  Vincent Selhorst-Jones

Newton's 2nd Law: Multiple Dimensions

Slide Duration:

Section 1: 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
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
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
Section 2: 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

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
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
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
Section 3: 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
Section 4: 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
Section 5: 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
Section 6: 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
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
Section 7: 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
22:30
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
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
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
Section 8: 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
8:47
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
Section 9: 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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• ## Related Books & Services 1 answer Last reply by: Professor Selhorst-JonesTue Apr 21, 2020 11:16 PMPost by Matthew Zhang on April 17, 2020For the normal force on an incline diagram, does (cos?) * Fg represent the Normal Force? Also, what does (sin?) * Fg represent?Thanks for the help! 0 answersPost by Pranav Thurai on March 28, 2018in example2 how you get the answers 126 1 answer Last reply by: Professor Selhorst-JonesSun Mar 12, 2017 6:39 PMPost by bienvenido villabroza on March 11, 2017For example 1, can my answer for the question "what is a for the object" be 1 m/s^2, 36.87 North of East? I understand why the answer in your slide is (4/5,3/5) m/s^2 but would my answer be acceptable as well? 2 answersLast reply by: Kuthala NathanSat Jun 6, 2015 3:34 AMPost by Kuthala Nathan on June 6, 2015Hi Professor, I really enjoy your lecture and it is very easy to understand. Thank you!In Example 3, why is the F net system 49N-33.5N and not 49N+33.5N ? Thanks in advance 2 answersLast reply by: Tori CarrollSun Oct 5, 2014 12:25 PMPost by Tori Carroll on October 4, 2014How would the acceleration be found if the plane was not frictionless? 4 answersLast reply by: Jack WilshereSat Jan 11, 2014 12:44 AMPost by Hoe Li En on January 4, 2014hi, with regards to the diagram at 10 min 04, the hypotenuse of the triangle represents the force of gravity, while the (cosÎ˜)Fg represents the normal force...what about the (sinÎ˜)Fg ? what does it represent? the force of friction acting on the object? 1 answer Last reply by: Professor Selhorst-JonesThu Oct 31, 2013 9:21 AMPost by Benny Hui on October 31, 2013Hi Professor,This is my first time to see your lecture. It is clear and easy to understand. Thank you for making this video.Going back to the example 3. There was a gravity acting on the 5Kg block. So, by F=ma, you deduced that there was a 49N downward force acting on this block. Using the same formula, you deduced that there was a 33.5N acting on the 10Kg block along the slide. My question is this. Why can't we see the body as the whole system and say the tension between two blocks was 49N - 33.5N = 15.5?Thanks 1 answer Last reply by: Professor Selhorst-JonesMon Nov 19, 2012 9:06 AMPost by varsha sharma on November 19, 2012In example 1 why the vertical component is considered x direction and vice versa ? should'nt the vertical components be y and horizontal be x components. 1 answer Last reply by: Professor Selhorst-JonesSun Oct 21, 2012 11:57 AMPost by Ahmed Almushqab on October 21, 2012In the slide "Example : force in componenet form" how did you get the result (8.66 & 5 ) cause 10sin30 & 10cos30 dont give the result that you wrote sir could you explain please ?

### Newton's 2nd Law: Multiple Dimensions

• With force in multiple dimensions, we switch to using vectors:
 →Fnet
 =
 m · →a ,
 ⇔
 (Fxnet,  Fynet)
 =
 (m ·ax,  m ·ay).
• 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 0:00
• Newton's 2nd Law in Multiple Dimensions 0:12
• Newton's 2nd Law in Multiple Dimensions
• Components 0:52
• Components
• Example: Force in Component Form
• Special Forces 2:39
• Review of Special Forces: Gravity, Normal Force, and Tension
• Normal Forces 3:35
• Why Do We Call It the Normal Forces?
• Normal Forces on a Flat Horizontal and Vertical Surface
• Normal Forces on an Incline
• 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

### Transcription: Newton's 2nd Law: Multiple Dimensions

Hi, welcome back to educator.com, today we are going to be talking about Newton's second law and applying to multiple dimensions.0000

Last time we only talked about applying it in one dimension, today we are going to be talking about what happens in more than one dimension.0006

As in kinematics, each dimension works independently.0011

Acceleration in the y direction is completely unrelated to acceleration in x direction.0016

As far as Newtonian mechanics is concerned, we can consider them completely independently.0020

Now we just turn our formula from before into vector based ones.0030

Now we have got, Fnet = ma, so we can consider them as the different components as separate pieces, xnet, ynet is going to have acceleration in the x and acceleration in the y, both going to be completely separate components.0033

It is possible to break a force vector into its components just as we did in kinematics to break velocity, acceleration, displacement into separate components.0053

