Center of Mass, Part 2, AP Physics C/Mechanics

Center of Mass, Part 2

I. Mechanics: Lecture 25 | 79:15 min

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Center of Mass, Part 2

Lecture Slides are screen-captured images of important points in the lecture. Students can download and print out these lecture slide images to do practice problems as well as take notes while watching the lecture.

Intro

Motion of a System of Particles

Exploding a Projectile

Rocket Propulsion

Rocket with Mass m and Velocity v

Rocket in Space

Extra Example 1: Ball Inelastic Hits Other Ball

Extra Example 2: Rocket Launch Thrust

I. Mechanics
	Introduction to Physics (Basic Math)	77:37
	Vector Addition	70:31
	Dot Product and Cross Product	66:17
	Derivatives	88:27
	Integrals	73:28
	Motion in One Dimension	79:35
	Kinematics Equation From Calculus	47:45
	Freely Falling Objects	88:59
	Motion in Two Dimensions, Part 1	68:38
	Motion in Two Dimensions, Part 2: Circular Dimension	61:54
	Newton's Laws of Motion	89:51
	Applications of Newton's Laws, Part 1: Inclines	84:35
	Applications of Newton's Laws, Part 2: Strings and Pulleys	70:03
	Accelerating Frames	73:28
	Circular Motion, Part 1	61:15
	Circular Motion, Part 2	50:29
	Work and Energy, Part 1	84:46
	Work and Energy, Part 2	72:53
	Conservation of Energy, Part 1	92:50
	Conservation of Energy, Part 2	67:48
	Conservation of Energy, Part 3 (Examples)	71:58
	Collisions, Part 1	91:19
	Collisions, Part 2	78:48
	Center of Mass, Part 1	93:46
	Center of Mass, Part 2	79:15
	Rotation of a Rigid Body About a Fixed Axis	73:20
	Moment of Inertia	92:22
	Angular Momentum	63:48
	Rotational Dynamics	79:59
	Energy Consideration by Rotational Motion	70:28
	Conservation of Angular Momentum	66:57
	Rolling Motion	96:09
	Universal Gravitation	69:20
	Kepler's Laws	72:25
	Energy and Gravitation	35:04
	Static Equilibrium	98:57
	Simple Harmonic System Spring Block System	62:35
	The Pendulum	61:55
	Damped and Forced Oscillation	53:35

