Newton's 2nd Law: Multiple Dimensions, High School Physics

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Newton's 2nd Law: Multiple Dimensions

With force in multiple dimensions, we switch to using vectors:

→

F_net

=

m ·
→

a

,

⇔

(F_{x_net}, F_{y_net})

=

(m ·a_x, m ·a_y).
We work with each component of the force vector separately. That also means we can break a force vector into its component vectors.
The normal force is called normal because that means (in math-speak) "perpendicular". A surface can not resist force that is parallel to it.
If something is on an incline, the portion of gravity that is perpendicular to the surface is cancelled out, but the portion of gravity that is parallel is not.
Be careful when figuring out how much of the force is parallel! It is very easy to make a mistake and put an angle in the wrong place. Make a diagram and think carefully.

Newton's 2nd Law: Multiple Dimensions

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

Newton's 2nd Law in Multiple Dimensions

Newton's 2nd Law in Multiple Dimensions

Components

Special Forces

Review of Special Forces: Gravity, Normal Force, and Tension

Normal Forces

Example 1: A 5kg Block is Pushed By a Force of 3N to the North and a Force of 4N to the East

Example 2: A 20kg Block is On an Incline of 50Â° With a Rope Holding It In Place

Example 3: A 10kg Block is On an Incline of 20Â° Attached By Rope to a Free-hanging Block of 5kg

I. Motion
	Math Review	16:49
	One Dimensional Kinematics	26:02
	Multi-Dimensional Kinematics	29:59
	Frames of Reference	18:36
	Uniform Circular Motion	16:34
II. Force
	Newton's 1st Law	12:37
	Newton's 2nd Law: Introduction	27:05
	Newton's 2nd Law: Multiple Dimensions	27:47
	Newton's 2nd Law: Advanced Examples	42:05
	Newton's Third Law	16:47
	Friction	50:11
	Force & Uniform Circular Motion	26:45
III. Energy
	Work	28:34
	Energy: Kinetic	39:07
	Energy: Gravitational Potential	28:10
	Energy: Elastic Potential	44:16
	Power & Simple Machines	29:19
IV. Momentum
	Center of Mass	36:55
	Linear Momentum	22:50
	Collisions & Linear Momentum	40:55
V. Gravity
	Gravity & Orbits	34:53
VI. Waves
	Intro to Waves	35:35
	Waves, Cont.	52:57
	Sound	36:24
	Light	19:38
VII. Thermodynamics
	Fluids	42:52
	Intro to Temperature & Heat	34:06
	Change Due to Heat	44:03
	Thermodynamics	27:30
VIII. Electricity
	Electric Force & Charge	41:35
	Electric Fields & Potential	34:44
	Electric Current	29:12
	Electric Circuits	52:02
IX. Magnetism
	Magnetism	25:47

Physics (Theory and Application)