If we had a force of 10 N acting on an object 30 degrees above the horizontal, what will that force be in component form?0063

First, we drop a perpendicular sown.0068

Now, we have a right triangle, we can easily apply trigonometry.0072

If we want to know what this side is, this is the side that is going to be connected to sin(30), we got the hypotenuse = 10, so it is going to be (10 N) × sin(30) , which comes from sin(30) = side opposite / hypotenuse, if you get used to doing stuff in component form, you will get really fast at this, it is just going to be sin(30) times whatever the full magnitude of the vector is.0075

Similarly on the other side, on the bottom part it is going to be, (10 N) × cos(30) .0120

Now we know what each side would be, so we just use basic trigonometry, and we get that from a table/calculator.0132

We get, the length (the width) is going to be 8.66, and the height is going to be 5, both in newtons, 8.66 N and 5 N in horizontal and vertical directions respectively.0139

Before we talked about some special forces, and they are all still there, the force of gravity (weight) is still there, now it is only going to pull down in one direction, it either gets canceled out, or works at the same time as the horizontal forces are working.0159

Normal force, force that holds you up, still there, if something is resting on the top of a surface, that surface is still going to support it against gravity.0187

Tension, force on whatever object is connecting things, still there, and it is going to pull in whatever direction that rope is angled at.0195

If you have a rope connected to something, and you pull like this, then it is going to cause a force of that, and if you pull like this, that is going to cause a force like that, it just have to do with what angle it is acting.0203

But, I have not explained why it is called the 'normal' force!0220

Why do we call it the normal force?0228

That is a great question.0230

The normal force, it is a fancy word for Math, it simply means perpendicular.0233

The word 'normal' comes from the Latin word 'norma', which is the word for a 'carpenter's square', which is a tool used for making right angles.0240

Normal just comes from a right angle, so it just means perpendicular.0249

Two normal segments would be any two that intersect with a right angle between them.0255

If you had a curve of some sort, you could have a number of right angles that is sprouted out of it.0262

Each one of them is a little bit different, but they are all normal even though they are attached to a curve, because what matters is that they are perpendicular at the point of intersection.0279

So normal is just another way of saying that it is perpendicular.0289

Normal force is the force that is perpendicular, the gravity the surface can cancel out, because the surface can only put up a perpendicular force.0293

Consider these two versions:0301

We have got a man standing on a perfectly flat plane, now what happens is, the force of gravity pulls down on him by a certain amount, and because he is standing on a perfectly flat plane, the normal force is going to be able to be exactly opposite, and the two are going to cancel one another out.0304

So that is great.0319

Now, what happens when force of gravity is pulling on a man, who stands on the side of a building.0320

He does not have anything connecting his feet to the building, so we are not going to think about how he managed to get there to his position where his feet are on the building for a brief second before he plummets down.0327

Does he have a normal force on him?0338

No, because the normal force would have to work by going this way, and that does not make sense because there is nothing pushing him against it.0341

So you cannot have that.0349

The normal force would only work if he were pushed against something, but he has nothing to be pushed against to, he is just going to plummet down to the ground.0350

What happens if you were on an incline?0367

So we looked at the two extreme cases, flat surface and vertical surface, either the normal force is going to be completely there, or it is going to have no effect.0369

If you were on an incline, them some of it is going to be able to be perpendicular.0390

We can now create a right triangle, that has this part perpendicular, and this part parallel to the top of the triangle.0394

There will be a parallel section and a perpendicular section.0406

The important part is that, this is a right angle, and this is a right angle, and this is parallel to this.0418

So we know this is a right angle, so we know how much is perpendicular to the surface, and we know how much is parallel to the surface.0428

Let us figure out what would be the angle up here.0434

If we look at this as a slightly larger version, here is angle θ , and here is a right angle, we can figure out from basic trigonometry what that angle is.0441

We know that across two intersections, we know that these have to equal angles.0462

So, this θ must be equal to this other angle over here, which means if we want to figure out what these two components are, we are going to get cos(θ) × Fg over here (because that is the side adjacent), and sin(θ) × Fg is going to be the parallel.0468

In general that is a rule to remember.0506

But it is important to make a diagram and understand yourself than slavishly fall over formula, if you do that you are liable to make mistake, the math can go wrong, it is up to us pay attention to what we are doing, and that is incredibly important.0517

But in general, if you are able to get this angle here in this right angle format, then we are going to have that sin(θ) is going to be the thing connected to the parallel part, and cos(θ) is going to be the thing connected to the perpendicular part, which makes sense,0546

because if θ was zero, if we were on a flat thing, then cos(0) would be 1, i.e. all of the force of gravity would be translated to the perpendicular and if it were 90 degree (perfectly vertical), then sin(90) = 1, which means all of the gravity would be translated into the parallel.0566