AP Physics C: Mechanics


Introduction to Physics (Basic Math)			77:37
	Intro		0:00
	What is Physics?		1:35
		Physicists and Philosophers	1:57
		Differences Between	2:48
		Experimental Observations	3:20
		Laws (Mathematical)	3:48
		Modification of Laws/Experiments	4:24
		Example: Newton's Laws of Mechanics	5:38
		Example: Einstein's Relativity	6:18
	Units		8:50
		Various Units	9:37
		SI Units	10:02
		Length (meter)	10:18
		Mass (kilogram)	10:35
		Time (second)	10:51
		MKS Units (meter kilogram second)	11:04
		Definition of Second	11:55
		Definition of Meter	14:06
		Definition of Kilogram	15:21
		Multiplying/Dividing Units	19:10
	Trigonometry Overview		21:24
		Sine and Cosine	21:31
		Pythagorean Theorem	23:44
		Tangent	24:15
		Sine and Cosine of Angles	24:35
		Similar Triangles	25:54
		Right Triangle (Opposite, Adjacent, Hypotenuse)	28:16
		Other Angles (30-60-90)	29:16
	Law of Cosines		31:38
		Proof of Law of Cosines	33:03
	Law of Sines		37:03
		Proof of Law of Sines	38:03
	Scalars and Vectors		41:00
		Scalar: Magnitude	41:22
		Vector: Magnitude and Direction	41:52
		Examples	42:31
	Extra Example 1: Unit Conversion		2:47
	Extra Example 2: Law of Cosines		12:52
	Extra Example 3: Dimensional Analysis		11:43
Vector Addition			70:31
	Intro		0:00
	Graphical Method		0:10
		Magnitude and Direction of Two Vectors	0:40
	Analytical Method or Algebraic Method		8:45
		Example: Addition of Vectors	9:12
		Parallelogram Rule	11:42
		Law of Cosines	14:22
		Law of Sines	18:32
	Components of a Vector		21:35
		Example: Vector Components	23:30
		Introducing Third Dimension	31:14
		Right Handed System	33:06
	Specifying a Vector		34:44
		Example: Calculate the Components of Vector	36:33
	Vector Addition by Means of Components		41:23
	Equality of Vectors		47:11
	Dot Product		48:39
	Extra Example 1: Vector Addition		9:57
	Extra Example 2: Angle Between Vectors		4:10
	Extra Example 3: Vector Addition		4:51
Dot Product and Cross Product			66:17
	Intro		0:00
	Dot Product		0:12
		Vectors in 3 Dimensions	1:36
		Right Handed System	2:15
		Vector With 3 Components (Ax,Ay,Az)	3:00
		Magnitude in 2 Dimension	3:59
		Magnitude in 3 Dimension	3:40
		Dot Product of i*i	7:21
		Two Vectors are Perpendicular	8:50
		A.B	13:34
	Angle Between Two Vectors		17:27
		Given Two Vectors	17:35
		Calculation Angle Between Vectors with (A.B)	18:25
	Cross Product		23:14
		Cross Product of AxB	23:42
		Magnitude of C=AxB cos Theta	24:35
		Right Hand Rule	27:07
		BxA	28:40
		Direction of IxJ=K	31:04
		JxK	33:15
		KxI	35:00
	Evaluation in Terms of Determinants		39:28
		Two Vectors A and B with Magnitude and Direction	39:35
		Calculate AxB	40:08
	Example		49:59
	Extra Example 1: Perpendicular Vectors		2:46
	Extra Example 2: Area of Triangle Given Vertices		8:29
Derivatives			88:27
	Intro		0:00
	Definition and Geometric Interpretation		1:06
		Example: F(x) is a Polynomial	1:14
		Example: Parabola	2:48
		F(x+h)	4:04
		F(x+h)-F(x)/h	5:38
		Slope of the Tangent	9:53
		df/dx=f'	10:30
	Derivatives of Power of x		13:11
		F(x)=1 or Any Constant =0	13:27
		F(x) =x = 1	15:13
		F(x)= x2 = 2x	16:15
		F(x)= x3 = 3x2	18:26
	Derivatives of Sin(x), Cos(x) , Exp(x)		22:40
		f(x)=Six x =cos(x)	22:51
		Cos(x)=1 X= in Radians	27:50
		Sin(x)=1 X= in Radians	28:55
		e^x where x= in Radians	29:49
	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 Rule		51:40
		Example: F(x) =(x^2-1)^5	51:53
		F(x)=Sin 3x	56:51
		F(x) =e^-2x	58:21
	Extra Example 1: Minima and Maxima		7:00
	Extra Example 2: Derivative		5:29
	Extra Example 3: Fermat's Principle to Derive Snell's Law		16:33
Integrals			73:28
	Intro		0:00
	Definite Integrals		0:20
		F(x)	0:29
		Area	10:43
	Indefinite Integrals		13:53
		Suppose Function f(y)=∫f(y) dy	15:07
		g(x)=∫ f(x) dx	21:45
		∫2 dx=2x+c	22:40
	Evaluation of Definite Integrals		25:20
		∫f(x') dx'=g(x)	25:35
	Integral of Sin(x) ,Cos(x) , and Exp(x)		36:18
		∫ sinx dx=-cos x+c	36:56
		∫ cosx dx=sin x+c	39:32
		∫ co2x dx=sin2x	40:09
		∫Cosωdt=1/ωsin ωdt	42:42
		∫e^x dx=e^x+c	43:32
	Integration by Substitution		45:23
		∫x(x^2 -1)dx	46:01
	Integration by Parts		52:30
		d/dx=(uv)'	52:45
		∫udv=∫d(uv)-∫Vdu =uv-∫vdu	54:20
		∫xe^x dx/dv	56:11
	Extra Example 1: Integral		6:26
	Extra Example 2: Integral		7:40
Motion in One Dimension			79:35
	Intro		0:00
		Position, Distance, and Displacement	0:12
		Position of the Object	0:30
		Distance Traveled by The Object	5:34
		Displacement of The Object	9:05
	Average Speed Over a Certain Time Interval		14:46
		Example Of an Object	15:15
		Example: Calculating Average Speed	20:19
	Average Velocity Over a Time Interval		22:22
		Example Calculating Average Velocity of an Object	22:45
	Instantaneous Velocity		30:45
	Average Acceleration Over a Time Interval		40:50
		Example: Average Acceleration of an Object	42:01