I. Motion
	Math Review			16:49
		Intro		0:00
		The Metric System		0:26
			Distance, Mass, Volume, and Time	0:27
		Scientific Notation		1:40
			Examples: 47,000,000,000 and 0.00000002	1:41
		Significant Figures		3:18
			Significant Figures Overview	3:19
			Properties of Significant Figures	4:04
			How Significant Figures Interact	7:00
		Trigonometry Review		8:57
			Pythagorean Theorem, sine, cosine, and tangent	8:58
		Inverse Trigonometric Functions		9:48
			Inverse Trigonometric Functions	9:49
		Vectors		10:44
			Vectors	10:45
		Scalars		12:10
			Scalars	12:11
		Breaking a Vector into Components		13:17
			Breaking a Vector into Components	13:18
		Length of a Vector		13:58
			Length of a Vector	13:59
			Relationship Between Length, Angle, and Coordinates	14:45
	One Dimensional Kinematics			26:02
		Intro		0:00
		Position		0:06
			Definition and Example of Position	0:07
		Distance		1:11
			Definition and Example of Distance	1:12
		Displacement		1:34
			Definition and Example of Displacement	1:35
		Comparison		2:45
			Distance vs. Displacement	2:46
		Notation		2:54
			Notation for Location, Distance, and Displacement	2:55
		Speed		3:32
			Definition and Formula for Speed	3:33
			Example: Speed	3:51
		Velocity		4:23
			Definition and Formula for Velocity	4:24
		∆ - Greek: 'Delta'		5:01
			∆ or 'Change In'	5:02
		Acceleration		6:02
			Definition and Formula for Acceleration	6:03
			Example: Acceleration	6:38
		Gravity		7:31
			Gravity	7:32
		Formulas		8:44
			Kinematics Formula 1	8:45
			Kinematics Formula 2	9:32
			Definitional Formulas	14:00
		Example 1: Speed of a Rock Being Thrown		14:12
		Example 2: How Long Does It Take for the Rock to Hit the Ground?		15:37
		Example 3: Acceleration of a Biker		21:09
		Example 4: Velocity and Displacement of a UFO		22:43
	Multi-Dimensional Kinematics			29:59
		Intro		0:00
		What's Different About Multiple Dimensions?		0:07
			Scalars and Vectors	0:08
		A Note on Vectors		2:12
			Indicating Vectors	2:13
		Position		3:03
			Position	3:04
		Distance and Displacement		3:35
			Distance and Displacement: Definitions	3:36
			Distance and Displacement: Example	4:39
		Speed and Velocity		8:57
			Speed and Velocity: Definition & Formulas	8:58
			Speed and Velocity: Example	10:06
		Speed from Velocity		12:01
			Speed from Velocity	12:02
		Acceleration		14:09
			Acceleration	14:10
		Gravity		14:26
			Gravity	14:27
		Formulas		15:11
			Formulas with Vectors	15:12
		Example 1: Average Acceleration		16:57
		Example 2A: Initial Velocity		19:14
		Example 2B: How Long Does It Take for the Ball to Hit the Ground?		21:35
		Example 2C: Displacement		26:46
	Frames of Reference			18:36
		Intro		0:00
		Fundamental Example		0:25
			Fundamental Example Part 1	0:26
			Fundamental Example Part 2	1:20
		General Case		2:36
			Particle P and Two Observers A and B	2:37
			Speed of P from A's Frame of Reference	3:05
		What About Acceleration?		3:22
			Acceleration Shows the Change in Velocity	3:23
			Acceleration when Velocity is Constant	3:48
		Multi-Dimensional Case		4:35
			Multi-Dimensional Case	4:36
		Some Notes		5:04
			Choosing the Frame of Reference	5:05
		Example 1: What Velocity does the Ball have from the Frame of Reference of a Stationary Observer?		7:27
		Example 2: Velocity, Speed, and Displacement		9:26
		Example 3: Speed and Acceleration in the Reference Frame		12:44
	Uniform Circular Motion			16:34
		Intro		0:00
		Centripetal Acceleration		1:21
			Centripetal Acceleration of a Rock Being Twirled Around on a String	1:22
			Looking Closer: Instantaneous Velocity and Tangential Velocity	2:35
			Magnitude of Acceleration	3:55
			Centripetal Acceleration Formula	5:14
		You Say You Want a Revolution		6:11
			What is a Revolution?	6:12
			How Long Does it Take to Complete One Revolution Around the Circle?	6:51
		Example 1: Centripetal Acceleration of a Rock		7:40
