Integrals, AP Physics C/Mechanics

Integrals

I. Mechanics: Lecture 5 | 73:28 min

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Integrals

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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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Integrals

AP Physics C: Mechanics