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Professor Jishi

Conservation of Energy, Part 2

Slide Duration:Table of Contents

I. Mechanics

Introduction to Physics (Basic Math)

1h 17m 37s

- Intro0:00
- What is Physics?1:35
- Physicists and Philosophers1:57
- Differences Between2:48
- Experimental Observations3:20
- Laws (Mathematical)3:48
- Modification of Laws/Experiments4:24
- Example: Newton's Laws of Mechanics5:38
- Example: Einstein's Relativity6:18
- Units8:50
- Various Units9:37
- SI Units10:02
- Length (meter)10:18
- Mass (kilogram)10:35
- Time (second)10:51
- MKS Units (meter kilogram second)11:04
- Definition of Second11:55
- Definition of Meter14:06
- Definition of Kilogram15:21
- Multiplying/Dividing Units19:10
- Trigonometry Overview21:24
- Sine and Cosine21:31
- Pythagorean Theorem23:44
- Tangent24:15
- Sine and Cosine of Angles24:35
- Similar Triangles25:54
- Right Triangle (Opposite, Adjacent, Hypotenuse)28:16
- Other Angles (30-60-90)29:16
- Law of Cosines31:38
- Proof of Law of Cosines33:03
- Law of Sines37:03
- Proof of Law of Sines38:03
- Scalars and Vectors41:00
- Scalar: Magnitude41:22
- Vector: Magnitude and Direction41:52
- Examples42:31
- Extra Example 1: Unit Conversion-1
- Extra Example 2: Law of Cosines-2
- Extra Example 3: Dimensional Analysis-3

Vector Addition

1h 10m 31s

- Intro0:00
- Graphical Method0:10
- Magnitude and Direction of Two Vectors0:40
- Analytical Method or Algebraic Method8:45
- Example: Addition of Vectors9:12
- Parallelogram Rule11:42
- Law of Cosines14:22
- Law of Sines18:32
- Components of a Vector21:35
- Example: Vector Components23:30
- Introducing Third Dimension31:14
- Right Handed System33:06
- Specifying a Vector34:44
- Example: Calculate the Components of Vector36:33
- Vector Addition by Means of Components41:23
- Equality of Vectors47:11
- Dot Product48:39
- Extra Example 1: Vector Addition-1
- Extra Example 2: Angle Between Vectors-2
- Extra Example 3: Vector Addition-3

Dot Product and Cross Product

1h 6m 17s

- Intro0:00
- Dot Product0:12
- Vectors in 3 Dimensions1:36
- Right Handed System2:15
- Vector With 3 Components (Ax,Ay,Az)3:00
- Magnitude in 2 Dimension3:59
- Magnitude in 3 Dimension3:40
- Dot Product of i*i7:21
- Two Vectors are Perpendicular8:50
- A.B13:34
- Angle Between Two Vectors17:27
- Given Two Vectors17:35
- Calculation Angle Between Vectors with (A.B)18:25
- Cross Product23:14
- Cross Product of AxB23:42
- Magnitude of C=AxB cos Theta24:35
- Right Hand Rule27:07
- BxA28:40
- Direction of IxJ=K31:04
- JxK33:15
- KxI35:00
- Evaluation in Terms of Determinants39:28
- Two Vectors A and B with Magnitude and Direction39:35
- Calculate AxB40:08
- Example49:59
- Extra Example 1: Perpendicular Vectors-1
- Extra Example 2: Area of Triangle Given Vertices-2

Derivatives

1h 28m 27s

- Intro0:00
- Definition and Geometric Interpretation1:06
- Example: F(x) is a Polynomial1:14
- Example: Parabola2:48
- F(x+h)4:04
- F(x+h)-F(x)/h5:38
- Slope of the Tangent9:53
- df/dx=f'10:30
- Derivatives of Power of x13:11
- F(x)=1 or Any Constant =013:27
- F(x) =x = 115:13
- F(x)= x2 = 2x16:15
- F(x)= x3 = 3x218:26
- Derivatives of Sin(x), Cos(x) , Exp(x)22:40
- f(x)=Six x =cos(x)22:51
- Cos(x)=1 X= in Radians27:50
- Sin(x)=1 X= in Radians28:55
- e^x where x= in Radians29:49
- Derivative of u(x) v(x)39:17
- Derivative of Product of Two Functions f(x) =x^2 Sin(x)39:30
- Derivative of u(x)/v(x)46:15
- F(u/v)= f(u(x+h)/v(x+h)46:23
- Chain Rule51:40
- Example: F(x) =(x^2-1)^551:53
- F(x)=Sin 3x56:51
- F(x) =e^-2x58:21
- Extra Example 1: Minima and Maxima-1
- Extra Example 2: Derivative-2
- Extra Example 3: Fermat's Principle to Derive Snell's Law-3

