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Vincent Selhorst-Jones

Vincent Selhorst-Jones

Linear Momentum

Slide Duration:

Table of Contents

I. Motion
Math Review

16m 49s

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

26m 2s

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

29m 59s

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

18m 36s

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

16m 34s

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

12m 37s

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

27m 5s

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

27m 47s

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

42m 5s

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

16m 47s

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

50m 11s

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

26m 45s

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

28m 34s

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

39m 7s

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

28m 10s

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

44m 16s

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

28m 54s

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
5:29
Block and Tackle Systems
5:30
Machines in General
9:44
Levers
9:45
Ramps
10:51
Example 1: Power of Force
12:22
Example 2: Power &Lifting a Watermelon
14:21
Example 3: Work and Instantaneous Power
16:05
Example 4: Power and Acceleration of a Race car
25:56
IV. Momentum
Center of Mass

36m 55s

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

22m 50s

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

40m 55s

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

34m 53s

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

35m 35s

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.

52m 57s

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

36m 24s

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

19m 38s

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

42m 52s

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

34m 6s

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

44m 3s

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

27m 30s

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

41m 35s

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

34m 44s

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

29m 12s

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

52m 2s

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

25m 47s

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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Lecture Comments (3)

2 answers

Last reply by: Enoch Lee
Wed Jan 6, 2016 5:25 AM

Post by Farzana Meem on June 16, 2015

Can you explain how an airbag "cushions" the blow for a passenger in a car collision using impulse and momentum.

Linear Momentum

  • Linear momentum (p) is the product of both velocity and mass:

    p
     
    = m

    v
     
    .
  • Notice that linear momentum uses velocity, not speed. That means momentum is a vector quantity.
  • The unit for linear momentum is kg ·[m/s].
  • Impulse (J) is a way to talk about changes in linear momentum:

    J
     
    =

    F
     
    t.
  • The change in linear momentum is equal to the impulse and vice-versa-J=∆p.

Linear Momentum

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 0:00
  • Introduction to Linear Momentum 0:04
    • Linear Momentum Overview
    • Consider the Scenarios
  • Linear Momentum 1:45
    • Definition of Linear Momentum
  • Impulse 3:10
    • Impulse
  • Relationship Between Impulse & Momentum 4:27
    • Relationship Between Impulse & Momentum
  • Why is It Linear Momentum? 6:55
    • Why is It Linear Momentum?
  • 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

Transcription: Linear Momentum

Hi, welcome back to educator.com, today we are going to be talking about linear momentum.0000

From our work and energy, we already know that the mass and the speed of an object is able to determine its kinetic energy.0006

But, when we were dealing with energy, we only had speed as the way of determining energy.0012

There was not anything talking about direction.0017

Kinetic energy was great for telling u slots of stuff, but it did not tell us if we were going to the north, south, up or down.0019

To capture that, we are going to introduce a new idea: Linear Momentum, what your motion is along a line.0026

We want the linear momentum to talk about an object's motion in a given direction, just like energy gave us an idea of speed and mass for an object, linear momentum will give us something that tells us about the motion of an object.0032

Consider two scenarios: We got a box moving at the same speed but in opposite direction.0045

To capture the difference, we will not be able to just use the speed, because it is moving in the speed in both the cases.0052

But we will need to also capture its direction.0057

To do that, we need to use vector.0060

We are going to have to use v, not just 'v', the speed, we need to have its actual velocity.0062

Also, what if the boxes had different masses?0071

If we had two different boxes, that were both moving in the same speed, one of them was say 1 kg, and the other a 100 kg, we probably want to think of them as being different things.0073

It will take a whole lot more effort to stop a 100 kg box than the 1 kg box.0083

So, direction is part of it, but we are also going to have to take into account, the mass.0088

Clearly, it is going to a good idea to include mass in our idea of linear momentum.0093

So, we are going to have to be able to deal with the velocity vector, not just the speed, and also mass.0097

Put in that together, we get, linear momentum, and we define it as, mass×(velocity vector), mv.0106

Notice that, since this is a vector quantity that we are dealing with, it is going to be, how much we are moving in the x coordinate, how much we are moving in the y coordinate, if you are also moving in the z coordinate, it is going to be, mvx + mvy + mvz.0116