		Example 2: Magnitude of a Car's Acceleration While Turning		9:20
		Example 3: Speed of a Point on the Edge of a US Quarter		13:10
II. Force
	Newton's 1st Law			12:37
		Intro		0:00
		Newton's First Law/ Law of Inertia		2:45
			A Body's Velocity Remains Constant Unless Acted Upon by a Force	2:46
		Mass & Inertia		4:07
			Mass & Inertia	4:08
		Mass & Volume		5:49
			Mass & Volume	5:50
		Mass & Weight		7:08
			Mass & Weight	7:09
		Example 1: The Speed of a Rocket		8:47
		Example 2: Which of the Following Has More Inertia?		10:06
		Example 3: Change in Inertia		11:51
	Newton's 2nd Law: Introduction			27:05
		Intro		0:00
		Net Force		1:42
			Consider a Block That is Pushed On Equally From Both Sides	1:43
			What if One of the Forces was Greater Than the Other?	2:29
			The Net Force is All the Forces Put Together	2:43
		Newton's Second Law		3:14
			Net Force = (Mass) x (Acceleration)	3:15
		Units		3:48
			The Units of Newton's Second Law	3:49
		Free-Body Diagram		5:34
			Free-Body Diagram	5:35
		Special Forces: Gravity (Weight)		8:05
			Force of Gravity	8:06
		Special Forces: Normal Force		9:22
			Normal Force	9:23
		Special Forces: Tension		10:34
			Tension	10:35
		Example 1: Force and Acceleration		12:19
		Example 2: A 5kg Block is Pushed by Five Forces		13:24
		Example 3: A 10kg Block Resting On a Table is Tethered Over a Pulley to a Free-Hanging 2kg Block		16:30
	Newton's 2nd Law: Multiple Dimensions			27:47
		Intro		0:00
		Newton's 2nd Law in Multiple Dimensions		0:12
			Newton's 2nd Law in Multiple Dimensions	0:13
		Components		0:52
			Components	0:53
			Example: Force in Component Form	1:02
		Special Forces		2:39
			Review of Special Forces: Gravity, Normal Force, and Tension	2:40
		Normal Forces		3:35
			Why Do We Call It the Normal Forces?	3:36
			Normal Forces on a Flat Horizontal and Vertical Surface	5:00
			Normal Forces on an Incline	6:05
		Example 1: A 5kg Block is Pushed By a Force of 3N to the North and a Force of 4N to the East		10:22
		Example 2: A 20kg Block is On an Incline of 50° With a Rope Holding It In Place		16:08
		Example 3: A 10kg Block is On an Incline of 20° Attached By Rope to a Free-hanging Block of 5kg		20:50
	Newton's 2nd Law: Advanced Examples			42:05
		Intro		0:00
		Block and Tackle Pulley System		0:30
			A Single Pulley Lifting System	0:31
			A Double Pulley Lifting System	1:32
			A Quadruple Pulley Lifting System	2:59
		Example 1: A Free-hanging, Massless String is Holding Up Three Objects of Unknown Mass		4:40
		Example 2: An Object is Acted Upon by Three Forces		10:23
		Example 3: A Chandelier is Suspended by a Cable From the Roof of an Elevator		17:13
		Example 4: A 20kg Baboon Climbs a Massless Rope That is Attached to a 22kg Crate		23:46
		Example 5: Two Blocks are Roped Together on Inclines of Different Angles		33:17
	Newton's Third Law			16:47
		Intro		0:00
		Newton's Third Law		0:50
			Newton's Third Law	0:51
		Everyday Examples		1:24
			Hammer Hitting a Nail	1:25
			Swimming	2:08
			Car Driving	2:35
			Walking	3:15
		Note		3:57
			Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 1	3:58
			Newton's Third Law Sometimes Doesn't Come Into Play When Solving Problems: Reason 2	5:36
		Example 1: What Force Does the Moon Pull on Earth?		7:04
		Example 2: An Astronaut in Deep Space Throwing a Wrench		8:38
		Example 3: A Woman Sitting in a Bosun's Chair that is Hanging from a Rope that Runs Over a Frictionless Pulley		12:51
	Friction			50:11
		Intro		0:00
		Introduction		0:04
			Our Intuition - Materials	0:30
			Our Intuition - Weight	2:48
			Our Intuition - Normal Force	3:45
		The Normal Force and Friction		4:11
			Two Scenarios: Same Object, Same Surface, Different Orientations	4:12
			Friction is Not About Weight	6:36
		Friction as an Equation		7:23
			Summing Up Friction	7:24
			Friction as an Equation	7:36
		The Direction of Friction		10:33
			The Direction of Friction	10:34
