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Vincent Selhorst-Jones

Vincent Selhorst-Jones

Math Review

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 (38)

0 answers

Post by Edward Han on August 14, 2017

you video could not load

2 answers

Last reply by: Professor Selhorst-Jones
Tue Oct 3, 2017 10:54 PM

Post by Kevin Wang on March 17, 2017

Just saying, 3*(4,5) is actually (12,15), and not (12,5)

1 answer

Last reply by: Professor Selhorst-Jones
Thu Aug 18, 2016 3:34 PM

Post by Claire yang on August 18, 2016

Do vectors continue forever?

1 answer

Last reply by: Professor Selhorst-Jones
Sun Oct 11, 2015 6:36 PM

Post by Peter Ke on October 10, 2015

Hi Professor I was wondering what math background do you need for THIS course?
Because I'm still new to this lecture so I want to know the topic you need to know for math. Thx!

2 answers

Last reply by: francisco marrero
Wed Aug 19, 2015 9:58 AM

Post by francisco marrero on July 26, 2015

Hello Professor: I am forty nine years old and would like to learn physics, as I was always intimidated by it in high school and so gave up.  Do you recommend that I study all of the other math courses, such as algebra and trigonometry on educator.com, in order to understand physics very well.  Please let me know your advice.  Thank you very much for your time.

2 answers

Last reply by: Anna Ha
Sun May 31, 2015 8:31 PM

Post by Anna Ha on May 31, 2015

Hi Professor Selhorst-Jones,

Thank you for your great lectures! I'm finding them very helpful :)

When rounding sig figs with the number 5 at the end, in chemistry I was taught to round to the nearest even, and in physics class I was taught to just round up. But considering science as a whole.. shouldn't the rule be all the same? Which one do you think is correct?

I just wanted to check when calculations are being continued, we have to bring the whole value down. not the rounded off value right?

Thank you!

1 answer

Last reply by: Professor Selhorst-Jones
Thu Apr 30, 2015 10:19 AM

Post by enya zh on April 29, 2015

In "How Significant Figures Interact" you said that we must use the sig fig of the less accurate figure for our answer.In example 2, the question was 6.083*2.1, but you rounded it to 13. Since 2.1 has 2 sig figs, shouldn't the final answer be 12.8?

1 answer

Last reply by: Professor Selhorst-Jones
Sun Oct 5, 2014 11:51 AM

Post by Zhengpei Luo on September 24, 2014

What's the essential difference between your course and the other physics course?

2 answers

Last reply by: Lexlyn Alexander
Thu Oct 23, 2014 4:36 PM

Post by adnan alsabty on July 19, 2014

Why in scalar example 3*(4,5) is equal to (12,5). Why is not (12,15) just like -2*(4,5) is equal to (-8,-10)?????

2 answers

Last reply by: Isaac Martinez
Wed Aug 31, 2016 3:49 PM

Post by justin Gwon on June 19, 2014

In the last segment of the lecture, I don't know why 5sin(36.87) is 3 ... also 5con(36.87) is 4.

1 answer

Last reply by: Professor Selhorst-Jones
Sat Jan 4, 2014 10:25 AM

Post by Karlo Wiley on January 3, 2014

In the last segment of the lecture, I'm not sure if the angle is 36.87 because I would plug in 5 * sin (36.87) and it would give me -3.686658423 and i also plugged in 5 * cos (36.87) and I got 3.377654463... It should have 3 and 4... so I did remember in the lecture there is a segment that you can find the angle if you know your sides... sin^-1 * b/c would give you the angle... so if c = 5 and b (y in the slide) = 3 then sin^-1 * 3/5 = 0.6435011088... So with this new angle i plugged in the numbers again in 5 * sin (0.6435011088) and it gave me 3 and I also plugged in 5 * cos (0.6435011088) and that gave me 4 which was your answer and checks out with pythagoreans theory... Sooo my question is am I right? honestly I still haven't taken trigonometry or physics, I'm in tenth grade taking geometry and biology.. I'm just interested in this subject so I don't know much at all about trigonometry or physics in general...

