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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 (306090)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 Conversion1
 Extra Example 2: Law of Cosines2
 Extra Example 3: Dimensional Analysis3
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 Addition1
 Extra Example 2: Angle Between Vectors2
 Extra Example 3: Vector Addition3
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 Vectors1
 Extra Example 2: Area of Triangle Given Vertices2
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^21)^551:53
 F(x)=Sin 3x56:51
 F(x) =e^2x58:21
 Extra Example 1: Minima and Maxima1
 Extra Example 2: Derivative2
 Extra Example 3: Fermat's Principle to Derive Snell's Law3
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: Integral1
 Extra Example 2: Integral2
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 Motion1
 Extra Example 2: Catching up with a Car2
 Extra Example 3: Velocity and Acceleration3
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=vv0/a29:26
 Extra Example 1: Velocity and Acceleration1
 Extra Example 2: Particle Acceleration2
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 Cliff1
 Extra Example 2: Object Released Off Roof2
 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 XY 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 Angle1
 Extra Example 2: What Angle2
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 Earth1
 Extra Example 2: Pendulum Acceleration2
 Extra Example 3: Radius of Curvature3
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 Tension1
 Extra Example 2: Car Friction2
 Extra Example 3: Big Block and Small Block3
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 Incline1
 Extra Example 2: Incline with Initial Velocity2
 Extra Example 3: Moving Down an Incline3
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 Strings1
 Extra Example 2: Three Objects on Rough Surface2
 Extra Example 3: Acceleration of a Block3
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 Pendulum1
 Extra Example 2: Person in Elevator Releases Object2
 Extra Example 3: Hanging Object in Elevator3
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 Strings1
 Extra Example 2: Car on Banked Road2
 Extra Example 3: Person Held Up in Spinning Cylinder3
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 Circle1
 Extra Example 2: Roller Coaster Vertical Circle2
 Extra Example 3: Bead in Frictionless Loop3
Work and Energy, Part 1
1h 24m 46s
 Intro0:00
 Work in One Dimension: Constant Force0:11
 Particle Moving in XAxis0:24
 Displacement Δx=x2x11:35
 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 Force1
 Extra Example 2: Mass on Half Ring2
 Extra Example 3: Force with Two Paths3
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 Force1
 Extra Example 2: Projectile Shot at Angle2
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 Gravity1
 Extra Example 2: Prove Constant Force is Conservative2
 Extra Example 3: Work Done by Force3
 Extra Example 4: Compression of Spring4
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 Energy1
 Extra Example 2: Mass with Two Springs2
 Extra Example 3: Block Pulled with Friction3
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 Friction1
 Extra Example 2: Loop the Loop2
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.EFinal 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 Wall1
 Extra Example 2: Clay Hits Block2
 Extra Example 3: Bullet Hits Block3
 Extra Example 4: Child Runs onto Sled4
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 SpringBlock 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 XDirection54:27
 Momentum in YDirection56:15
 Maximum Height after Collision1
 Extra Example 2: Two Objects Hitting a Spring2
 Extra Example 3: Mass Hits and Sticks3
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 Objects1
 Extra Example 2: Bent Rod Center of Mass2
 Extra Example 3: Triangle Center of Mass3
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 xz 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 Ball1
 Extra Example 2: Rocket Launch Thrust2
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 xAxis (Linear Case)33:05
 If Alpha= Constant35:15
 Rotational Kinetic Energy42:11
 Rod in XY 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 Wheel1
 Extra Example 2: Two Spheres Attached to Rotating Rod2
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 Disk1
 Extra Example 2: Moment of Inertia for Sphere2
 Extra Example 3: Moment of Inertia for Spherical Shell3
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 ZAxis18:57
 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 ZComponent of Angular Momentum40:56
 Consider any Dmi on The Surface41:57
 Example49:40
 Cylinder49:55
 Extra Example 1: Rod Angular Momentum1
 Extra Example 2: Particle Angular Momentum2
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 Rod1
 Extra Example 2: Two Blocks with Strings2
 Extra Example 3: Thin Disk3
Energy Consideration by Rotational Motion
1h 10m 28s
 Intro0:00
 Work Done By Torque0:15
 Rigid Body Rotating about Zaxis1:33
 Rigid Body Rotating about Zaxis3:01
 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=KfKi20:31
 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 String1
 Extra Example 2: Solid Disk2
 Extra Example 3: Rod and Sphere3
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 Beads1
 Extra Example 2: Mass Striking Rod2
 Extra Example 3: Wood Block and Bullet3
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 Cylinder1
 Extra Example 2: Nonuniform Cylinder2
 Extra Example 3: String Around Disk3
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 Moon1
 Extra Example 2: Satellite Orbiting Earth2
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 Comet1
 Extra Example 2: Two Planets Around Star2
 Extra Example 3: Neutron Star3
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 XY 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 Basket1
 Extra Example 2: Sliding Cabinet2
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
 Example00:05
 Wire With Torsional K00:11
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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