We are going to break it up as a vector, and m will just scale the vector.0135

These two characteristics, they define, what we are going to create as momentum.0138

Momentum, p = mv.0142

Why do we use a p?0146

I honestly do not have a good answer, I wish I did, there are possibilities, it has a Latin root, but I was not able to figure it out, sometimes there are mysteries in the world.0148

An important thing to notice here is that, this p is not just a scalar quantity, it is not just a single number, it is a vector.0166

If v comes in (x,y,z), our p is also going to have to come in (x,y,z).0174

Units of linear momentum are, mv, so kg×(m/s).0183

We are going to consider a new idea: Impulse.0191

What if we want to talk about how much an object's momentum changes, that is important.0193

If we got a box moving along, and if we put a force on the box, we are going to change the momentum of the box, because we will change the speed that it is moving at.0198

So we are going to define the idea of impulse.0205

What really changes the velocity of the thing?0207

It is just going to be the fore involved, but not just the force.0212

The same force is going to be very different if you put a 100 N on an object for 0 s, 1 s, 10 s, 100 s, totally different things are going to happen depending on the amount of time that the force is acting on it.0217

The objects mass remains constant, pretty reasonable.0227

The object's velocity, and thus its momentum, is going to change based on the force applied, and how the long that force lasts.0232

We define impulse as the letter 'j' (no particularly good reason here, just making sure we are using letters that have not already been taken by somebody else), j= force×time = Ft, just like before, j is a vector because force is a vector.0238

Makes sense, because we are talking about change in a vector quantity.0255

Note that impulse is a vector, and its units are going to be, Ft, so N s.0259

At this point, we have created some definitions, and we can see that linear momentum and impulse are connected because we wanted impulse to represent a way of shifting around momentum.0268

You put force into an object for a certain object of time, it is going to change the momentum that the object has, because we will be changing the speed that it is changing at.0279

But, what is the precise mathematical relationship?0286

Let us figure it out.0288

We look more closely at the formula for impulse.0289

j = Ft, if we expand that out, we can get this.0292

F = ma, so, j = mat = mΔv, (since 'a' is how much your velocity is changing with time).0299

Since mass is not changing, we can pull that change outside, and we get, Δv, because we do not have to worry about, since velocity is the only thing that can change, we are assuming that the mass is constant, so, mΔv is the same thing as, Δ(mv), because mass is just a constant, and velocity is the variable, at this point.0328

Remember, we defined, p = mv, so it has to be the case that, Δ(mv) is the same as, Δp.0350

So, in the end, j = Δp, so impulse is simply the change in the momentum.0362

Note that impulse and momentum have the same units, 'N s' is the same thing as 'kg m/s', because N comes from, if F = ma is kg m/s/s, so, N is kg m/s/s, and multiply with s, so kg m/s, is what we had for momentum.0371

It makes a lot of sense, our units wind up working out, so, j = Δp.0404

In this section, we have talked about what linear momentum is, but why have we talked about 'linear' momentum, when we have not heard about any other kinds of momentum, why is it called linear momentum if it is the only momentum that we are concerned with?0417

The thing that is going on, is there are other kinds of momentum, there is angular or rotational momentum.0438

Spinning objects, objects that are spinning, if you take a wheel and you spin it really fast, it will keep spinning, right?0445

It has a momentum, it is not moving anywhere, it is just sitting there in space and spinning, but it takes effort to start it spinning, and it takes effort to stop it spinning, so there are torques involved, we have not talked about rotational mechanics.0452

The entire thing in Physics you cannot talk about, but we just do not have quite enough math to really feel comfortable handling it, we are almost there, this is definitely close to being within our grasp, but a little too much math for us to tackle there, so we are holding off on it, that is why we have not talked about angular momentum, which is also similar to rotational momentum.0465

We have been talking about linear momentum, because we want to make sure that this is kept clear, as this is linear momentum as opposed to this other kind of momentum, but often when we are talking about linear momentum, we will also just refer to it simply as momentum, because that is the thing that is more common, but it is important to keep in mind that there are other kinds of momentum.0485

Just because we are talking about one of them, does not mean that there is nothing else out there.0501

Let us start with our examples.0506

A skate board of mass 4 kg is rolling along at 10 m/s.0508

What is its momentum? This one is pretty easy.0512

What is the basic definition for momentum? p = mv = 4 kg × 10 m/s = 40 kg m/s. (since one dimension, velocity becomes a single number).0513