3 answers

Last reply by: Professor Selhorst-Jones
Mon Aug 26, 2013 11:23 PM

Post by Jeremy Canaday on August 16, 2013

i didn't know that tensor calculus x vector analysis/differential equations were prerequisites to high school physics.

2 answers

Last reply by: James Pelezo
Sun Mar 24, 2013 3:12 PM

Post by Al Khurasani on October 8, 2012

Shouldn't the SI unit of Volume be "Cubic Metre" ?

"In the International System of Units (SI), the standard unit of volume is the cubic metre (m3)"
[WikiPedia]

4 answers

Last reply by: Robert Mills
Thu Oct 3, 2013 12:58 PM

Post by Nigel Hessing on June 2, 2012

I don't understand why is 3 x (4, 5) = 12,5 shouldn't it be 12, 15?

Related Articles:

Math Review

  • Science is almost always done in the metric (SI) system. This course will only use this system of units.
  • Scientific Notation: We can condense numbers that would require many zeros to write by using powers of 10. For example: 0.027 = 2.7·10−2 and 4700 = 4.7 ·103.
  • Significant Figures: How many digits we have in a number tells us how much we can "trust" the number. Just because your calculator gives you a lot of digits does not mean you can trust it more than the data you started off with.
  • Trigonometry: If you don't remember trigonometry, go look up a quick refresher on the basics. We won't need very complex trig in this course, but we use the core ideas a lot.
  • Vectors: A vector is a way to show both length and direction. Equivalently, we can name a vector by naming its components.
  • When working with vectors, we add them together component-wise.
  • If you multiply a scalar (a single number) with a vector, it just multiplies each component of the vector. [Notice that there is no definition for multiplying two vectors together. It wouldn't make sense!]
  • We can find the length of a vector by using the Pythagorean Theorem. If v = (vx , vy), then its length is | v | = √{vx 2 + vy 2}.

Math Review

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
  • The Metric System 0:26
    • Distance, Mass, Volume, and Time
  • Scientific Notation 1:40
    • Examples: 47,000,000,000 and 0.00000002
  • Significant Figures 3:18
    • Significant Figures Overview
    • Properties of Significant Figures
    • How Significant Figures Interact
  • Trigonometry Review 8:57
    • Pythagorean Theorem, sine, cosine, and tangent
  • Inverse Trigonometric Functions 9:48
    • Inverse Trigonometric Functions
  • Vectors 10:44
    • Vectors
  • Scalars 12:10
    • Scalars
  • Breaking a Vector into Components 13:17
    • Breaking a Vector into Components
  • Length of a Vector 13:58
    • Length of a Vector
    • Relationship Between Length, Angle, and Coordinates

Transcription: Math Review

Hi, welcome to educator.com. This is the beginning of Physics.0000

We are going to do first up, before we get into the Physics, we are going to do a quick Math review.0004

So, even if you feel really strong at Maths, just make sure to real quickly skin through the section, because we want to make sure you understand all these concepts clearly,0008

because they might come up in this course, and they might also come up in whatever course you are taking.0015

This is a supplement to your other Physics courses.0020

So, it is a good idea to make sure you have definitely got the background and the skills inside of this Math review.0021

Let's get started: First off, the metric system. Also, called the S.I. units, which is from the French System Internationale, which is the people who first created the metric system and first propagated its use.0026

So, the metric system is created in 1800's to, actually may be the sub 1800's, I should know that, anyway, I am sorry, so, anyway the metric system was created to standardize the measurements and it has done a great job at that.0038

Almost all the countries in the world, the exception, the United States of America are completely standardized on it, and even in the United States, everybody in Science, in Physics, they all use the metric system.0052