Integrals

1h 13m 28s

- Intro0:00
- Definite Integrals0:20
- F(x)0:29
- Area10:43
- Indefinite Integrals13:53
- Suppose Function f(y)=∫f(y) dy15:07
- g(x)=∫ f(x) dx21:45
- ∫2 dx=2x+c22:40
- Evaluation of Definite Integrals25:20
- ∫f(x') dx'=g(x)25:35
- Integral of Sin(x) ,Cos(x) , and Exp(x)36:18
- ∫ sinx dx=-cos x+c36:56
- ∫ cosx dx=sin x+c39:32
- ∫ co2x dx=sin2x40:09
- ∫Cosωdt=1/ωsin ωdt42:42
- ∫e^x dx=e^x+c43:32
- Integration by Substitution45:23
- ∫x(x^2 -1)dx46:01
- Integration by Parts52:30
- d/dx=(uv)'52:45
- ∫udv=∫d(uv)-∫Vdu =uv-∫vdu54:20
- ∫xe^x dx/dv56:11
- Extra Example 1: Integral-1
- Extra Example 2: Integral-2

Motion in One Dimension

1h 19m 35s

- Intro0:00
- Position, Distance, and Displacement0:12
- Position of the Object0:30
- Distance Traveled by The Object5:34
- Displacement of The Object9:05
- Average Speed Over a Certain Time Interval14:46
- Example Of an Object15:15
- Example: Calculating Average Speed20:19
- Average Velocity Over a Time Interval22:22
- Example Calculating Average Velocity of an Object22:45
- Instantaneous Velocity30:45
- Average Acceleration Over a Time Interval40:50
- Example: Average Acceleration of an Object42:01
- Instantaneous Acceleration47:17
- Example: Acceleration of Time T47:33
- Example with Realistic Equation49:52
- Motion With Constant Acceleration: Kinematics Equation53:39
- Example: Motion of an Object with Constant Acceleration53:55
- Extra Example 1: Uniformly Accelerated Motion-1
- Extra Example 2: Catching up with a Car-2
- Extra Example 3: Velocity and Acceleration-3

Kinematics Equation From Calculus

47m 45s

- Intro0:00
- Velocity and Acceleration0:27
- Particle moves In x Direction0:35
- Instantaneous Velocity for Δt =03:05
- Acceleration (Change in Time) v(t+=Δt)-v(t) /Δt4:58
- Example8:08
- x(t) =(-4+3t+2t^2)8:18
- Finding Average velocity at 10sec8:45
- V at t=3s10:28
- x(t) =0 ,0.2 sin (2t)12:20
- Finding Velocity12:50
- Constant Acceleration15:29
- Object Moving with Constant Acceleration15:40
- Find Velocity and Position at Later Time t18:23
- v=∫a dt19:50
- V(t) =v0+at23:33
- v(t) =dx/dt x=∫vdt24:14
- T=v-v0/a29:26
- Extra Example 1: Velocity and Acceleration-1
- Extra Example 2: Particle Acceleration-2

Freely Falling Objects

1h 28m 59s

- Intro0:00
- Acceleration Due to Gravity0:11
- Dropping an Object at Certain Height0:25
- Signs : V , A , D7:07
- Example: Shooting an Object Upwards7:34
- Example: Ground To Ground12:13
- Velocity at Maximum Height14:30
- Time From Ground to Ground23:10
- Shortcut: Calculate Time Spent in Air24:07
- Example: Object Short Downwards30:19
- Object Short Downwards From a Height H30:30
- Use of Quadratic Formula36:23
- Example: Bouncing Ball41:00
- Ball Released From Certain Height41:22
- Time Until Stationary43:10
- Coefficient of Restitution46:40
- Example: Bouncing Ball. Continued53:02
- Extra Example 1: Object Shot Off Cliff-1
- Extra Example 2: Object Released Off Roof-2
- Extra Example 3: Rubber Ball (Coefficient of Restitution)-3

Motion in Two Dimensions, Part 1

1h 8m 38s

- Intro0:00
- Position, Displacement, Velocity, Acceleration0:10
- Position of an Object in X-Y Plane0:19
- Displacement of an Object2:48
- Average Velocity4:30
- Instantaneous Velocity at Time T5:22
- Acceleration of Object8:49
- Projectile Motion9:57
- Object Shooting at Angle10:15
- Object Falling Vertically14:48
- Velocity of an Object18:17
- Displacement of an Object19:20
- Initial Velocity Remains Constant21:24
- Deriving Equation of a Parabola25:23
- Example: Shooting a Soccer Ball25:25
- Time Ball Spent in Air (Ignoring Air Resistance)27:48
- Range of Projectile34:49
- Maximum Height Reached by the Projectile36:25
- Example: Shooting an Object Horizontally40:38
- Time Taken for Shooting42:34
- Range46:01
- Velocity Hitting Ground46:30
- Extra Example 1: Projectile Shot with an Angle-1
- Extra Example 2: What Angle-2