So, sin(θ) correlates to the parallel, cos(θ) correlates to the perpendicular, once we draw the diagram this way.0590

Depending on the diagram you use, you might wind up changing it out, or it might be that your problem works differently, so it is important for you to pay attention to what you are doing, and have it make sense, but this is a general structure that you can follow, also you would like somebody else to understand your work later.0596

First example:0623

We have got an object with mass of 5 kg sitting on a perfectly flat frictionless plane.0624

It is pushed by a force of 3 N to the North, and a force of 4 N to the East.0629

What is the acceleration of the object, what is the magnitude of that acceleration, and at what angle does the combined force move the object along at?0634

When we are saying it is on a perfectly flat frictionless plane, we imagine it like the middle of a frozen lake.0647

We are looking down from above.0653

So, we have got North, East, South, West like on a compass.0655

We make East-West the x positive direction.0666

That seems pretty reasonable, we could make North as x positive, but we want to make it something we are used to, not complicated, so we make East x positive and North y positive.0670

Some if we were to go South, that would be negative in the y component of our vector, and if West, that would be negative in the x component of our vector.0685

With that let us look at what our picture is, we have got our block sitting still at the moment, and it is pushed by a force of 3 N to the North, so 3 N 'up', and 4 N to the East, so 4 N to the 'right', 'up' and 'right' from the way we are visualizing it.0692

The important thing is that we have set up a new coordinate system to understand this.0725

So, 3 N positive y, and 4 N positive x.0730

That means now x component of our force is 4 N and y component of our force is 3 N .0733

So, if we want to find out what the acceleration of our object is, we are going to have to find out what the acceleration is for each of the components, in x and y, and together that will give us the acceleration vector, the combined acceleration.0745

We appeal to Newton's second law: Fnet = ma, there is no other forces than this one force, actually two forces, but they do not interact since they are in different coordinates axes.0760

So we do not have to worry about any other forces, so Fx = max , 4 N = (5 kg) × ax , ax = (4/5) m/s/s .0772

We do that for the y, Fy = may , 3 N = (5 kg) × ay , ay = (3/5) m/s/s .0800

Now we have got our two pieces, we can put them together, we get, a = (4/5,3/5) m/s/s .0831

If we want to find out what the magnitude of the vector is, that is just going to be the square root of each of the components squared.0852

So, square root of (4/5)2 + (3/5)2 = square root of (16/25) +(9/25) = square root of (25/25) = 1 .0859

So, the magnitude of our acceleration vector is 1 m/s/s .0883

Finally, to figure out what the angle it is coming at, we want to set up a triangle so we can see the angle more easily.0888

So, here is a picture of what is going on.0897

We have got 4 N to the right, which has now become (4/5) m/s/s to the right, and also (3/5) m/s/s to the up.0899

If we want to figure out what angle that is, now we have got a triangle where we can set things up, we can see where the angle goes.0919

The angle above the horizontal, above the East, the angle North of East, we are going to able to figure that out by saying, tan(θ) = (y component)/(x component) = (3/5)/(4/5) = 3/4 .0929

Taking the arctan of that, θ = arctan(3/4) = 36.87 degrees .0954

Next example:0967

A 20 kg block is on an incline of 50 degrees with a rope holding in its place.0968

Assuming that the incline is frictionless, what would be the tension in the rope?0973

Then if we cut the rope, what acceleration would the block have?0976

First, what forces are at play here?0980

We got tension pulling this way, force of gravity pulling down.0982

Force of gravity = (20 kg) × (9.8 m/s/s) = 196 N .0991

So, how much of this is perpendicular, and how much of this is parallel?1006

Up here, we are able to get this as θ from the geometry, so this is going to be equal to 50 degrees.1013

So, force of gravity perpendicular = cos(50) × (196 N) = 126 N, and the force of gravity parallel = sin(50) × (196 N) = 150 N .1028

Now, there is one more force operating over here, and that is going to be the normal force.1058

So, the normal force, it can only work on what is operating perpendicular to the surface, how much is operating perpendicular to the surface?1066

The force normal = force of gravity perpendicular, which means that this force will cancel out this force, so the net force is only going to be the force of gravity parallel and the tension in the rope.1073

Now, is this thing moving?1087

We know that it is not, it is currently still, the rope is taut and it is staying in place.1089

So we know that the tension, we will make this the positive direction, Tension - force of gravity (parallel) = mass × acceleration = 0, because we got zero acceleration.1094

So, T = Fg(parallel) = 150 N .1112

So we have got the tension.1121

If we cut the rope, how much acceleration will the block have?1124

Now, it is not going to have anything pulling it away, it is only going to be moving parallel, because what we have done is, we have broken down it into the perpendicular and parallel.1128