	Instantaneous Acceleration		47:17
		Example: Acceleration of Time T	47:33
		Example with Realistic Equation	49:52
	Motion With Constant Acceleration: Kinematics Equation		53:39
		Example: Motion of an Object with Constant Acceleration	53:55
	Extra Example 1: Uniformly Accelerated Motion		6:14
	Extra Example 2: Catching up with a Car		8:33
	Extra Example 3: Velocity and Acceleration		6:41
Kinematics Equation From Calculus			47:45
	Intro		0:00
	Velocity and Acceleration		0:27
		Particle moves In x Direction	0:35
		Instantaneous Velocity for Δt =0	3:05
		Acceleration (Change in Time) v(t+=Δt)-v(t) /Δt	4:58
	Example		8:08
		x(t) =(-4+3t+2t^2)	8:18
		Finding Average velocity at 10sec	8:45
		V at t=3s	10:28
		x(t) =0 ,0.2 sin (2t)	12:20
		Finding Velocity	12:50
	Constant Acceleration		15:29
		Object Moving with Constant Acceleration	15:40
		Find Velocity and Position at Later Time t	18:23
		v=∫a dt	19:50
		V(t) =v0+at	23:33
		v(t) =dx/dt x=∫vdt	24:14
		T=v-v0/a	29:26
	Extra Example 1: Velocity and Acceleration		8:25
	Extra Example 2: Particle Acceleration		5:49
Freely Falling Objects			88:59
	Intro		0:00
	Acceleration Due to Gravity		0:11
		Dropping an Object at Certain Height	0:25
	Signs : V , A , D		7:07
		Example: Shooting an Object Upwards	7:34
	Example: Ground To Ground		12:13
		Velocity at Maximum Height	14:30
		Time From Ground to Ground	23:10
		Shortcut: Calculate Time Spent in Air	24:07
	Example: Object Short Downwards		30:19
		Object Short Downwards From a Height H	30:30
		Use of Quadratic Formula	36:23
	Example: Bouncing Ball		41:00
		Ball Released From Certain Height	41:22
		Time Until Stationary	43:10
		Coefficient of Restitution	46:40
	Example: Bouncing Ball. Continued		53:02
	Extra Example 1: Object Shot Off Cliff		13:30
	Extra Example 2: Object Released Off Roof		7:13
	Extra Example 3: Rubber Ball (Coefficient of Restitution)		13:50
Motion in Two Dimensions, Part 1			68:38
	Intro		0:00
		Position, Displacement, Velocity, Acceleration	0:10
		Position of an Object in X-Y Plane	0:19
		Displacement of an Object	2:48
		Average Velocity	4:30
		Instantaneous Velocity at Time T	5:22
		Acceleration of Object	8:49
	Projectile Motion		9:57
		Object Shooting at Angle	10:15
		Object Falling Vertically	14:48
		Velocity of an Object	18:17
		Displacement of an Object	19:20
		Initial Velocity Remains Constant	21:24
		Deriving Equation of a Parabola	25:23
	Example: Shooting a Soccer Ball		25:25
		Time Ball Spent in Air (Ignoring Air Resistance)	27:48
		Range of Projectile	34:49
		Maximum Height Reached by the Projectile	36:25
	Example: Shooting an Object Horizontally		40:38
		Time Taken for Shooting	42:34
		Range	46:01
		Velocity Hitting Ground	46:30
	Extra Example 1: Projectile Shot with an Angle		12:37
	Extra Example 2: What Angle		6:55
Motion in Two Dimensions, Part 2: Circular Dimension			61:54
	Intro		0:00
	Uniform Circular Motion		0:15
		Object Moving in a Circle at Constant Speed	0:26
		Calculation Acceleration	3:30
		Change in Velocity	3:45
		Magnitude of Acceleration	14:21
		Centripetal Acceleration	18:15
	Example: Earth Rotating Around The Sun		18:42
		Center of the Earth	20:45
		Distance Travelled in Making One Revolution	21:34
		Acceleration of the Revolution	23:37
	Tangential Acceleration and Radial Acceleration		25:35
		If Magnitude and Direction Change During Travel	26:22
		Tangential Acceleration	27:45
	Example: Car on a Curved Road		29:50
		Finding Total Acceleration at Time T if Car is at Rest	31:13
	Extra Example 1: Centripetal Acceleration on Earth		8:11
	Extra Example 2: Pendulum Acceleration		7:12
	Extra Example 3: Radius of Curvature		9:08
Newton's Laws of Motion			89:51
	Intro		0:00
	Force		0:21
		Contact Force (Push or Pull)	1:02
		Field Forces	1:49
		Gravity	2:06
		Electromagnetic Force	2:43
		Strong Force	4:12
		Weak Force	5:17
		Contact Force as Electromagnetic Force	6:08
		Focus on Contact Force and Gravitational Force	6:50
	Newton's First Law		7:37
		Statement of First Law of Motion	7:50
		Uniform Motion (Velocity is Constant)	9:38
		Inertia	10:39
	Newton's Second Law		11:19
		Force as a Vector	11:35
		Statement of Second Law of Motion	12:02
		Force (Formula)	12:22
		Example: 1 Force	13:04
		Newton (Unit of Force)	13:31
		Example: 2 Forces	14:09
	Newton's Third Law		19:38
		Action and Reaction Law	19:46
		Statement of Third Law of Motion	19:58
		Example: 2 Objects	20:15
		Example: Objects in Contact	21:54
		Example: Person on Earth	22:54
	Gravitational Force and the Weight of an Object		24:01
		Force of Attraction Formula	24:42
		Point Mass and Spherical Objects	26:56
		Example: Gravity on Earth	28:37
		Example: 1 kg on Earth	35:31
	Friction		37:09
		Normal Force	37:14
		Example: Small Force	40:01
		Force of Static Friction	43:09
		Maximum Force of Static Friction	46:03
