42:00
- Problem 53:05
- Problem 64:19
- Problem 74:48
- Problem 85:18
- Problem 95:38
- Problem 106:26
- Problem 117:21
- Problem 128:08
- Problem 138:35
- Problem 149:20
- Problem 1510:09
- Problem 1610:25
- Problem 1711:30
- Problem 1812:27
- Problem 1913:00
- Problem 2014:40
- Problem 2115:44
- Problem 2216:42
- Problem 2317:35
- Problem 2417:54
- Problem 2518:32
- Problem 2619:08
- Problem 2720:56
- Problem 2822:19
- Problem 2922:36
- Problem 3023:18
- Problem 3124:06
- Problem 3224:40

28m 11s

- Intro0:00
- Question 10:15
- Part A: I0:16
- Part A: II0:46
- Part A: III1:13
- Part B1:40
- Part C2:49
- Part D: I4:46
- Part D: II5:15
- Question 25:46
- Part A: I6:13
- Part A: II7:05
- Part B: I7:48
- Part B: II8:42
- Part B: III9:03
- Part B: IV9:26
- Part B: V11:32
- Question 313:30
- Part A: I13:50
- Part A: II14:16
- Part A: III14:38
- Part A: IV14:56
- Part A: V15:36
- Part B16:11
- Part C17:00
- Part D: I19:56
- Part D: II21:08

For more information, please see full course syllabus of AP Physics C: Mechanics

1 answer

Last reply by: Professor Dan Fullerton

Sun Aug 14, 2016 12:53 PM

Post by Cathy Zhao on August 14, 2016

On Example 5, why the acceleration of the block is in the x direction not y direction?

2 answers

Last reply by: Professor Dan Fullerton

Sun Aug 14, 2016 12:45 PM

Post by Cathy Zhao on August 14, 2016

At 4:54, why Fnet y=0? Is Fnet x also=O?

0 answers

Post by Professor Dan Fullerton on March 3, 2016

Assuming you're looking at roughly 5:45, you could write it that way as well. I defined down the ramp as my positive x-direction, so I have mgsin(theta)-F=0. You could just as easily write -mgsintheta+F=0. Regardless, you'll come up with F=mgsin(theta).

1 answer

Last reply by: Professor Dan Fullerton

Thu Mar 3, 2016 5:48 AM

Post by Joy Ojukwu on March 2, 2016

why is it not -mgsintheta + F on x axis