The perpendicular is canceled out by the normal force, because that is how much force is translated to through the surface perpendicular into the object.1136

So the force of gravity that is perpendicular to the surface gets canceled out, but the force of gravity parallel to the surface will be able to accelerate the block along a parallel vector to the surface of the triangle, it will accelerate this way.1143

We do not know what 'a' is yet, but we can figure it out.1161

We had, T - Fg(parallel), but now there is no more T, so all we have is Fg(parallel) = (20 kg) × acceleration, (150 N)/(20 kg) = acceleration.1164

So our acceleration = 7.5 m/s/s .1198

What direction is that going?1207

It goes in the direction parallel to this.1209

This is just an acceleration, not a vector, we could figure out what the components are to the Fg(parallel), but that is going to take a lot of time, there will be some part x, some part y, and it will take a lot of effort, instead we can just know what it is off of our diagram,1212

because we do not have to say specifically what it is, we can just say it is working parallel to the top of the triangle, it is working parallel to the hypotenuse of the triangle, because that is really the most interesting thing, that gives us the useful information.1227

So, a =7.5 m/s/s, parallel and sloping down along the triangle.1238

Final example:1252

We have got a 10 kg block on an incline of 20 degrees, and it is attached by a rope to a free hanging block of 5 kg .1254

Assuming that it is frictionless, the rope and the pulley are mass-less, what is the acceleration of the blocks, and what is the tension in the rope?1260

As done before, we are going to look at this as a system.1270

It is a lot easier, although we could break it into the tensions and the gravities experienced by the blocks.1274

This one does not have any force normal operating on it, it is just going to have the force of gravity, which in its case, = 5 × 9.8 = 49 N .1282

How much gravity does this one have operating on it?1298

Its force of gravity = 10 × 9.8 = 98 N .1301

If we want to break this into its perpendicular and its parallel component, then here is our angle of 20 degrees.1310

So here we are going to have, cos(20) × Fg, so force of gravity (perpendicular) will be canceled out by the normal force, Fg(perpendicular) = cos(20) × 98 N = 33.5 N, but sorry!!, I gave you the wrong one there (parallel), but there is no need to worry since the normal and Fg (perpendicular) are going to cancel out, so we just have to worry about the parallel here.1320

We know the acceleration perpendicular to the surface of the triangle, because we know that they are going to get canceled out, because of the way the normal force works.1386

So, all we care about is, how much is parallel.1394

How much is parallel will be, sin(20) × Fg (parallel) = sin(20) × 33.5 N .1396

Like before, we are going to consider this as positive direction, so positive goes around the corner, goes down, we are going to consider it the same as we did in the last lesson when we worked out a problem similar to this.1420

The only thing left, we have not talked about these tensions working in the rope.1432

But, if we look at the system as a whole, the only thing pulling in an external fashion, are the two forces of gravity (the one that is going completely down), the tensions are going to be canceled out when we look it as a system, because the rope is going to be taut the entire time, so we can consider it to be a rigidly moving system, where the accelerations are going to be the same.1440

We have done a problem like this before, you should go back a lesson and look at the final example from that one, because that is very similar, we are just throwing in the incline to make the things little bit more difficult.1469

Now we know what our forces are, the only two forces we need to care about, are forces of gravity, for this one, = 49 N, we want to find out the acceleration and the tension in the rope.1478

For this one, force of gravity (parallel) = 33.5 N .1496

So, what is the mass over here?1505

This has a mass of 10 kg, this has a mass of 5 kg .1507

So, what are the forces acting on the system?1513

This is the positive direction, Fnet (system) = mass (system) × acceleration, the accelerations being the same (since rigid).1515

So, 49 N - 33.5 N = (10 kg +5 kg) × a , 15.5 N = 15 × a, a = 1.03 m/s/s .1536

So there is going to be an acceleration this way, and an acceleration this way.1563

For this one it is going to be going directly down (for the smaller block), and for the larger one it is going to move parallel and up the surface of the triangle, and they are both going to be 1.03 m/s/s .1568

What is the tension?1580

For this, we just look at the free-body diagram.1582

Let us consider the smaller one.1585

It has some tension T, and it has some force of gravity pulling down.1587

We know what the force of gravity already is, it is 49 N .1593

What is the tension, we do not know that, but we do know that it has an acceleration = 1.03 m/s/s, and we know its mass = 5 kg .1596

We have got that, Fnet = ma , Fg - T = 5 × 1.03 , 49 - (5 × 1.03) = T , T = 43.85 N , which makes a lot of sense because if the block is going to be able to fall, there need to be slightly less tension in the rope, because it has to have a net force that is stronger downwards than upwards, otherwise it will not accelerate down, it will accelerate up.1610

That finishes it for this lesson, hope you enjoyed it.1661

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