		A Quick Example		11:16
			Which Block Will Accelerate Faster?	11:17
		Static vs. Kinetic		14:52
			Static vs. Kinetic	14:53
			Static and Kinetic Coefficient of Friction	16:31
		How to Use Static Friction		17:40
			How to Use Static Friction	17:41
		Some Examples of μs and μk		19:51
			Some Examples of μs and μk	19:52
		A Remark on Wheels		22:19
			A Remark on Wheels	22:20
		Example 1: Calculating μs and μk		28:02
		Example 2: At What Angle Does the Block Begin to Slide?		31:35
		Example 3: A Block is Against a Wall, Sliding Down		36:30
		Example 4: Two Blocks Sitting Atop Each Other		40:16
	Force & Uniform Circular Motion			26:45
		Intro		0:00
		Centripetal Force		0:46
			Equations for Centripetal Force	0:47
			Centripetal Force in Action	1:26
		Where Does Centripetal Force Come From?		2:39
			Where Does Centripetal Force Come From?	2:40
		Centrifugal Force		4:05
			Centrifugal Force Part 1	4:06
			Centrifugal Force Part 2	6:16
		Example 1: Part A - Centripetal Force On the Car		8:12
		Example 1: Part B - Maximum Speed the Car Can Take the Turn At Without Slipping		8:56
		Example 2: A Bucket Full of Water is Spun Around in a Vertical Circle		15:13
		Example 3: A Rock is Spun Around in a Vertical Circle		21:36
III. Energy
	Work			28:34
		Intro		0:00
		Equivocation		0:05
			Equivocation	0:06
		Introduction to Work		0:32
			Scenarios: 10kg Block on a Frictionless Table	0:33
			Scenario: 2 Block of Different Masses	2:52
		Work		4:12
			Work and Force	4:13
			Paralleled vs. Perpendicular	4:46
			Work: A Formal Definition	7:33
		An Alternate Formula		9:00
			An Alternate Formula	9:01
		Units		10:40
			Unit for Work: Joule (J)	10:41
		Example 1: Calculating Work of Force		11:32
		Example 2: Work and the Force of Gravity		12:48
		Example 3: A Moving Box & Force Pushing in the Opposite Direction		15:11
		Example 4: Work and Forces with Directions		18:06
		Example 5: Work and the Force of Gravity		23:16
	Energy: Kinetic			39:07
		Intro		0:00
		Types of Energy		0:04
			Types of Energy	0:05
		Conservation of Energy		1:12
			Conservation of Energy	1:13
		What is Energy?		4:23
			Energy	4:24
		What is Work?		5:01
			Work	5:02
		Circular Definition, Much?		5:46
			Circular Definition, Much?	5:47
		Derivation of Kinetic Energy (Simplified)		7:44
			Simplified Picture of Work	7:45
			Consider the Following Three Formulas	8:42
		Kinetic Energy Formula		11:01
			Kinetic Energy Formula	11:02
		Units		11:54
			Units for Kinetic Energy	11:55
		Conservation of Energy		13:24
			Energy Cannot be Made or Destroyed, Only Transferred	13:25
		Friction		15:02
			How Does Friction Work?	15:03
		Example 1: Velocity of a Block		15:59
		Example 2: Energy Released During a Collision		18:28
		Example 3: Speed of a Block		22:22
		Example 4: Speed and Position of a Block		26:22
	Energy: Gravitational Potential			28:10
		Intro		0:00
		Why Is It Called Potential Energy?		0:21
			Why Is It Called Potential Energy?	0:22
		Introduction to Gravitational Potential Energy		1:20
			Consider an Object Dropped from Ever-Increasing heights	1:21
		Gravitational Potential Energy		2:02
			Gravitational Potential Energy: Derivation	2:03
			Gravitational Potential Energy: Formulas	2:52
			Gravitational Potential Energy: Notes	3:48
		Conservation of Energy		5:50
			Conservation of Energy and Formula	5:51
		Example 1: Speed of a Falling Rock		6:31
		Example 2: Energy Lost to Air Drag		10:58
		Example 3: Distance of a Sliding Block		15:51
		Example 4: Swinging Acrobat		21:32
	Energy: Elastic Potential			44:16
		Intro		0:00
		Introduction to Elastic Potential		0:12
			Elastic Object	0:13
			Spring Example	1:11
		Hooke's Law		3:27
			Hooke's Law	3:28
			Example of Hooke's Law	5:14
		Elastic Potential Energy Formula		8:27
			Elastic Potential Energy Formula	8:28
		Conservation of Energy		10:17
			Conservation of Energy	10:18