Motion in Two Dimensions, Part 2: Circular Dimension

1h 1m 54s

- Intro0:00
- Uniform Circular Motion0:15
- Object Moving in a Circle at Constant Speed0:26
- Calculation Acceleration3:30
- Change in Velocity3:45
- Magnitude of Acceleration14:21
- Centripetal Acceleration18:15
- Example: Earth Rotating Around The Sun18:42
- Center of the Earth20:45
- Distance Travelled in Making One Revolution21:34
- Acceleration of the Revolution23:37
- Tangential Acceleration and Radial Acceleration25:35
- If Magnitude and Direction Change During Travel26:22
- Tangential Acceleration27:45
- Example: Car on a Curved Road29:50
- Finding Total Acceleration at Time T if Car is at Rest31:13
- Extra Example 1: Centripetal Acceleration on Earth-1
- Extra Example 2: Pendulum Acceleration-2
- Extra Example 3: Radius of Curvature-3

Newton's Laws of Motion

1h 29m 51s

- Intro0:00
- Force0:21
- Contact Force (Push or Pull)1:02
- Field Forces1:49
- Gravity2:06
- Electromagnetic Force2:43
- Strong Force4:12
- Weak Force5:17
- Contact Force as Electromagnetic Force6:08
- Focus on Contact Force and Gravitational Force6:50
- Newton's First Law7:37
- Statement of First Law of Motion7:50
- Uniform Motion (Velocity is Constant)9:38
- Inertia10:39
- Newton's Second Law11:19
- Force as a Vector11:35
- Statement of Second Law of Motion12:02
- Force (Formula)12:22
- Example: 1 Force13:04
- Newton (Unit of Force)13:31
- Example: 2 Forces14:09
- Newton's Third Law19:38
- Action and Reaction Law19:46
- Statement of Third Law of Motion19:58
- Example: 2 Objects20:15
- Example: Objects in Contact21:54
- Example: Person on Earth22:54
- Gravitational Force and the Weight of an Object24:01
- Force of Attraction Formula24:42
- Point Mass and Spherical Objects26:56
- Example: Gravity on Earth28:37
- Example: 1 kg on Earth35:31
- Friction37:09
- Normal Force37:14
- Example: Small Force40:01
- Force of Static Friction43:09
- Maximum Force of Static Friction46:03
- Values of Coefficient of Static Friction47:37
- Coefficient of Kinetic Friction47:53
- Force of Kinetic Friction48:27
- Example: Horizontal Force49:36
- Example: Angled Force52:36
- Extra Example 1: Wire Tension-1
- Extra Example 2: Car Friction-2
- Extra Example 3: Big Block and Small Block-3

Applications of Newton's Laws, Part 1: Inclines

1h 24m 35s

- Intro0:00
- Acceleration on a Frictionless Incline0:35
- Force Action on the Object(mg)1:31
- Net Force Acting on the Object2:20
- Acceleration Perpendicular to Incline8:45
- Incline is Horizontal Surface11:30
- Example: Object on an Inclined Surface13:40
- Rough Inclines and Static Friction20:23
- Box Sitting on a Rough Incline20:49
- Maximum Values of Static Friction25:20
- Coefficient of Static Friction27:53
- Acceleration on a Rough Incline29:00
- Kinetic Friction on Rough Incline29:15
- Object Moving up the Incline33:20
- Net force on the Object36:36
- Example: Time to Reach the Bottom of an Incline41:50
- Displacement is 5m Down the Incline45:26
- Velocity of the Object Down the Incline47:49
- Extra Example 1: Bottom of Incline-1
- Extra Example 2: Incline with Initial Velocity-2
- Extra Example 3: Moving Down an Incline-3

Applications of Newton's Laws, Part 2: Strings and Pulleys

1h 10m 3s

- Intro0:00
- Atwood's Machine0:19
- Object Attached to a String0:39
- Tension on a String2:15
- Two Objects Attached to a String2:23
- Pulley Fixed to the Ceiling, With Mass M1 , M24:53
- Applying Newton's 2nd Law to Calculate Acceleration on M1, M29:21
- One Object on a Horizontal Surface: Frictionless Case17:36
- Connecting Two Unknowns, Tension and Acceleration20:27
- One Object on a Horizontal Surface: Friction Case23:57
- Two Objects Attached to a String with a Pulley24:14
- Applying Newton's 2nd Law26:04
- Tension of an Object Pulls to the Right27:31
- One of the Object is Incline : Frictionless Case32:59
- Sum of Two Forces on Mass M234:39
- If M1g is Larger Than M2g36:29
- One of the Object is Incline : Friction Case40:29
- Coefficient of Kinetic Friction41:18
- Net Force Acting on M245:12
- Extra Example 1: Two Masses on Two Strings-1
- Extra Example 2: Three Objects on Rough Surface-2
- Extra Example 3: Acceleration of a Block-3