		Values of Coefficient of Static Friction	47:37
		Coefficient of Kinetic Friction	47:53
		Force of Kinetic Friction	48:27
		Example: Horizontal Force	49:36
		Example: Angled Force	52:36
	Extra Example 1: Wire Tension		10:37
	Extra Example 2: Car Friction		11:43
	Extra Example 3: Big Block and Small Block		9:17
Applications of Newton's Laws, Part 1: Inclines			84:35
	Intro		0:00
	Acceleration on a Frictionless Incline		0:35
		Force Action on the Object(mg)	1:31
		Net Force Acting on the Object	2:20
		Acceleration Perpendicular to Incline	8:45
		Incline is Horizontal Surface	11:30
		Example: Object on an Inclined Surface	13:40
	Rough Inclines and Static Friction		20:23
		Box Sitting on a Rough Incline	20:49
		Maximum Values of Static Friction	25:20
		Coefficient of Static Friction	27:53
	Acceleration on a Rough Incline		29:00
		Kinetic Friction on Rough Incline	29:15
		Object Moving up the Incline	33:20
		Net force on the Object	36:36
	Example: Time to Reach the Bottom of an Incline		41:50
		Displacement is 5m Down the Incline	45:26
		Velocity of the Object Down the Incline	47:49
	Extra Example 1: Bottom of Incline		12:23
	Extra Example 2: Incline with Initial Velocity		15:31
	Extra Example 3: Moving Down an Incline		8:09
Applications of Newton's Laws, Part 2: Strings and Pulleys			70:03
	Intro		0:00
	Atwood's Machine		0:19
		Object Attached to a String	0:39
		Tension on a String	2:15
		Two Objects Attached to a String	2:23
		Pulley Fixed to the Ceiling, With Mass M1 , M2	4:53
		Applying Newton's 2nd Law to Calculate Acceleration on M1, M2	9:21
	One Object on a Horizontal Surface: Frictionless Case		17:36
		Connecting Two Unknowns, Tension and Acceleration	20:27
	One Object on a Horizontal Surface: Friction Case		23:57
		Two Objects Attached to a String with a Pulley	24:14
		Applying Newton's 2nd Law	26:04
		Tension of an Object Pulls to the Right	27:31
	One of the Object is Incline : Frictionless Case		32:59
		Sum of Two Forces on Mass M2	34:39
		If M1g is Larger Than M2g	36:29
	One of the Object is Incline : Friction Case		40:29
		Coefficient of Kinetic Friction	41:18
		Net Force Acting on M2	45:12
	Extra Example 1: Two Masses on Two Strings		5:28
	Extra Example 2: Three Objects on Rough Surface		7:11
	Extra Example 3: Acceleration of a Block		8:52
Accelerating Frames			73:28
	Intro		0:00
	What Does a Scale Measure		0:11
		Example: Elevator on a Scale	0:22
		Normal Force	4:57
	Apparent Weight in an Elevator		7:42
		Example: Elevator Starts Moving Upwards	9:05
		Net Force (Newton's Second Law)	11:34
		Apparent Weight	14:36
	Pendulum in an Accelerating Train		15:58
		Example: Object Hanging on the Ceiling of a Train	16:15
		Angle In terms of Increased Acceleration	22:04
	Mass and Spring in an Accelerating Truck		23:40
		Example: Spring on a Stationary Truck	23:55
		Surface of Truck is Frictionless	27:38
		Spring is Stretched by distance X	28:40
	Cup of Coffee		29:55
		Example: Moving Train and Stationary Objects inside Train	30:05
		Train Moving With Acceleration A	32:45
		Force of Static Friction Acting on Cup	36:30
	Extra Example 1: Train Slows with Pendulum		11:54
	Extra Example 2: Person in Elevator Releases Object		13:06
	Extra Example 3: Hanging Object in Elevator		10:26
Circular Motion, Part 1			61:15
	Intro		0:00
	Object Attached to a String Moving in a Horizontal Circle		0:09
		Net Force on Object (Newton's Second Law)	1:51
		Force on an Object	3:03
		Tension of a String	4:40
	Conical Pendulum		5:40
		Example: Object Attached to a String in a Horizontal Circle	5:50
		Weight of an Object Vertically Down	8:05
		Velocity And Acceleration in Vertical Direction	11:20
		Net Force on an Object	13:02
	Car on a Horizontal Road		16:09
		Net Force on Car (Net Vertical Force)	18:03
		Frictionless Road	18:43
		Road with Friction	22:41
		Maximum Speed of Car Without Skidding	26:05
	Banked Road		28:13
		Road Inclined at an Angle ø	28:32
		Force on Car	29:50
		Frictionless Road	30:45
		Road with Friction	36:22
	Extra Example 1: Object Attached to Rod with Two Strings		11:27
	Extra Example 2: Car on Banked Road		9:29
	Extra Example 3: Person Held Up in Spinning Cylinder		3:05
Circular Motion, Part 2			50:29
	Intro		0:00
	Normal Force by a Pilot Seat		0:14
		Example : Pilot Rotating in a Circle r and Speed s	0:33
		Pilot at Vertical Position in a Circle of Radius R	4:18
		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 Motion		10:46
		Example: Object in a Circle Attached to String	10:59
		Case 1: Object with speed v and Object is at Bottom	11:30
		Case 2: Object at Top in Vertical Motion	15:24
		Object at Angle ø (General Position)	17:48
		2 Radial Forces (Inward & Outward)	20:32
		Tension of String	23:44
	Extra Example 1: Pail of Water in Vertical Circle		5:16
	Extra Example 2: Roller Coaster Vertical Circle		3:57