		You Ain't Seen Nothin' Yet		12:12
			You Ain't Seen Nothin' Yet	12:13
		Example 1: Spring-Launcher		13:10
		Example 2: Compressed Spring		18:34
		Example 3: A Block Dangling From a Massless Spring		24:33
		Example 4: Finding the Spring Constant		36:13
	Power & Simple Machines			29:19
		Intro		0:00
		Introduction to Power & Simple Machines		0:06
			What's the Difference Between a Go-Kart, a Family Van, and a Racecar?	0:07
			Consider the Idea of Climbing a Flight of Stairs	1:13
		Power		2:35
			P= W / t	2:36
		Alternate Formulas		2:59
			Alternate Formulas	3:00
		Units		4:24
			Units for Power: Watt, Horsepower, and Kilowatt-hour	4:25
		Block and Tackle, Redux		5:54
			Block and Tackle Systems	5:55
		Machines in General		10:09
			Levers	10:10
			Ramps	11:16
		Example 1: Power of Force		12:47
		Example 2: Power &Lifting a Watermelon		14:46
		Example 3: Work and Instantaneous Power		16:30
		Example 4: Power and Acceleration of a Race car		26:21
IV. Momentum
	Center of Mass			36:55
		Intro		0:00
		Introduction to Center of Mass		0:04
			Consider a Ball Tossed in the Air	0:05
		Center of Mass		1:27
			Definition of Center of Mass	1:28
			Example of center of Mass	2:13
			Center of Mass: Derivation	4:21
			Center of Mass: Formula	6:44
			Center of Mass: Formula, Multiple Dimensions	8:15
			Center of Mass: Symmetry	9:07
			Center of Mass: Non-Homogeneous	11:00
		Center of Gravity		12:09
			Center of Mass vs. Center of Gravity	12:10
		Newton's Second Law and the Center of Mass		14:35
			Newton's Second Law and the Center of Mass	14:36
		Example 1: Finding The Center of Mass		16:29
		Example 2: Finding The Center of Mass		18:55
		Example 3: Finding The Center of Mass		21:46
		Example 4: A Boy and His Mail		28:31
	Linear Momentum			22:50
		Intro		0:00
		Introduction to Linear Momentum		0:04
			Linear Momentum Overview	0:05
			Consider the Scenarios	0:45
		Linear Momentum		1:45
			Definition of Linear Momentum	1:46
		Impulse		3:10
			Impulse	3:11
		Relationship Between Impulse & Momentum		4:27
			Relationship Between Impulse & Momentum	4:28
		Why is It Linear Momentum?		6:55
			Why is It Linear Momentum?	6:56
		Example 1: Momentum of a Skateboard		8:25
		Example 2: Impulse and Final Velocity		8:57
		Example 3: Change in Linear Momentum and magnitude of the Impulse		13:53
		Example 4: A Ball of Putty		17:07
	Collisions & Linear Momentum			40:55
		Intro		0:00
		Investigating Collisions		0:45
			Momentum	0:46
			Center of Mass	1:26
		Derivation		1:56
			Extending Idea of Momentum to a System	1:57
			Impulse	5:10
		Conservation of Linear Momentum		6:14
			Conservation of Linear Momentum	6:15
		Conservation and External Forces		7:56
			Conservation and External Forces	7:57
		Momentum Vs. Energy		9:52
			Momentum Vs. Energy	9:53
		Types of Collisions		12:33
			Elastic	12:34
			Inelastic	12:54
			Completely Inelastic	13:24
			Everyday Collisions and Atomic Collisions	13:42
		Example 1: Impact of Two Cars		14:07
		Example 2: Billiard Balls		16:59
		Example 3: Elastic Collision		23:52
		Example 4: Bullet's Velocity		33:35
V. Gravity
	Gravity & Orbits			34:53
		Intro		0:00
		Law of Universal Gravitation		1:39
			Law of Universal Gravitation	1:40
			Force of Gravity Equation	2:14
		Gravitational Field		5:38
			Gravitational Field Overview	5:39
			Gravitational Field Equation	6:32
		Orbits		9:25
			Orbits	9:26
		The 'Falling' Moon		12:58
			The 'Falling' Moon	12:59
		Example 1: Force of Gravity		17:05
		Example 2: Gravitational Field on the Surface of Earth		20:35
		Example 3: Orbits		23:15
		Example 4: Neutron Star		28:38
VI. Waves
	Intro to Waves			35:35
		Intro		0:00
		Pulse		1:00
			Introduction to Pulse	1:01
		Wave		1:59
			Wave Overview	2:00
		Wave Types		3:16
			Mechanical Waves	3:17
			Electromagnetic Waves	4:01
			Matter or Quantum Mechanical Waves	4:43
			Transverse Waves	5:12
			Longitudinal Waves	6:24
