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Vincent Selhorst-Jones

Vincent Selhorst-Jones

Uniform Circular Motion

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 (2)

1 answer

Last reply by: Professor Selhorst-Jones
Wed Aug 31, 2016 5:54 PM

Post by Claire yang on August 31, 2016

What is magnitude?

Uniform Circular Motion

  • For an object to maintain the same speed while moving in a circle, its velocity must constantly be changing-the object has an acceleration.
  • The formula for acceleration if you have uniform circular motion (the same speed throughout the circle):
    |

    a
     
    | =
    |

    v
     
    |2

    r
    .
  • The acceleration vector always points from the object to the center of the circle.
  • The velocity vector is always tangential to the circle.
  • Remember: in the above equation, those are the magnitudes of the vectors, since the direction of both acceleration and velocity must constantly be changing.
  • A revolution is one complete circuit of the circle.
  • The circumference of a circle is 2πr and the speed is |v|, so the time it takes for one revolution is
    T = 2πr

    |

    v
     
    |
    .

Uniform Circular Motion

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
  • Centripetal Acceleration 1:21
    • Centripetal Acceleration of a Rock Being Twirled Around on a String
    • Looking Closer: Instantaneous Velocity and Tangential Velocity
    • Magnitude of Acceleration
    • Centripetal Acceleration Formula
  • You Say You Want a Revolution 6:11
    • What is a Revolution?
    • How Long Does it Take to Complete One Revolution Around the Circle?
  • 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

Transcription: Uniform Circular Motion

Hi, welcome back to educator.com, Today we are going to be talking about uniform circular motion.0000

We have not really talked about what does it mean to have a uniform circular motion.0005

Uniform circular motion just means that you have got something traveling at a uniform rate, or a constant rate.0010

If you have got something move at a constant speed uniformly in a circle, say we have got a rock on a string, moving around in a circle at a constant speed.0016

The rock has a constant speed, but what does it mean about the velocity, does it have a constant velocity?0030

It might be going at say, 10 m/s at this point, and at this point, and at this point, and at this point, but will the velocity remain the same?0040

Well, that does not quite make sense.0050

Because we have got something that is going around in a circle, that means at this point that is actually moving something like this, and at this point it is moving something like this, and at this point it is moving something like this, so it is actually changing as it goes around.0051

Speed remains the same, but its velocity actually changes.0064

Otherwise, if its velocity were not changing, it would just continue to go off in a straight line.0067

It would not be able to make a circle, it would go off in a straight line if it did not have a changing velocity.0071

So, its velocity cannot be constant even though speed is constant.0077

What exactly is that change in 'v'?0081

We do not know quite yet what the change in v is precisely, but let us consider two opposite cases.0084

What about the string has the rock at the very top, and the string has the rock at the very bottom?0090

If you have ever swung something around by its end and let go at a certain point, like a slinky or a yoyo, and you are spinning it around in a circle and let go (like here), you might notice that it does not go off like this, it goes off like this.0099

That is because, as it curves around the circle, for it to be moving in that circle at that moment in time, it has to be going off directly this way.0118

At the bottom it has to be going off directly this way.0126

If you cut the string at that specific moment, the rock would fly off in a tangential path, a tangent is something that barely brushes the edge and goes off straight.0131

It is parallel to the curve at that one point.0143

The instantaneous velocity is the tangent at that point on the circle.0146

Wherever it is, it is going to be tangential.0151

What about if we look at a bunch of really close positions?0155

If we looked at a rock moving just a little bit each time, what is going to happen then is that we are going to have, is these little lines are only going to change by a bit each time.0158

So they are only sort of like, tick down only a teensy bit every time as they move their way around the circle.0168

What does that mean f we are doing that?0174

With each little step forward, the instantaneous velocity, (the instantaneous velocity is this part right here, that moment if we were to take a freeze frame what would its velocity be),0179

the instantaneous velocity has to be tugged down a bit with each one of these freeze frames.0190

Otherwise it is going to move off in a straight line, it is just going to turtle off away from the circle.0194