	Extra Example 3: Bead in Frictionless Loop		16:56
Work and Energy, Part 1			84:46
	Intro		0:00
	Work in One Dimension: Constant Force		0:11
		Particle Moving in X-Axis	0:24
		Displacement Δx=x2-x1	1:35
		Work Done by the Force W=FΔX	2:25
		Example: Object Being Pushed for 10 m (Frictionless case)	3:31
		Example: Elevator Descends with constant Velocity	5:37
		Work by Tension	9:06
	Work in One Dimension: Variable Force		11:28
		Object Displaced from a to b Under Action of Force	12:06
		Total Work= F(x1) Δx1	19:48
		Special Case : F(x) =F	22:56
	Work Done by a Spring		24:30
		Spring Attached to a Object	24:42
		Spring Stretched	25:40
		Spring Compressed and Released	30:30
		Hookes Law	32:05
		W=∫F(x) dx ,Initial Position to Final Position	36:25
	Work in Three Dimension: Constant Force		41:54
		3 Components Of 3 Dimensions	45:45
		Work Done By F=F.Δx	47:30
	Example		48:58
		Object Moves Up and Inclined	49:10
		Work Done by Gravity=F.Δr	49:50
		W=F.Δr= -mgz	53:50
		Work Done By Normal Force=0	54:33
	Work in Three Dimension: Variable Force		55:45
		Object Moving From A to B with Time	56:03
		W=∫f.dr	57:45
	Extra Example 1: Work Done By Force		3:19
	Extra Example 2: Mass on Half Ring		12:07
	Extra Example 3: Force with Two Paths		9:03
Work and Energy, Part 2			72:53
	Intro		0:00
	Work Kinetic Energy Theorem		0:16
		Object Moves in 3 Dimensions	1:51
		Work Done by Net Force =W=∫f.dr	3:27
		W=Change in Kinetic Energy	15:11
	Example		16:00
		Object Moving on Surface with Mass 10 N	16:12
		Using Newton's Second Law	18:26
		Using Work Kinetic Energy Theorem	21:32
	Gravitational Potential Energy		24:30
		Example of a Particle in 3 Dimensions	24:47
		Work Done By Force of Gravity	26:09
	Conservation of Energy		36:37
		Object in a Projectile	36:48
		Work Done by Gravity	39:50
	Example		43:45
		Frictionless Track	44:20
	Example		50:49
		Pendulum: Object Attached to a String at Height H	51:07
		Finding Tension in a String	52:20
	Extra Example 1: Object Pulled by Angled Force		8:13
	Extra Example 2: Projectile Shot at Angle		6:30
Conservation of Energy, Part 1			92:50
	Intro		0:00
	Conservative Forces		0:10
		Given a Force	4:01
		Consider a Particle Moves from P1 to P2 on Path	5:40
		Work Done by Force	8:28
	Example		14:56
		Gravity	15:20
		Spring with Block Moves and Stretched	17:36
		Friction is Net Conservative	23:29
		Path 1 Straight	27:04
		Along Path 2	30:07
	Potential Energy by a Conservative Force		33:23
		Choose Reference Point (Potential Energy =0)	33:51
		Define Potential Energy at Point P	35:23
	Conservation of Energy		40:58
		Object Moving from P1 -P2	41:50
		Work Kinetic Energy Theorem	41:58
	Potential Energy of a Spring		48:42
		Spring Stretched with Mass M, Find Potential Energy	49:13
	Example		53:45
		Force Acting on Particle in One Dimension	54:10
	Extra Example 1: Work Done By Gravity		8:14
	Extra Example 2: Prove Constant Force is Conservative		4:03
	Extra Example 3: Work Done by Force		13:07
	Extra Example 4: Compression of Spring		8:18
Conservation of Energy, Part 2			67:48
	Intro		0:00
	In Presence of Friction		0:13
		Work Energy Theorem	3:05
		Work Done BY Friction is Negative	6:51
	Example		10:12
		Object on Inclined Surface with Friction	10:20
		Heat, Magnitude by Friction	12:42
		Work Done By Friction	13:01
	Calculation of the Force From The Potential Energy		19:15
		Defining Potential Energy with Conservation of Energy	19:35
	Potential Energy and Equilibrium		31:16
		Spring Stretched with Mass M	31:28
		Stable Equilibrium	35:52
		Unstable Equilibrium	40:50
	Example		41:02
		Two Objects or Two Atoms	41:12
		Leonard John's Potential	42:15
	Power		47:38
		Rate at Force Work Done	47:54
		Average Power	49:01
		Instant Power Delivered at Time t	49:20
		Horse Power	53:10
	Extra Example 1: Force from Potential Energy		3:36
	Extra Example 2: Mass with Two Springs		4:17
	Extra Example 3: Block Pulled with Friction		6:04
Conservation of Energy, Part 3 (Examples)			71:58
	Intro		0:00
	Spring Loaded Gun		0:26
		Spring with Bullet	0:43
		Finding the Force Constant if Mass of Bullet is Given	2:48
		Compression of a Spring	5:10
	Sliding Object		11:33
		Object Sliding on a Frictionless Surface	12:15
		Spring at the End of a Slide	12:46
		Using Conservation of Energy K1+u1=K2+U2	15:06
		Finding Velocity and Energy	17:36
	Block Spring System with Friction		33:05
		Spring is Unstretched at Equilibrium	33:35
		Spring is Compressed	33:57
		Finding Total Energy	39:02
	Losing Contact on a Circular Track		46:16
		Objects Slides on a Circular Track	47:25
		Normal Force=0	48:10
		Centripetal Force	48:57
		Finding Velocity at Given Angle	49:25
		Energy at the Top	50:55
		Contact Lost	54:55
	Horse Pulling a Carriage		56:07
		Horse Power	56:40
		Power=FV	57:11
	Extra Example 1: Elevator with Friction		7:02