		Wave Characteristics		7:24
			Amplitude and Wavelength	7:25
			Wave Speed (v)	10:13
			Period (T)	11:02
			Frequency (f)	12:33
			v = λf	14:51
		Wave Equation		16:15
			Wave Equation	16:16
			Angular Wave Number	17:34
			Angular Frequency	19:36
		Example 1: CPU Frequency		24:35
		Example 2: Speed of Light, Wavelength, and Frequency		26:11
		Example 3: Spacing of Grooves		28:35
		Example 4: Wave Diagram		31:21
	Waves, Cont.			52:57
		Intro		0:00
		Superposition		0:38
			Superposition	0:39
		Interference		1:31
			Interference	1:32
			Visual Example: Two Positive Pulses	2:33
			Visual Example: Wave	4:02
			Phase of Cycle	6:25
		Phase Shift		7:31
			Phase Shift	7:32
		Standing Waves		9:59
			Introduction to Standing Waves	10:00
			Visual Examples: Standing Waves, Node, and Antinode	11:27
			Standing Waves and Wavelengths	15:37
			Standing Waves and Resonant Frequency	19:18
		Doppler Effect		20:36
			When Emitter and Receiver are Still	20:37
			When Emitter is Moving Towards You	22:31
			When Emitter is Moving Away	24:12
			Doppler Effect: Formula	25:58
		Example 1: Superposed Waves		30:00
		Example 2: Superposed and Fully Destructive Interference		35:57
		Example 3: Standing Waves on a String		40:45
		Example 4: Police Siren		43:26
		Example Sounds: 800 Hz, 906.7 Hz, 715.8 Hz, and Slide 906.7 to 715.8 Hz		48:49
	Sound			36:24
		Intro		0:00
		Speed of Sound		1:26
			Speed of Sound	1:27
		Pitch		2:44
			High Pitch & Low Pitch	2:45
			Normal Hearing	3:45
			Infrasonic and Ultrasonic	4:02
		Intensity		4:54
			Intensity: I = P/A	4:55
			Intensity of Sound as an Outwardly Radiating Sphere	6:32
		Decibels		9:09
			Human Threshold for Hearing	9:10
			Decibel (dB)	10:28
			Sound Level β	11:53
		Loudness Examples		13:44
			Loudness Examples	13:45
		Beats		15:41
			Beats & Frequency	15:42
			Audio Examples of Beats	17:04
		Sonic Boom		20:21
			Sonic Boom	20:22
		Example 1: Firework		23:14
		Example 2: Intensity and Decibels		24:48
		Example 3: Decibels		28:24
		Example 4: Frequency of a Violin		34:48
	Light			19:38
		Intro		0:00
		The Speed of Light		0:31
			Speed of Light in a Vacuum	0:32
			Unique Properties of Light	1:20
		Lightspeed!		3:24
			Lightyear	3:25
		Medium		4:34
			Light & Medium	4:35
		Electromagnetic Spectrum		5:49
			Electromagnetic Spectrum Overview	5:50
		Electromagnetic Wave Classifications		7:05
			Long Radio Waves & Radio Waves	7:06
			Microwave	8:30
			Infrared and Visible Spectrum	9:02
			Ultraviolet, X-rays, and Gamma Rays	9:33
		So Much Left to Explore		11:07
			So Much Left to Explore	11:08
		Example 1: How Much Distance is in a Light-year?		13:16
		Example 2: Electromagnetic Wave		16:50
		Example 3: Radio Station & Wavelength		17:55
VII. Thermodynamics
	Fluids			42:52
		Intro		0:00
		Fluid?		0:48
			What Does It Mean to be a Fluid?	0:49
		Density		1:46
			What is Density?	1:47
			Formula for Density: ρ = m/V	2:25
		Pressure		3:40
			Consider Two Equal Height Cylinders of Water with Different Areas	3:41
			Definition and Formula for Pressure: p = F/A	5:20
		Pressure at Depth		7:02
			Pressure at Depth Overview	7:03
			Free Body Diagram for Pressure in a Container of Fluid	8:31
			Equations for Pressure at Depth	10:29
		Absolute Pressure vs. Gauge Pressure		12:31
			Absolute Pressure vs. Gauge Pressure	12:32
			Why Does Gauge Pressure Matter?	13:51
		Depth, Not Shape or Direction		15:22
			Depth, Not Shape or Direction	15:23
		Depth = Height		18:27
			Depth = Height	18:28
		Buoyancy		19:44
			Buoyancy and the Buoyant Force	19:45
		Archimedes' Principle		21:09
			Archimedes' Principle	21:10
		Wait! What About Pressure?		22:30
			Wait! What About Pressure?	22:31
		Example 1: Rock & Fluid		23:47
		Example 2: Pressure of Water at the Top of the Reservoir		28:01
		Example 3: Wood & Fluid		31:47
		Example 4: Force of Air Inside a Cylinder		36:20
	Intro to Temperature & Heat			34:06