Accelerating Frames

1h 13m 28s

- Intro0:00
- What Does a Scale Measure0:11
- Example: Elevator on a Scale0:22
- Normal Force4:57
- Apparent Weight in an Elevator7:42
- Example: Elevator Starts Moving Upwards9:05
- Net Force (Newton's Second Law)11:34
- Apparent Weight14:36
- Pendulum in an Accelerating Train15:58
- Example: Object Hanging on the Ceiling of a Train16:15
- Angle In terms of Increased Acceleration22:04
- Mass and Spring in an Accelerating Truck23:40
- Example: Spring on a Stationary Truck23:55
- Surface of Truck is Frictionless27:38
- Spring is Stretched by distance X28:40
- Cup of Coffee29:55
- Example: Moving Train and Stationary Objects inside Train30:05
- Train Moving With Acceleration A32:45
- Force of Static Friction Acting on Cup36:30
- Extra Example 1: Train Slows with Pendulum-1
- Extra Example 2: Person in Elevator Releases Object-2
- Extra Example 3: Hanging Object in Elevator-3

Circular Motion, Part 1

1h 1m 15s

- Intro0:00
- Object Attached to a String Moving in a Horizontal Circle0:09
- Net Force on Object (Newton's Second Law)1:51
- Force on an Object3:03
- Tension of a String4:40
- Conical Pendulum5:40
- Example: Object Attached to a String in a Horizontal Circle5:50
- Weight of an Object Vertically Down8:05
- Velocity And Acceleration in Vertical Direction11:20
- Net Force on an Object13:02
- Car on a Horizontal Road16:09
- Net Force on Car (Net Vertical Force)18:03
- Frictionless Road18:43
- Road with Friction22:41
- Maximum Speed of Car Without Skidding26:05
- Banked Road28:13
- Road Inclined at an Angle ø28:32
- Force on Car29:50
- Frictionless Road30:45
- Road with Friction36:22
- Extra Example 1: Object Attached to Rod with Two Strings-1
- Extra Example 2: Car on Banked Road-2
- Extra Example 3: Person Held Up in Spinning Cylinder-3

Circular Motion, Part 2

50m 29s

- Intro0:00
- Normal Force by a Pilot Seat0:14
- Example : Pilot Rotating in a Circle r and Speed s0:33
- Pilot at Vertical Position in a Circle of Radius R4:18
- Net Force on Pilot Towards Center (At Bottom)5:53
- Net Force on Pilot Towards Center (At Top)7:55
- Object Attached to a String in Vertical Motion10:46
- Example: Object in a Circle Attached to String10:59
- Case 1: Object with speed v and Object is at Bottom11:30
- Case 2: Object at Top in Vertical Motion15:24
- Object at Angle ø (General Position)17:48
- 2 Radial Forces (Inward & Outward)20:32
- Tension of String23:44
- Extra Example 1: Pail of Water in Vertical Circle-1
- Extra Example 2: Roller Coaster Vertical Circle-2
- Extra Example 3: Bead in Frictionless Loop-3

Work and Energy, Part 1

1h 24m 46s

- Intro0:00
- Work in One Dimension: Constant Force0:11
- Particle Moving in X-Axis0:24
- Displacement Δx=x2-x11:35
- Work Done by the Force W=FΔX2:25
- Example: Object Being Pushed for 10 m (Frictionless case)3:31
- Example: Elevator Descends with constant Velocity5:37
- Work by Tension9:06
- Work in One Dimension: Variable Force11:28
- Object Displaced from a to b Under Action of Force12:06
- Total Work= F(x1) Δx119:48
- Special Case : F(x) =F22:56
- Work Done by a Spring24:30
- Spring Attached to a Object24:42
- Spring Stretched25:40
- Spring Compressed and Released30:30
- Hookes Law32:05
- W=∫F(x) dx ,Initial Position to Final Position36:25
- Work in Three Dimension: Constant Force41:54
- 3 Components Of 3 Dimensions45:45
- Work Done By F=F.Δx47:30
- Example48:58
- Object Moves Up and Inclined49:10
- Work Done by Gravity=F.Δr49:50
- W=F.Δr= -mgz53:50
- Work Done By Normal Force=054:33
- Work in Three Dimension: Variable Force55:45
- Object Moving From A to B with Time56:03
- W=∫f.dr57:45
- Extra Example 1: Work Done By Force-1
- Extra Example 2: Mass on Half Ring-2
- Extra Example 3: Force with Two Paths-3

Work and Energy, Part 2

1h 12m 53s

- Intro0:00
- Work Kinetic Energy Theorem0:16
- Object Moves in 3 Dimensions1:51
- Work Done by Net Force =W=∫f.dr3:27
- W=Change in Kinetic Energy15:11
- Example16:00
- Object Moving on Surface with Mass 10 N16:12
- Using Newton's Second Law18:26
- Using Work Kinetic Energy Theorem21:32
- Gravitational Potential Energy24:30
- Example of a Particle in 3 Dimensions24:47
- Work Done By Force of Gravity26:09
- Conservation of Energy36:37
- Object in a Projectile36:48
- Work Done by Gravity39:50
- Example43:45
- Frictionless Track44:20
- Example50:49
- Pendulum: Object Attached to a String at Height H51:07
- Finding Tension in a String52:20
- Extra Example 1: Object Pulled by Angled Force-1
- Extra Example 2: Projectile Shot at Angle-2