	Extra Example 2: Loop the Loop		5:34
Collisions, Part 1			91:19
	Intro		0:00
	Linear Momentum		0:10
		Example: Object of Mass m with Velocity v	0:25
		Example: Object Bounced on a Wall	1:08
		Momentum of Object Hitting a Wall	2:20
		Change in Momentum	4:10
	Force is the Rate of Change of Momentum		4:30
		Force=Mass*Acceleration (Newton's Second Law)	4:45
	Impulse		10:24
		Example: Baseball Hitting a Bat	10:40
		Force Applied for a Certain Time	11:50
		Magnitude Plot of Force vs Time	13:35
		Time of Contact of Baseball = 2 milliseconds (Average Force by Bat)	17:42
	Collision Between Two Particles		22:40
		Two Objects Collide at Time T	23:00
		Both Object Exerts Force on Each Other (Newton's Third Law)	24:28
		Collision Time	25:42
		Total Momentum Before Collision = Total momentums After Collision	32:52
	Collision		33:58
		Types of Collisions	34:13
		Elastic Collision ( Mechanical Energy is Conserved)	34:38
		Collision of Particles in Atoms	35:50
		Collision Between Billiard Balls	36:54
		Inelastic Collision (Rubber Ball)	39:40
		Two Objects Collide and Stick (Completely Inelastic)	40:35
	Completely Inelastic Collision		41:07
		Example: Two Objects Colliding	41:23
		Velocity After Collision	42:14
		Heat Produced=Initial K.E-Final K.E	47:13
	Ballistic Pendulum		47:37
		Example: Determine the Speed of a Bullet	47:50
		Mass Swings with Bulled Embedded	49:20
		Kinetic Energy of Block with the Bullet	50:28
	Extra Example 1: Ball Strikes a Wall		10:41
	Extra Example 2: Clay Hits Block		8:35
	Extra Example 3: Bullet Hits Block		11:37
	Extra Example 4: Child Runs onto Sled		7:24
Collisions, Part 2			78:48
	Intro		0:00
	Elastic Collision: One Object Stationary		0:28
		Example: Stationary Object and Moving Object	0:42
		Conservation of Momentum	2:48
		Mechanical Energy Conservation	3:43
	Elastic Collision: Both Objects Moving		17:34
		Example: Both Objects Moving Towards Each Other	17:48
		Kinetic Energy Conservation	19:20
	Collision With a Spring-Block System		29:17
		Example: Object of Mass Moving with Velocity	29:30
		Object Attached to Spring of Mass with Velocity	29:50
		Two Objects Attached to a Spring	31:30
		Compression of Spring after Collision	33:41
		Before Collision: Total Energy (Conservation of Energy)	37:25
		After Collision: Total Energy	38:49
	Collision in Two Dimensions		42:29
		Object Stationary and Other Object is Moving	42:46
		Head on Collision (In 1 Dimension)	44:07
		Momentum Before Collision	45:45
		Momentum After Collision	46:06
		If Collision is Elastic (Conservation of Kinetic Energy) Before Collision	50:29
	Example		51:58
		Objects Moving in Two Directions	52:33
		Objects Collide and Stick Together (Inelastic Collision)	53:28
		Conservation of Momentum	54:17
		Momentum in X-Direction	54:27
		Momentum in Y-Direction	56:15
	Maximum Height after Collision		10:34
	Extra Example 2: Two Objects Hitting a Spring		7:05
	Extra Example 3: Mass Hits and Sticks		2:58
Center of Mass, Part 1			93:46
	Collection of Particles		0:13
		System of Coordinates	0:40
		Coordinates of Center of Mass	2:25
	Four Particles		10:10
		Center of Mass at Xcm	13:20
		Center of Mass at Ycm	15:07
	Extended Objects		17:00
		Consider a Object	17:30
		Dividing Object in to Smaller Particles	19:07
		Divide the Volume N into Pieces	23:10
	Center of Mass of a Rod		31:02
		Total Mass of Rod	35:30
	Center of Mass of a Right Angle		42:27
		Right Triangle Placed in Coordinates	42:40
		Tiny Strip on a Triangle	45:05
		Intersection of a Point	56:19
	Extra Example 1: Center of Mass Two Objects		12:56
	Extra Example 2: Bent Rod Center of Mass		15:17
	Extra Example 3: Triangle Center of Mass		7:50
Center of Mass, Part 2			79:15
	Intro		0:00
	Motion of a System of Particles		0:53
		Position Vector of Center of Mass	2:30
		Total Momentum	7:08
		Net Force Acting on a Particle	9:32
	Exploding a Projectile		19:12
		Shooting a Projectile in x-z Plane	19:50
		Projectile Explodes into 2 pieces of Equal Mass	27:19
	Rocket Propulsion		35:09
		Rocket with Mass m and Velocity v	35:25
	Rocket in Space		53:39
		Rocket in Space with Speed=3000m/s	53:48
		Engine is Turned On	54:19
		Final Mass=1/2 Initial Mass	57:15
		Speed after Fuel is Burned	58:09
	Extra Example 1: Ball Inelastic Hits Other Ball		12:35
	Extra Example 2: Rocket Launch Thrust		6:47
Rotation of a Rigid Body About a Fixed Axis			73:20
	Intro		0:00
	Particle in Circular Motion		0:11
		Specify a Position of a Particle	0:55
		Radian	3:02
		Angular Displacement	8:50
	Rotation of a Rigid Body		15:36
		Example: Rotating Disc	16:17
		Disk at 5 Revolution/Sec	17:24
		Different Points on a Disk Have Different Speeds	21:56
		Angular Velocity	23:03
	Constant Angular Acceleration: Kinematics		31:11
		Rotating Disc	31:42
		Object Moving Along x-Axis (Linear Case)	33:05