So to keep it in a circle, we have to have something pulling it in.0199

What do we have pulling it in?0202

We have got the string pulling it in.0203

So we are pulling it in with the string.0205

The string is going to keep it tangential, keep the velocity tangential by giving us an acceleration pulling directly in.0208

So we need something to pull this velocity directly in to the circle by just a little bit each time.0214

Wherever we go, we have an acceleration pulling in to keep that velocity tangential.0220

So velocity always tangential, and acceleration directly in for us to be able to maintain the circle.0227

What exactly would be the size or the magnitude of the acceleration, the size of a is the same as the magnitude of a.0234

The magnitude is going to depend on v.0245

If we have got a circle, and something is moving around very very quickly, we are going to need a very fast, very large acceleration to pull that in, to keep it in a circle continuously.0247

On the other hand, if we have got something that is making a very slow circle, we do not need a very fast acceleration at all.0258

We can just have something to pull, tug lightly to be able to keep it in a circle because it is moving so slowly.0266

The magnitude of a very clearly depends on how fast the object is traveling.0271

High speed require a big acceleration to be able to keep it in the circle.0276

Also, the radius is going to have an effect.0279

Think about this: You have two circles, one like this, and one like this.0282

At constant velocity, this acceleration is going to have to be able to pull a lot harder to be a able to keep it in the circle.0287

This one, it has got all this time.0295

It has got his time because it takes so much longer to make its way around the circle.0296

In the time it takes for this object with constant velocity this far, this one will manage to wrap its whole way around the circle.0301

With this one, it has got the time, it can take its time pulling that thing in, so the acceleration does not have to be as large.0307

That reasoning which we just talked about brings us to this formula.0314

We cannot derive it explicitly because that takes some calculus, and we do not have that yet.0321

But we can at least understand intuitively why this comes about.0324

Your acceleration, and you do not have the precise acceleration because the acceleration will always be changing, remember, the acceleration always points in.0328

It pulls in to the circle.0336

So, that reasoning leads us to this formula.0338

The magnitude of the acceleration = (speed)2/radius, which lets us have an understanding that the velocity has an effect, a larger velocity is going to cause a large acceleration, and a larger radius is going t o cause a smaller acceleration.0341

That gives us the centripetal acceleration.0359

Centripetal means 'to the centre', so centripetal acceleration is based off this, this formula right here.0362

It is an important formula for all things in uniform circular motion.0368

What about a revolution, what does it mean to make a revolution?0371

A revolution is really simple, it is just the time that it takes for an object to make its way one time around the circle.0376

A 360 degree turn is a single revolution of an object or if you have gotten into trigonometry, in terms of radians it would be 2 π radians. (2×π)0384

We are going to be using degrees in this course for most part, but 360 degrees or 2 π radians, these are all names for the same thing, which is just a single circle.0395

A revolution is complete when a point on the edge has made all the way around the circle.0411

For this point, for it to make all the way around the circle, what does that mean?0415

That means it has managed to travel the entire distance of this circle.0419

We know its speed, we know what the distance on a circle is, we know how long the track is, it is 2 π times the radius (2 π r), or π times diameter, so distance/speed is going to give us the time that it took.0424

Time for a revolution = circumference / speed = (2 π r) / speed0446

Let us take some examples.0459

We have got a rock, twirled around at 8 m/s on a rope of length 1 m .0462

What is the rock's acceleration?0478

We just use our formula, magnitude of the acceleration = (speed)2 / (radius of the circle) = (82) / 1 = 64 m/s/s , is the acceleration.0480

That is the magnitude of the acceleration, remember, depending on where we are, the acceleration is going to be constantly be changing, it is always going to be pulling in.0505

We know that magnitude is going to be 64 m/s/s .0512

The specific components of that vector will change, we could solve that if we knew what angle it was at, we could solve for what it was.0516

But we know it is always going to 64 m/s/s pointing to the centre of the circle, from the point that we are looking at.0523

How long will it take the object to complete one revolution?0530

We know what the velocity is, we have the information to figure out what the circumference is, so from here we just use our formula.0532

So, the time for a revolution = (2 π r) / (speed) = (2 π × 1m) / (8 m/s) = 0.79 seconds, it is how long it will take to complete a revolution.0540