Conservation of Energy, Part 1

1h 32m 50s

- Intro0:00
- Conservative Forces0:10
- Given a Force4:01
- Consider a Particle Moves from P1 to P2 on Path5:40
- Work Done by Force8:28
- Example14:56
- Gravity15:20
- Spring with Block Moves and Stretched17:36
- Friction is Net Conservative23:29
- Path 1 Straight27:04
- Along Path 230:07
- Potential Energy by a Conservative Force33:23
- Choose Reference Point (Potential Energy =0)33:51
- Define Potential Energy at Point P35:23
- Conservation of Energy40:58
- Object Moving from P1 -P241:50
- Work Kinetic Energy Theorem41:58
- Potential Energy of a Spring48:42
- Spring Stretched with Mass M, Find Potential Energy49:13
- Example53:45
- Force Acting on Particle in One Dimension54:10
- Extra Example 1: Work Done By Gravity-1
- Extra Example 2: Prove Constant Force is Conservative-2
- Extra Example 3: Work Done by Force-3
- Extra Example 4: Compression of Spring-4

Conservation of Energy, Part 2

1h 7m 48s

- Intro0:00
- In Presence of Friction0:13
- Work Energy Theorem3:05
- Work Done BY Friction is Negative6:51
- Example10:12
- Object on Inclined Surface with Friction10:20
- Heat, Magnitude by Friction12:42
- Work Done By Friction13:01
- Calculation of the Force From The Potential Energy19:15
- Defining Potential Energy with Conservation of Energy19:35
- Potential Energy and Equilibrium31:16
- Spring Stretched with Mass M31:28
- Stable Equilibrium35:52
- Unstable Equilibrium40:50
- Example41:02
- Two Objects or Two Atoms41:12
- Leonard John's Potential42:15
- Power47:38
- Rate at Force Work Done47:54
- Average Power49:01
- Instant Power Delivered at Time t49:20
- Horse Power53:10
- Extra Example 1: Force from Potential Energy-1
- Extra Example 2: Mass with Two Springs-2
- Extra Example 3: Block Pulled with Friction-3

Conservation of Energy, Part 3 (Examples)

1h 11m 58s

- Intro0:00
- Spring Loaded Gun0:26
- Spring with Bullet0:43
- Finding the Force Constant if Mass of Bullet is Given2:48
- Compression of a Spring5:10
- Sliding Object11:33
- Object Sliding on a Frictionless Surface12:15
- Spring at the End of a Slide12:46
- Using Conservation of Energy K1+u1=K2+U215:06
- Finding Velocity and Energy17:36
- Block Spring System with Friction33:05
- Spring is Unstretched at Equilibrium33:35
- Spring is Compressed33:57
- Finding Total Energy39:02
- Losing Contact on a Circular Track46:16
- Objects Slides on a Circular Track47:25
- Normal Force=048:10
- Centripetal Force48:57
- Finding Velocity at Given Angle49:25
- Energy at the Top50:55
- Contact Lost54:55
- Horse Pulling a Carriage56:07
- Horse Power56:40
- Power=FV57:11
- Extra Example 1: Elevator with Friction-1
- Extra Example 2: Loop the Loop-2

Collisions, Part 1

1h 31m 19s

- Intro0:00
- Linear Momentum0:10
- Example: Object of Mass m with Velocity v0:25
- Example: Object Bounced on a Wall1:08
- Momentum of Object Hitting a Wall2:20
- Change in Momentum4:10
- Force is the Rate of Change of Momentum4:30
- Force=Mass*Acceleration (Newton's Second Law)4:45
- Impulse10:24
- Example: Baseball Hitting a Bat10:40
- Force Applied for a Certain Time11:50
- Magnitude Plot of Force vs Time13:35
- Time of Contact of Baseball = 2 milliseconds (Average Force by Bat)17:42
- Collision Between Two Particles22:40
- Two Objects Collide at Time T23:00
- Both Object Exerts Force on Each Other (Newton's Third Law)24:28
- Collision Time25:42
- Total Momentum Before Collision = Total momentums After Collision32:52
- Collision33:58
- Types of Collisions34:13
- Elastic Collision ( Mechanical Energy is Conserved)34:38
- Collision of Particles in Atoms35:50
- Collision Between Billiard Balls36:54
- Inelastic Collision (Rubber Ball)39:40
- Two Objects Collide and Stick (Completely Inelastic)40:35
- Completely Inelastic Collision41:07
- Example: Two Objects Colliding41:23
- Velocity After Collision42:14
- Heat Produced=Initial K.E-Final K.E47:13
- Ballistic Pendulum47:37
- Example: Determine the Speed of a Bullet47:50
- Mass Swings with Bulled Embedded49:20
- Kinetic Energy of Block with the Bullet50:28
- Extra Example 1: Ball Strikes a Wall-1
- Extra Example 2: Clay Hits Block-2
- Extra Example 3: Bullet Hits Block-3
- Extra Example 4: Child Runs onto Sled-4