Same skateboard, m = 4 kg, is rolling along with an initial velocity of 10 m/s, just like before.0538

A force of F = -6 N is applied to it, for t = 6 s.0547

At the beginning of this problem, we got some skateboard rolling along on the ground, and it is moving this way.0551

However, as time moves on, there winds up being a force applied to it in this direction, so later on, this skateboard is going to be rolling along with a much smaller velocity vector.0558

It is still going to be moving forward, potentially, depends on how long that force is actually, may be that force is going to push it so hard that it winds up going in the other direction, we are going to have to do some math to figure it out.0569

But, the force is acting on it in the direction opposite of current travel, we are travelling in the positive direction (right), and now force is going to wind up in the negative direction.0583

That is the importance of using vectors, we know how positive and negative direction, even if we are still on one dimension.0596

So, What is the impulse vector?0602

Impulse, j = Ft = -6×6 = -36 N s, so what is the final velocity that it is going to have?0604

In this case, we know that change in momentum is equal to the impulse.0629

We already figured out what the initial momentum is.0635

In the last problem, it wound up being, 4×10 = 40 kg m/s, so the final one is going to be, pi + j = pf, since pf - pi = j.0638

pi = 40, and the change is -36, so in the end we get, 4 kg m/s = pf, is the final momentum.0670

Final momentum does not quite tells us the final velocity.0684

But we can figure that out pretty easily from there.0687

pf = mvf, 4 = 4vf, so, vf = 1 m/s, is the final velocity.0688

It is still moving in the positive direction.0709

It would be possible to figure this out without using momentum and impulse, but momentum and impulse may dissolve pretty simple things that we have to do, very direct, multiplying and then adding, and then doing some really simple algebra.0711

but, we could go back to doing this with Newton's second law.0725

If we want to do this in Newton's second law, we have got, F = ma, -6 = 4a, a = -1.5 m/s/s.0729

What does the change in velocity wind up being?0753

Δv = -1.5×t = -1.5×6 = -9 m/s, and so, if you started with initial velocity of 10 m/s, then, vf = 10 + (-9) = +1 m/s.0755

So, if we wanted, we could do this in terms of basic fundamental, Newton's second law, but in this case it is pretty easy.0780

Remember, the way momentum works, the way we have defined it, is really just sort of jumping off the point of using Newton's second law.0789

That is how we got impulse.0796

Impulse was based around the fact that, the reason why impulse is equal to the change in momentum is because we used F = ma, at what point we got, Ft, so in the end, they are deeply interconnected.0797

So, we can decide to go with Newton's second law, but in lots of problems, it is going to wind up being the case that it is actually a little bit easier the way of linear momentum, especially when we are dealing with momentum problems.0812

In the next lesson, we are going to wind up seeing why it is really useful to have momentum when we get to the conservation of momentum, and that is why this stuff really matters.0821

Example 3: A ball of mass m = 0.5 kg is moving horizontally with vi = 10 m/s.0835

It bounces off a wall, after which it moves with vf = -7 m/s.0842

What is the change in linear momentum, what is the magnitude of the impulse?0848

We got this ball, moving along the positive direction, and it hits the wall, and afterwards it changes, rebounds, and it is moving in the negative direction.0851

What is the initial momentum? mv = 0.5×10 = 5 kg m/s.0862

What is the final momentum? 0.5×(-7) = -3.5 kg m/s.0885

So, the change is, final - initial, Δp = -3.5 - 5, seems a bit weird, but makes sense, we started off in the positive direction, and ended up going in the negative direction, so the entire change has got to be one of negative momentum occurring.0898

So, -8.5 kg m/s is the change in the linear momentum.0937

The magnitude of impulse, remember, the magnitude is the size of something, so the size of this, j = Δp = magnitude(-8.5 kg m/s) = 8.5 kg m/s.0945

In the end, when we are dealing with magnitude, it does not care about direction, it does not care about positive or negative, it just cares what [unclear] like the thing we are dealing with.0972

In this case, we had -8.5 as the change in momentum, but the magnitude of the change in momentum was just the total moment, 8.5.0983

This is sort of similar to what we saw in energy before, instead of using velocity, it was the length of the velocity vector that we cared about, its speed.0993