Here is another example, we got a car driving at a constant speed of 20 m/s .0560

It is driving on some road, and it is currently driving to the East.0566

It is going to go through a turn , and it is going to come out going to the North.0569

If the car is driving at a constant speed throughout the turn, and it goes through a quarter circle turn, that has a radius of 150 m, (part of an imaginary circle if we were to complete this quarter circle),0576

...so this is a really big slow turn, what will be the acceleration that the car will experience during the turn?0590

It is going to experience it as soon as it enters the circle, and it is always going to be pointing in, to the middle.0597

What will that be?, use our formula.0613

The size of the acceleration, the magnitude = (speed)2 / radius = (20)2 / (150m) , it is a good idea to keep your units in it, because it gives us a chance to double check, if units are wrong in the end, you missed something!,0615

Sometimes, when the problems are easier, when you know for sure what you are doing, it is OK to omit it, but in general you are encouraged to keep your units because it helps you to understand what you are doing with your work.0655

So, (20 m/s)2 / (150 m) = (400 m2/s2) / 150 m = 400/150 = 2.67 m/s/s .0674

m/s2 is also the normal, acceptable form for acceleration, I just prefer m/s/s because it gives you a better idea of what is happening.0714

Now we have got our answer, 2.67 m/s/s is the amount that the car is being pulled in to the centre of the turn at all times.0720

Keep in mind, that is a pretty fair acceleration, if gravity = 9.8 m/s/s, 2.67 m/s/s/ is a pretty considerable amount.0729

This person is pulling about more than a quarter of a 'g' is pulling them in, quarter of a 'g' being quarter of a 'g' acceleration, 'g' being 9.8 m/s/s.0740

So, that is a fair amount of acceleration being pulled in, which is why when you are turning in a car you experience that feeling of being pulled somewhere.0750

We will talk about later on, you do not feel like you are being pulled in to the centre of the car, you feel like you are being pulled in to the centre of the circle.0757

If you feel like you are being pulled out, that is the difference between centripetal and centrifugal, and we will explain why you will have that experience.0766

But, now you have an understanding of why there is that acceleration taking place , and a little bit later in the course, when we get to talking about uniform circular motion and force, you will get the chance to understand why it is that feels like you are being pulled against the car.0777

You are being pushed up against the door, but you will understand why that is later.0785

Example 3, final example.0789

We have got a US quarter on a turn table.0793

The quarter is spinning at 1776 rpm, which is revolutions per minute.0795

It has a diameter of 24.26 mm.0804

What will be the speed of a point on the edge of the quarter in m/s?0813

To get this in m/s, we need to get everything in S.I. units.0818

Right now, none of our stuff is in S.I. units.0821

We need to work towards that.0823

Starting off, 1776 rpm, what would that be if we were to get this in seconds?0825

We divide that by 60, 1776/60 =29.6 rev. per second.0833

But that is not equal to 'T'.0846

T is equal to that number flipped, because T = 1/29.6 = number of seconds to the revolution.0848

So, it takes (1/29.6) seconds per revolution.0861

It makes a lot of sense, if we had 29.6 revolutions in a second, then if we want to see how many seconds it takes to do that, we are going to have to flip it, take the reciprocal, 1/29.6 = 0.0338 s.0868

That is how long it takes to give us a single revolution.0885

What is the diameter, if we want that in S.I. units?0888

Diameter = 24.26 mm = 0.02426 m , (move once to cm, another to dm, another to m.)0893

Now we have got the information we need to solve.0912

T = (diameter × π) / speed = D × π / speed , we do not know speed, but we do know T and D and π is just a constant, so we can solve this now.0914

Remember that velocity will always be tangential to the point we are looking at, speed is the only thing we can solve that will be truly constant.0931

speed = (0.02426 m × π) / 0.0338 = 2.255 m/s, is the speed that a point on the edge is moving at. (Once again, I encourage you to keep the units.)0944

And that tells us the answer.0987

Hope you enjoyed this, hope you learned something.0988

See you later when you come back to educator.com for the next lesson.0990