Collisions, Part 2

1h 18m 48s

- Intro0:00
- Elastic Collision: One Object Stationary0:28
- Example: Stationary Object and Moving Object0:42
- Conservation of Momentum2:48
- Mechanical Energy Conservation3:43
- Elastic Collision: Both Objects Moving17:34
- Example: Both Objects Moving Towards Each Other17:48
- Kinetic Energy Conservation19:20
- Collision With a Spring-Block System29:17
- Example: Object of Mass Moving with Velocity29:30
- Object Attached to Spring of Mass with Velocity29:50
- Two Objects Attached to a Spring31:30
- Compression of Spring after Collision33:41
- Before Collision: Total Energy (Conservation of Energy)37:25
- After Collision: Total Energy38:49
- Collision in Two Dimensions42:29
- Object Stationary and Other Object is Moving42:46
- Head on Collision (In 1 Dimension)44:07
- Momentum Before Collision45:45
- Momentum After Collision46:06
- If Collision is Elastic (Conservation of Kinetic Energy) Before Collision50:29
- Example51:58
- Objects Moving in Two Directions52:33
- Objects Collide and Stick Together (Inelastic Collision)53:28
- Conservation of Momentum54:17
- Momentum in X-Direction54:27
- Momentum in Y-Direction56:15
- Maximum Height after Collision-1
- Extra Example 2: Two Objects Hitting a Spring-2
- Extra Example 3: Mass Hits and Sticks-3

Center of Mass, Part 1

1h 33m 46s

- Collection of Particles0:13
- System of Coordinates0:40
- Coordinates of Center of Mass2:25
- Four Particles10:10
- Center of Mass at Xcm13:20
- Center of Mass at Ycm15:07
- Extended Objects17:00
- Consider a Object17:30
- Dividing Object in to Smaller Particles19:07
- Divide the Volume N into Pieces23:10
- Center of Mass of a Rod31:02
- Total Mass of Rod35:30
- Center of Mass of a Right Angle42:27
- Right Triangle Placed in Coordinates42:40
- Tiny Strip on a Triangle45:05
- Intersection of a Point56:19
- Extra Example 1: Center of Mass Two Objects-1
- Extra Example 2: Bent Rod Center of Mass-2
- Extra Example 3: Triangle Center of Mass-3

Center of Mass, Part 2

1h 19m 15s

- Intro0:00
- Motion of a System of Particles0:53
- Position Vector of Center of Mass2:30
- Total Momentum7:08
- Net Force Acting on a Particle9:32
- Exploding a Projectile19:12
- Shooting a Projectile in x-z Plane19:50
- Projectile Explodes into 2 pieces of Equal Mass27:19
- Rocket Propulsion35:09
- Rocket with Mass m and Velocity v35:25
- Rocket in Space53:39
- Rocket in Space with Speed=3000m/s53:48
- Engine is Turned On54:19
- Final Mass=1/2 Initial Mass57:15
- Speed after Fuel is Burned58:09
- Extra Example 1: Ball Inelastic Hits Other Ball-1
- Extra Example 2: Rocket Launch Thrust-2

Rotation of a Rigid Body About a Fixed Axis

1h 13m 20s

- Intro0:00
- Particle in Circular Motion0:11
- Specify a Position of a Particle0:55
- Radian3:02
- Angular Displacement8:50
- Rotation of a Rigid Body15:36
- Example: Rotating Disc16:17
- Disk at 5 Revolution/Sec17:24
- Different Points on a Disk Have Different Speeds21:56
- Angular Velocity23:03
- Constant Angular Acceleration: Kinematics31:11
- Rotating Disc31:42
- Object Moving Along x-Axis (Linear Case)33:05
- If Alpha= Constant35:15
- Rotational Kinetic Energy42:11
- Rod in X-Y Plane, Fixed at Center42:43
- Kinetic Energy46:45
- Moment of Inertia52:46
- Moment of Inertia for Certain Shapes54:06
- Rod at Center54:47
- Ring55:45
- Disc56:35
- Cylinder56:56
- Sphere57:20
- Extra Example 1: Rotating Wheel-1
- Extra Example 2: Two Spheres Attached to Rotating Rod-2

Moment of Inertia

1h 32m 22s

- Intro0:00
- Review of Kinematic Rotational Equation0:12
- Rigid Body Rotation on a Axis0:29
- Constant Angular Acceleration10:17
- Rotational Kinetic Energy16:33
- Particle Moving in a Circle16:42
- Moment of Inertia22:43
- Moment of Inertia of a Uniform Rod25:10
- Dividing the Body in Many Pieces27:40
- Total Mass=M Lamda=m/l29:21
- Axis Through the Center of Mass34:02
- Uniform Solid Cylinder35:13
- Cylinder of Length L35:25
- Finding Moment of Inertia I=∫r2 dm36:04
- Volume of Cylinder40:02
- Other Shapes44:37
- Ring45:08
- Disc45:22
- Sphere45:50
- Spherical Shell45:49
- Parallel Axis Theorem46:46
- Object with Center of Mass47:12
- Consider Another Axis Parallel to Primary Axis47:35
- Extra Example 1: Moment of Inertia for Ring and Disk-1
- Extra Example 2: Moment of Inertia for Sphere-2
- Extra Example 3: Moment of Inertia for Spherical Shell-3