		Intro		0:00
		Absolute Zero		1:50
			Absolute Zero	1:51
		Kelvin		2:25
			Kelvin	2:26
		Heat vs. Temperature		4:21
			Heat vs. Temperature	4:22
		Heating Water		5:32
			Heating Water	5:33
		Specific Heat		7:44
			Specific Heat: Q = cm(∆T)	7:45
		Heat Transfer		9:20
			Conduction	9:24
			Convection	10:26
			Radiation	11:35
		Example 1: Converting Temperature		13:21
		Example 2: Calories		14:54
		Example 3: Thermal Energy		19:00
		Example 4: Temperature When Mixture Comes to Equilibrium Part 1		20:45
		Example 4: Temperature When Mixture Comes to Equilibrium Part 2		24:55
	Change Due to Heat			44:03
		Intro		0:00
		Linear Expansion		1:06
			Linear Expansion: ∆L = Lα(∆T)	1:07
		Volume Expansion		2:34
			Volume Expansion: ∆V = Vβ(∆T)	2:35
		Gas Expansion		3:40
			Gas Expansion	3:41
		The Mole		5:43
			Conceptual Example	5:44
			The Mole and Avogadro's Number	7:30
		Ideal Gas Law		9:22
			Ideal Gas Law: pV = nRT	9:23
			p = Pressure of the Gas	10:07
			V = Volume of the Gas	10:34
			n = Number of Moles of Gas	10:44
			R = Gas Constant	10:58
			T = Temperature	11:58
		A Note On Water		12:21
			A Note On Water	12:22
		Change of Phase		15:55
			Change of Phase	15:56
			Change of Phase and Pressure	17:31
			Phase Diagram	18:41
		Heat of Transformation		20:38
			Heat of Transformation: Q = Lm	20:39
		Example 1: Linear Expansion		22:38
		Example 2: Explore Why β = 3α		24:40
		Example 3: Ideal Gas Law		31:38
		Example 4: Heat of Transformation		38:03
	Thermodynamics			27:30
		Intro		0:00
		First Law of Thermodynamics		1:11
			First Law of Thermodynamics	1:12
		Engines		2:25
			Conceptual Example: Consider a Piston	2:26
		Second Law of Thermodynamics		4:17
			Second Law of Thermodynamics	4:18
		Entropy		6:09
			Definition of Entropy	6:10
			Conceptual Example of Entropy: Stick of Dynamite	7:00
		Order to Disorder		8:22
			Order and Disorder in a System	8:23
		The Poets Got It Right		10:20
			The Poets Got It Right	10:21
		Engines in General		11:21
			Engines in General	11:22
		Efficiency		12:06
			Measuring the Efficiency of a System	12:07
		Carnot Engine ( A Limit to Efficiency)		13:20
			Carnot Engine & Maximum Possible Efficiency	13:21
		Example 1: Internal Energy		15:15
		Example 2: Efficiency		16:13
		Example 3: Second Law of Thermodynamics		17:05
		Example 4: Maximum Efficiency		20:10
VIII. Electricity
	Electric Force & Charge			41:35
		Intro		0:00
		Charge		1:04
			Overview of Charge	1:05
			Positive and Negative Charges	1:19
		A Simple Model of the Atom		2:47
			Protons, Electrons, and Neutrons	2:48
		Conservation of Charge		4:47
			Conservation of Charge	4:48
		Elementary Charge		5:41
			Elementary Charge and the Unit Coulomb	5:42
		Coulomb's Law		8:29
			Coulomb's Law & the Electrostatic Force	8:30
			Coulomb's Law Breakdown	9:30
		Conductors and Insulators		11:11
			Conductors	11:12
			Insulators	12:31
		Conduction		15:08
			Conduction	15:09
			Conceptual Examples	15:58
		Induction		17:02
			Induction Overview	17:01
			Conceptual Examples	18:18
		Example 1: Electroscope		20:08
		Example 2: Positive, Negative, and Net Charge of Iron		22:15
		Example 3: Charge and Mass		27:52
		Example 4: Two Metal Spheres		31:58
	Electric Fields & Potential			34:44
		Intro		0:00
		Electric Fields		0:53
			Electric Fields Overview	0:54
			Size of q2 (Second Charge)	1:34
			Size of q1 (First Charge)	1:53
			Electric Field Strength: Newtons Per Coulomb	2:55
		Electric Field Lines		4:19
			Electric Field Lines	4:20
			Conceptual Example 1	5:17
			Conceptual Example 2	6:20
			Conceptual Example 3	6:59
			Conceptual Example 4	7:28
		Faraday Cage		8:47
			Introduction to Faraday Cage	8:48
			Why Does It Work?	9:33
		Electric Potential Energy		11:40
			Electric Potential Energy	11:41
		Electric Potential		13:44
			Electric Potential	13:45
			Difference Between Two States	14:29
			Electric Potential is Measured in Volts	15:12