		If Alpha= Constant	35:15
	Rotational Kinetic Energy		42:11
		Rod in X-Y Plane, Fixed at Center	42:43
		Kinetic Energy	46:45
		Moment of Inertia	52:46
	Moment of Inertia for Certain Shapes		54:06
		Rod at Center	54:47
		Ring	55:45
		Disc	56:35
		Cylinder	56:56
		Sphere	57:20
	Extra Example 1: Rotating Wheel		6:44
	Extra Example 2: Two Spheres Attached to Rotating Rod		8:45
Moment of Inertia			92:22
	Intro		0:00
	Review of Kinematic Rotational Equation		0:12
		Rigid Body Rotation on a Axis	0:29
		Constant Angular Acceleration	10:17
	Rotational Kinetic Energy		16:33
		Particle Moving in a Circle	16:42
		Moment of Inertia	22:43
	Moment of Inertia of a Uniform Rod		25:10
		Dividing the Body in Many Pieces	27:40
		Total Mass=M Lamda=m/l	29:21
		Axis Through the Center of Mass	34:02
	Uniform Solid Cylinder		35:13
		Cylinder of Length L	35:25
		Finding Moment of Inertia I=∫r2 dm	36:04
		Volume of Cylinder	40:02
	Other Shapes		44:37
		Ring	45:08
		Disc	45:22
		Sphere	45:50
		Spherical Shell	45:49
	Parallel Axis Theorem		46:46
		Object with Center of Mass	47:12
		Consider Another Axis Parallel to Primary Axis	47:35
	Extra Example 1: Moment of Inertia for Ring and Disk		10:39
	Extra Example 2: Moment of Inertia for Sphere		12:56
	Extra Example 3: Moment of Inertia for Spherical Shell		11:41
Angular Momentum			63:48
	Intro		0:00
	Angular Momentum of Particle		0:06
		Magnitude of Angular Momentum	2:27
		Right Hand Rule	3:00
		Particle Moving in Circular Motions	4:18
	Angular Momentum of a Rigid Body		6:44
		Consider a Rigid Body	7:06
		Z Axis Through Center	7:27
		Rotate About the Z-Axis	18:57
	Example		19:36
		Rotating in Circular Motion	20:08
		Consider a Mass on the Rigid Body	20:38
		Angular Momentum of Disk	26:14
	Rotation About an Axis of Symmetry		26:27
		Perpendicular to Symmetry	27:35
		Cylinder	29:02
		Sphere	29:23
		Rotating on Axis	29:40
		Rigid Body Rotates About Axis of Symmetry	40:33
	The Z-Component of Angular Momentum		40:56
		Consider any Dmi on The Surface	41:57
	Example		49:40
		Cylinder	49:55
	Extra Example 1: Rod Angular Momentum		5:46
	Extra Example 2: Particle Angular Momentum		4:20
Rotational Dynamics			79:59
	Intro		0:00
	Torque		0:10
		Object Fixed at Center	1:34
		τ=r Fsin θ	11:14
	Relation of Torque to Angular Momentum		11:47
		Derivative of Momentum	12:34
		Consider a Particle With Velocity =V	13:51
		For a Rigid Body	16:45
	Equation of Rotational Motion		25:23
		Object Rigid Body Rotating on Axis	27:14
		Torque Acting on the Object	27:36
		Torque About Axis of Rotation	30:55
	Block and a Pulley		31:55
		Rope with Mass=m and Radius of Pulley	32:40
		Finding Acceleration and Tension	37:26
	Atwood's Machine		41:57
		Pulley with Masses m1, m2 and Radius R	42:49
		Acceleration	50:15
	Extra Example 1: Uniform Rod		8:49
	Extra Example 2: Two Blocks with Strings		12:40
	Extra Example 3: Thin Disk		7:00
Energy Consideration by Rotational Motion			70:28
	Intro		0:00
	Work Done By Torque		0:15
		Rigid Body Rotating about Z-axis	1:33
		Rigid Body Rotating about Z-axis	3:01
		Point p Rotates on Circle and Perpendicular to z	4:19
	Work Kinetic Energy Theorem for Rotational Motion		15:36
		Work Done By Torque	16:43
		Work Done By Net Torque=Kf-Ki	20:31
	Conservation of Mechanical Energy in Rotational Motion		21:41
		Conservation Force Acting	22:40
		Work Done by Gravity	23:15
		Work Done by Torque	25:38
	Power Delivered by Torque		27:12
		Power by Force	27:58
	Rotating Rod		30:03
		Rod Clamped at One End	30:35
		Angular Speed	30:50
		Moment of Inertia About Axis of Rotation	35:15
		Speed of Free End	37:40
	Another Rotating Rod		37:59
		Rod Standing on Surface	38:37
		End Does Not Slip	39:01
		Speed of Free End	41:20
		Strikes Ground	42:13
	Extra Example 1: Peg and String		5:51
	Extra Example 2: Solid Disk		9:50
	Extra Example 3: Rod and Sphere		12:03
Conservation of Angular Momentum			66:57
	Intro		0:00
	Conservation of Angular Momentum in an Isolated System		0:13
		Linear Case	0:45
		Torque=Rate if Changed in Angular Momentum	1:29
		Isolated System	1:59
	Neutron Star		4:13
		Star Rotates About Some Axis	4:31
	Merry Go Round		12:50
		Consider a Large Disc	13:06
		Total Angular Momentum Calculated	18:59
	Sticky Clay Sticking a Rod		19:07
		Rod of Length L With Pivot at End	19:37
		Piece of Clay of Mass m and Velocity v	19:45
		Angular Momentum Calculated	28:58
	Extra Example 1: Rod with Beads		8:38
	Extra Example 2: Mass Striking Rod		8:42
	Extra Example 3: Wood Block and Bullet		20:32
Rolling Motion			96:09
	Intro		0:00
	Pure Rolling Motion		0:10
		Disc Rolling on a Surface R (Rolling Without Sipping)	0:50
		When Disc Rotates, Center of Mass Moves	5:48
		Acceleration of Center of Mass	8:43
	Kinetic Energy		11:03
		Object in Pure Rotation	11:16
		Pure Translation	13:28
		Rotation and Translation	15:24