Angular Momentum

1h 3m 48s

- Intro0:00
- Angular Momentum of Particle0:06
- Magnitude of Angular Momentum2:27
- Right Hand Rule3:00
- Particle Moving in Circular Motions4:18
- Angular Momentum of a Rigid Body6:44
- Consider a Rigid Body7:06
- Z Axis Through Center7:27
- Rotate About the Z-Axis18:57
- Example19:36
- Rotating in Circular Motion20:08
- Consider a Mass on the Rigid Body20:38
- Angular Momentum of Disk26:14
- Rotation About an Axis of Symmetry26:27
- Perpendicular to Symmetry27:35
- Cylinder29:02
- Sphere29:23
- Rotating on Axis29:40
- Rigid Body Rotates About Axis of Symmetry40:33
- The Z-Component of Angular Momentum40:56
- Consider any Dmi on The Surface41:57
- Example49:40
- Cylinder49:55
- Extra Example 1: Rod Angular Momentum-1
- Extra Example 2: Particle Angular Momentum-2

Rotational Dynamics

1h 19m 59s

- Intro0:00
- Torque0:10
- Object Fixed at Center1:34
- τ=r Fsin θ11:14
- Relation of Torque to Angular Momentum11:47
- Derivative of Momentum12:34
- Consider a Particle With Velocity =V13:51
- For a Rigid Body16:45
- Equation of Rotational Motion25:23
- Object Rigid Body Rotating on Axis27:14
- Torque Acting on the Object27:36
- Torque About Axis of Rotation30:55
- Block and a Pulley31:55
- Rope with Mass=m and Radius of Pulley32:40
- Finding Acceleration and Tension37:26
- Atwood's Machine41:57
- Pulley with Masses m1, m2 and Radius R42:49
- Acceleration50:15
- Extra Example 1: Uniform Rod-1
- Extra Example 2: Two Blocks with Strings-2
- Extra Example 3: Thin Disk-3

Energy Consideration by Rotational Motion

1h 10m 28s

- Intro0:00
- Work Done By Torque0:15
- Rigid Body Rotating about Z-axis1:33
- Rigid Body Rotating about Z-axis3:01
- Point p Rotates on Circle and Perpendicular to z4:19
- Work Kinetic Energy Theorem for Rotational Motion15:36
- Work Done By Torque16:43
- Work Done By Net Torque=Kf-Ki20:31
- Conservation of Mechanical Energy in Rotational Motion21:41
- Conservation Force Acting22:40
- Work Done by Gravity23:15
- Work Done by Torque25:38
- Power Delivered by Torque27:12
- Power by Force27:58
- Rotating Rod30:03
- Rod Clamped at One End30:35
- Angular Speed30:50
- Moment of Inertia About Axis of Rotation35:15
- Speed of Free End37:40
- Another Rotating Rod37:59
- Rod Standing on Surface38:37
- End Does Not Slip39:01
- Speed of Free End41:20
- Strikes Ground42:13
- Extra Example 1: Peg and String-1
- Extra Example 2: Solid Disk-2
- Extra Example 3: Rod and Sphere-3

Conservation of Angular Momentum

1h 6m 57s

- Intro0:00
- Conservation of Angular Momentum in an Isolated System0:13
- Linear Case0:45
- Torque=Rate if Changed in Angular Momentum1:29
- Isolated System1:59
- Neutron Star4:13
- Star Rotates About Some Axis4:31
- Merry Go Round12:50
- Consider a Large Disc13:06
- Total Angular Momentum Calculated18:59
- Sticky Clay Sticking a Rod19:07
- Rod of Length L With Pivot at End19:37
- Piece of Clay of Mass m and Velocity v19:45
- Angular Momentum Calculated28:58
- Extra Example 1: Rod with Beads-1
- Extra Example 2: Mass Striking Rod-2
- Extra Example 3: Wood Block and Bullet-3

Rolling Motion

1h 36m 9s

- Intro0:00
- Pure Rolling Motion0:10
- Disc Rolling on a Surface R (Rolling Without Sipping)0:50
- When Disc Rotates, Center of Mass Moves5:48
- Acceleration of Center of Mass8:43
- Kinetic Energy11:03
- Object in Pure Rotation11:16
- Pure Translation13:28
- Rotation and Translation15:24
- Cylinder Rolling Down an Incline23:55
- Incline24:15
- Cylinder Starts From Rest24:44
- Which Moves Faster37:02
- Rolling a Ring, Disc, Sphere37:19
- Ring I=Mr241:30
- Disc I= 1/2 Mr242:31
- Sphere I= 2/5 mr243:21
- Which Goes Faster49:15
- Incline with a Object Towards the Inclination49:30
- Extra Example 1: Rolling Cylinder-1
- Extra Example 2: Nonuniform Cylinder-2
- Extra Example 3: String Around Disk-3