		Ground Voltage		16:09
			Potential Differences and Reference Voltage	16:10
			Ground Voltage	17:20
		Electron-volt		19:17
			Electron-volt	19:18
		Equipotential Surfaces		20:29
			Equipotential Surfaces	20:30
		Equipotential Lines		21:21
			Equipotential Lines	21:22
		Example 1: Electric Field		22:40
		Example 2: Change in Energy		24:25
		Example 3: Constant Electrical Field		27:06
		Example 4: Electrical Field and Change in Voltage		29:06
		Example 5: Voltage and Energy		32:14
	Electric Current			29:12
		Intro		0:00
		Electric Current		0:31
			Electric Current	0:32
			Amperes	1:27
		Moving Charge		1:52
			Conceptual Example: Electric Field and a Conductor	1:53
			Voltage	3:26
		Resistance		5:05
			Given Some Voltage, How Much Current Will Flow?	5:06
			Resistance: Definition and Formula	5:40
		Resistivity		7:31
			Resistivity	7:32
			Resistance for a Uniform Object	9:31
		Energy and Power		9:55
			How Much Energy Does It take to Move These Charges Around?	9:56
			What Do We Call Energy Per Unit Time?	11:08
			Formulas to Express Electrical Power	11:53
		Voltage Source		13:38
			Introduction to Voltage Source	13:39
			Obtaining a Voltage Source: Generator	15:15
			Obtaining a Voltage Source: Battery	16:19
		Speed of Electricity		17:17
			Speed of Electricity	17:18
		Example 1: Electric Current & Moving Charge		19:40
		Example 2: Electric Current & Resistance		20:31
		Example 3: Resistivity & Resistance		21:56
		Example 4: Light Bulb		25:16
	Electric Circuits			52:02
		Intro		0:00
		Electric Circuits		0:51
			Current, Voltage, and Circuit	0:52
		Resistor		5:05
			Definition of Resistor	5:06
			Conceptual Example: Lamps	6:18
			Other Fundamental Components	7:04
		Circuit Diagrams		7:23
			Introduction to Circuit Diagrams	7:24
			Wire	7:42
			Resistor	8:20
			Battery	8:45
			Power Supply	9:41
			Switch	10:02
			Wires: Bypass and Connect	10:53
			A Special Not in General	12:04
			Example: Simple vs. Complex Circuit Diagram	12:45
		Kirchoff's Circuit Laws		15:32
			Kirchoff's Circuit Law 1: Current Law	15:33
			Kirchoff's Circuit Law 1: Visual Example	16:57
			Kirchoff's Circuit Law 2: Voltage Law	17:16
			Kirchoff's Circuit Law 2: Visual Example	19:23
		Resistors in Series		21:48
			Resistors in Series	21:49
		Resistors in Parallel		23:33
			Resistors in Parallel	23:34
		Voltmeter and Ammeter		28:35
			Voltmeter	28:36
			Ammeter	30:05
		Direct Current vs. Alternating Current		31:24
			Direct Current vs. Alternating Current	31:25
			Visual Example: Voltage Graphs	33:29
		Example 1: What Voltage is Read by the Voltmeter in This Diagram?		33:57
		Example 2: What Current Flows Through the Ammeter When the Switch is Open?		37:42
		Example 3: How Much Power is Dissipated by the Highlighted Resistor When the Switch is Open? When Closed?		41:22
		Example 4: Design a Hallway Light Switch		45:14
IX. Magnetism
	Magnetism			25:47
		Intro		0:00
		Magnet		1:27
			Magnet Has Two Poles	1:28
			Magnetic Field	1:47
		Always a Dipole, Never a Monopole		2:22
			Always a Dipole, Never a Monopole	2:23
		Magnetic Fields and Moving Charge		4:01
			Magnetic Fields and Moving Charge	4:02
		Magnets on an Atomic Level		4:45
			Magnets on an Atomic Level	4:46
			Evenly Distributed Motions	5:45
			Unevenly Distributed Motions	6:22
		Current and Magnetic Fields		9:42
			Current Flow and Magnetic Field	9:43
			Electromagnet	11:35
		Electric Motor		13:11
			Electric Motor	13:12
		Generator		15:38
			A Changing Magnetic Field Induces a Current	15:39
		Example 1: What Kind of Magnetic Pole must the Earth's Geographic North Pole Be?		19:34
		Example 2: Magnetic Field and Generator/Electric Motor		20:56
		Example 3: Destroying the Magnetic Properties of a Permanent Magnet		23:08

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Newton's 2nd Law: Multiple Dimensions

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