	Cylinder Rolling Down an Incline		23:55
		Incline	24:15
		Cylinder Starts From Rest	24:44
	Which Moves Faster		37:02
		Rolling a Ring, Disc, Sphere	37:19
		Ring I=Mr2	41:30
		Disc I= 1/2 Mr2	42:31
		Sphere I= 2/5 mr2	43:21
	Which Goes Faster		49:15
		Incline with a Object Towards the Inclination	49:30
	Extra Example 1: Rolling Cylinder		15:16
	Extra Example 2: Nonuniform Cylinder		7:55
	Extra Example 3: String Around Disk		15:05
Universal Gravitation			69:20
	Intro		0:00
	Newton's Law of Gravity		0:09
		Two Particles of Mass m1,m2	1:22
		Force of Attraction	3:02
		Sphere and Small Particle of Mass m	4:39
		Two Spheres	5:35
	Variation of g With Altitude		7:24
		Consider Earth as an Object	7:33
		Force Applied To Object	9:27
		At or Near Surface of Earth	11:51
	Satellites		15:39
		Earth and Satellite	15:45
		Geosynchronous Satellite	21:25
	Gravitational Potential Energy		27:32
		Object and Earth Potential Energy=mgh	24:45
		P.E=0 When Objects are Infinitely Separated	30:32
		Total Energy	38:28
		If Object is Very Far From Earth, R=Infinity	40:25
	Escape		42:33
		Shoot an Object Which Should Not Come Back Down	43:06
		Conservation of Energy	48:48
		Object at Maximum Height (K.E=0)	45:22
		Escape Velocity (Rmax = Infinity)	46:50
	Extra Example 1: Density of Earth and Moon		7:09
	Extra Example 2: Satellite Orbiting Earth		11:54
Kepler's Laws			72:25
	Intro		0:00
	Kepler's First law		2:18
		Any Point on Ellipse	4:33
		Semi Major Axis	6:35
		Semi Minor Axis	7:05
		Equation of Ellipse	7:32
		Eccentricity	16:05
	Kepler's Second Law		19:46
		Radius Vector	20:31
		Torque by Force of Gravity	25:00
	Kepler's Third Law		36:49
		Time Take for the Planet to make 1 Revolution	37:20
		Period	41:26
	Mass of Sun		43:39
		Orbit of Earth is Almost Circle	45:11
	Extra Example 1: Halley's Comet		11:18
	Extra Example 2: Two Planets Around Star		6:27
	Extra Example 3: Neutron Star		3:34
Energy and Gravitation			35:04
	Intro		0:00
	Gravitational Potential Energy		0:10
		Conservative Force	1:45
		Along Path A ∫f.dr=0	7:35
		Along Path B ∫f.dr=-1	10:30
		Δu= ∫f r1 to r2	10:58
	Near the Surface of the Earth		17:07
		Two Points on Surface of Earth	17:22
	Planets and Satellites		24:40
		Circular Orbits	24:59
		Elliptical Orbits	30:54
Static Equilibrium			98:57
	Intro		0:00
	Torque		0:09
		Introduction to Torque	0:16
		Rod in X-Y Direction	0:30
	Particle in Equilibrium		18:15
		Particle in Equilibrium, Net Force=0	18:30
		Extended Object Like a Rod	19:13
		Conditions of Equilibrium	26:34
		Forces Acting on Object (Proof of Torque)	31:46
	The Lever		35:38
		Rod on Lever with Two Masses	35:51
	Standing on a Supported Beam		40:53
		Example : Wall and Beam Rope Connect Beam and Wall	41:00
		Net Force	45:38
		Net Torque	48:33
		Finding ø	52:50
	Ladder About to Slip		53:38
		Example: Finding Angle ø Where Ladder Doesn't slip	53:44
	Extra Example 1: Bear Retrieving Basket		19:42
	Extra Example 2: Sliding Cabinet		20:09
Simple Harmonic System Spring Block System			62:35
	Intro		0:00
	Restoring Force		0:41
		Spring Attached to a Block	0:53
		Spring Stretched	1:58
		Force=Kx (K=Force Constant)	5:45
	Simple Harmonic Motion		11:31
		According to Newton's Law F=mxa	11:55
		Equation of Motion	15:15
	Frequency, Period, Velocity, and Acceleration		34:23
		Object Without Stretching	34:52
		Object Stretched	35:15
		Acceleration a=dv/dt	43:20
	Block Spring System		53:01
		Object Being Compressed	53:26
	Energy Consideration		57:47
	Example		59:48
		Spring Being Compressed	59:55
The Pendulum			61:55
	Intro		0:00
	Simple Pendulum		0:07
		Mass Attached to the String	0:25
		Torque=mgr Perpendicular	7:34
		Moment of Inertia	15:36
		When φ<<1	24:30
	Example		33:13
		Mass Hanging with 1kg and Length 1 M and Velocity 2m	33:26
		Period	34:50
		Frequency	35:40
		Ki+ui=Kf+uf	37:01
	Physical Pendulum		41:39
		Rigid Body with a Pivot and let it Oscillate	42:00
		Torque Produced	47:58
	Example		53:35
		Rod Fixed and Made to Oscillated	53:40
		Period	54:40
		Torsional Pendulum	57:57
		Mass Suspended with a Torsional Fiber	58:15
		Torque Produced	58:55
	Example		60:05
		Wire With Torsional -K	60:11
Damped and Forced Oscillation			53:35
	Intro		0:00
	Damped Oscillation		0:11
		Spring Oscillation	0:45
		Force of Friction F=-bv	5:20
		Spring in Absence of Friction	6:10
		No Damping	8:29
		In Presence of Damping	8:41
	Example		21:07
		Pendulum Oscillating at 10 Degrees	21:23
		After 10 Min Amplitude Becomes 5 Degrees	22:10
	Forced Oscillation		30:18
		Spring Oscillating up and Down, Applying Force	35:25
		Steady State Solution	41:49
	Example		46:48
		Spring with Object Mass=0.1 kg	47:05

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Center of Mass, Part 2

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Center of Mass, Part 2

AP Physics C: Mechanics