Universal Gravitation

1h 9m 20s

- Intro0:00
- Newton's Law of Gravity0:09
- Two Particles of Mass m1,m21:22
- Force of Attraction3:02
- Sphere and Small Particle of Mass m4:39
- Two Spheres5:35
- Variation of g With Altitude7:24
- Consider Earth as an Object7:33
- Force Applied To Object9:27
- At or Near Surface of Earth11:51
- Satellites15:39
- Earth and Satellite15:45
- Geosynchronous Satellite21:25
- Gravitational Potential Energy27:32
- Object and Earth Potential Energy=mgh24:45
- P.E=0 When Objects are Infinitely Separated30:32
- Total Energy38:28
- If Object is Very Far From Earth, R=Infinity40:25
- Escape42:33
- Shoot an Object Which Should Not Come Back Down43:06
- Conservation of Energy48:48
- Object at Maximum Height (K.E=0)45:22
- Escape Velocity (Rmax = Infinity)46:50
- Extra Example 1: Density of Earth and Moon-1
- Extra Example 2: Satellite Orbiting Earth-2

Kepler's Laws

1h 12m 25s

- Intro0:00
- Kepler's First law2:18
- Any Point on Ellipse4:33
- Semi Major Axis6:35
- Semi Minor Axis7:05
- Equation of Ellipse7:32
- Eccentricity16:05
- Kepler's Second Law19:46
- Radius Vector20:31
- Torque by Force of Gravity25:00
- Kepler's Third Law36:49
- Time Take for the Planet to make 1 Revolution37:20
- Period41:26
- Mass of Sun43:39
- Orbit of Earth is Almost Circle45:11
- Extra Example 1: Halley's Comet-1
- Extra Example 2: Two Planets Around Star-2
- Extra Example 3: Neutron Star-3

Energy and Gravitation

35m 4s

- Intro0:00
- Gravitational Potential Energy0:10
- Conservative Force1:45
- Along Path A ∫f.dr=07:35
- Along Path B ∫f.dr=-110:30
- Δu= ∫f r1 to r210:58
- Near the Surface of the Earth17:07
- Two Points on Surface of Earth17:22
- Planets and Satellites24:40
- Circular Orbits24:59
- Elliptical Orbits30:54

Static Equilibrium

1h 38m 57s

- Intro0:00
- Torque0:09
- Introduction to Torque0:16
- Rod in X-Y Direction0:30
- Particle in Equilibrium18:15
- Particle in Equilibrium, Net Force=018:30
- Extended Object Like a Rod19:13
- Conditions of Equilibrium26:34
- Forces Acting on Object (Proof of Torque)31:46
- The Lever35:38
- Rod on Lever with Two Masses35:51
- Standing on a Supported Beam40:53
- Example : Wall and Beam Rope Connect Beam and Wall41:00
- Net Force45:38
- Net Torque48:33
- Finding ø52:50
- Ladder About to Slip53:38
- Example: Finding Angle ø Where Ladder Doesn't slip53:44
- Extra Example 1: Bear Retrieving Basket-1
- Extra Example 2: Sliding Cabinet-2

Simple Harmonic System Spring Block System

1h 2m 35s

- Intro0:00
- Restoring Force0:41
- Spring Attached to a Block0:53
- Spring Stretched1:58
- Force=Kx (K=Force Constant)5:45
- Simple Harmonic Motion11:31
- According to Newton's Law F=mxa11:55
- Equation of Motion15:15
- Frequency, Period, Velocity, and Acceleration34:23
- Object Without Stretching34:52
- Object Stretched35:15
- Acceleration a=dv/dt43:20
- Block Spring System53:01
- Object Being Compressed53:26
- Energy Consideration57:47
- Example59:48
- Spring Being Compressed59:55

The Pendulum

1h 1m 55s

- Intro0:00
- Simple Pendulum0:07
- Mass Attached to the String0:25
- Torque=mgr Perpendicular7:34
- Moment of Inertia15:36
- When φ<<124:30
- Example33:13
- Mass Hanging with 1kg and Length 1 M and Velocity 2m33:26
- Period34:50
- Frequency35:40
- Ki+ui=Kf+uf37:01
- Physical Pendulum41:39
- Rigid Body with a Pivot and let it Oscillate42:00
- Torque Produced47:58
- Example53:35
- Rod Fixed and Made to Oscillated53:40
- Period54:40
- Torsional Pendulum57:57
- Mass Suspended with a Torsional Fiber58:15
- Torque Produced58:55
- Example1:00:05
- Wire With Torsional -K1:00:11

Damped and Forced Oscillation

53m 35s

- Intro0:00
- Damped Oscillation0:11
- Spring Oscillation0:45
- Force of Friction F=-bv5:20
- Spring in Absence of Friction6:10
- No Damping8:29
- In Presence of Damping8:41
- Example21:07
- Pendulum Oscillating at 10 Degrees21:23
- After 10 Min Amplitude Becomes 5 Degrees22:10
- Forced Oscillation30:18
- Spring Oscillating up and Down, Applying Force35:25
- Steady State Solution41:49
- Example46:48
- Spring with Object Mass=0.1 kg47:05

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

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

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