It did not matter if it was pointing flat, it was pointing straight up , pointing at a 45 degree angle, all that mattered was what the total length was.1001

That is what we are seeing here, when we ask what the magnitude of the impulse, we are asking for what is the length of that thing.1010

In multiple dimensions, we take, sqrt(x2+y2+z2), because that is how we take the magnitude of a vector.1017

Last example: A ball of putty with a mass of 1 kg is about to fall on your head.1027

The velocity initially is -5 m/s, makes sense since it is falling down.1032

Which one is going to hurt worse, it lands and sticks on your head, so it lands and sticks, so the final velocity is zero, or, it lands and bounces off your head, with a final velocity of 4 m/s.1037

Let us call these cases, A and B.1048

In case A, it hits your head, and it sticks in place.1052

In case B, it bounces off your head.1059

Which one of these is going to hurt worse?1062

Normally we think of things being bouncy as good, they are easy right?1065

A super ball being bounced on your head, and bouncing off your head, it would not hurt much.1069

But what is really going on, which one is taking more force, the super ball that hits your head and just sort of sits there, or the ball that hits your head and ricochets right off?1075

We can break this down with Physics and Math.1083

In both cases, what is really going to be defined as hurting?1086

The way that we define as 'hurt' is probably the amount of force that it exerts on you.1092

So, you would rather have 2 N of force shoved on you than a billion newtons of force being shoved on you, a billion newtons force applied on you, your body is going to look like a pancake.1097

But 2 N of force, a small amount of force is going to hurt less than large amounts of force.1108

What we are looking for is, which one of these cases is going to produce less force on impact.1115

In both of these cases, it is going to be important to know how long the balls contacting your head, we will be able to figure out what average force is going to be.1121

Impact time for both of these cases will be 0.25 s, so let us figure out how much force is involved.1128

To do that, we need to figure out what the impulse in both cases are.1135

To do that, we need to know what the initial velocities are, what the initial momentum is, and what the final momentum is.1139

From there, we will be able to figure out the impulse, and from impulse, we will be able to figure out pretty easily what the force is.1145

In both them, we need to know what is their initial momentum.1150

Initial momentum = m×vi = 1×(-5) = -5 kg m/s.1154

Case A, it lands and sticks on you head, so its vf = 0.1168

If that is the case, what is the final momentum?1174

Still mass of 'm', but now it sticks, so it now has no velocity, so it has got a momentum of zero in the end, 0 kg m/s.1177

Compare that to B, where we have got a final momentum = 1×4 = 4 kg m/s.1189

It might make good sense at this point to go, 'Okay, the one with less momentum is case B, because we go from 5 to 4'.1207

But that is not the case.1215

The whole case is, we go from -5 to 4.1217

So which is a bigger change, going from -5 to 0, or -5 to 4?1220

We check that out, we get, Δp = (final) - (initial) = +5 kg m/s, is in A.1224

In B, Δp = 4 - (-5) = 9 kg m/s.1240

So, there is more change in momentum in case B than in case A.1254

So it is going to make more sense for B to hurt, because that force, to change that momentum, has to come from somewhere.1257

We have got a constant time, so it has got to be, the amount of force involved is going to have to be more in case B.1264

We will finish this out, at this point we can see that the answer is going to be case B.1272

So, j = Ft, we also know that j = Δp, so for case A, we got, 5 = F×0.25 s, F = 20 N.1276

So, 20 N is how much force you wind up undergoing for A.1301

Now, how much force does you wind up undergoing in B?1306

j =Ft = Δp, so, 9 = F×0.25, so, F = 36 N, in part B.1310

So, part B winds up putting more force on your head, in both cases, they are pretty small, so worst case you are going to have a little bit of headache, but 36 N is more force you have to suffer than 20 N.1328

So, it is actually better to have an object that lands on your head and just sticks there, something that goes 'splat!', than something that goes, 'boing!', because 'boing!', that force to make it bounce off is going to have to come from somewhere.1340

It is coming from your head, that is going to make it hurt more.1351

It is better to have it land and splat, it has less force, because it has to change its momentum if it is going to be able to bounce off your head.1354

I hope this lesson made sense, I hope you got a good understanding of linear momentum, because the next thing that is coming is conservation of momentum, and that is where the real point of momentum is.1361

Alright, good day!1368

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