The metric system is great, and it's the way to do things.0063

So, the basic units we work with in Physics are, distance, just the metre denoted by a small 'm' mass, which is the kilogram, denoted by 'kg'.0066

I would like to point out it's the kilogram, so it's not actually the gram that we consider our basic unit of mass, we consider the kilogram our basic unit of mass, just an interesting thing to point out.0076

The volume, volume which comes in litres denoted by a small 'l' or sometimes a 'cursive l', if it gets confused as a '1' sometimes, and finally time, the second, which is denoted by 's'.0085

Scientific notation.0101

What if we had a problem involving the number say 47 billion or 0.00000002?0103

If you had to write down that number, more than two or three times, I think you would be unhappy, and I think you should be unhappy.0111

That is a lot of times that you have to write a number.0117

That many digits is just a pain, and you are not really putting in much information as you feels like in those zeros.0120

So we wouldn't want to write that all those times.0124

So, how else could we write it. The trick here is scientific notation. The idea here is, that you can convert it by using powers of ten.0126

So, 47000000000 is the same as 47 × 109, because we got 1,2,3..4,5,6..7,8,9 , so times ten to the 9th, and if we wanted to have it so we only had one digit at the very front, we could push it over for one more and we could have 4.7 times ten to the tenth.0135

Same idea if we want to move a digit up, we go back 1,2,3..4,5,6,7,8 spaces, so that would be 2 × 10-8.0154

We are able to compact information this way because, ten to the one is equal to 10, so ten to the two is equal to hundred and so on and so forth.0165

We can also go negative, so ten to the negative one is 0.1, so ten to the negative two is 0.01.0171

This allows us to slide digits around, so we don't have to write really really long numbers, because when we are dealing with say number of atoms or the charge of an electron or the distance from here to the sun, we are going to be dealing with very large and very small numbers depending.0177

So Physics deals some extreme values of numbers, and we don't want to get cramps, because we are going to write 30 zeroes every time a number comes up.0191

Significant figures.0199

Also called sig figs. Significant figures are a way of showing, how precise our information is.0200

Since all information are susceptible to some amount of error, even if you look at a really fine ruler, it's hard tell what is the difference between one hundredth of a millimetre to the left or the right.0206

There is always some amount where it's a judgment call, and you might be slightly wrong.0216

There is always uncertainty in every measurement, there is always some little bit of possible error.0220

So significant figures expresses how certain we are with the measurement, or what the uncertainty in the measurement is.0226

It says how much we can trust our info.0232

Significant figures give us a way in letting us know how much we should rely on the information we have.0236

Which figures are significant? That requires a little thought.0241

Significant digit is any of the following: Any digit that is not a zero.0246

The zeroes between non-zero digits, and zeroes to the right of significant digits.0250

The only digits that are not significant are the digits to the left of significant digits, which makes a lot of sense.0255

If I wrote two, and if I wrote a bunch of zeroes in front of it, well, that is the exact same thing.0260

There is no way to measure the difference between two and a two with a bunch of zeroes in front of it.0266

It means the exact same thing, and there is no way you can measure the difference, and there is no significance in all of these zeroes.0270

We would not care about them, knock them out.0277

This would only have a significant digit of 'one', one significant digit, one sig fig.0279

Let's try some other examples: Our first one, we got 1,2,3,4.0284

So this one would have four significant figures.0289

This one has 1,2,3, what about that times 10 to the fourth.0292

Well, that times ten to fourth if we would have 10 to the fourth, well that would be, 1-0-3-0-0.0297

So, 10300.0307

But if we had 10300, what we would be saying is, we have precisely measured 10300.0309

Precisely measured 10300 metres.0315

But what we really did, we only managed to precisely measure the first 10300, but it might be up or down a little bit.0317

It could be 10349, or 10251.0325

It could be something that is close to what we could round, we are only sure up to that 10300.0330

So that is the point of the sig fig here.0335

So, that scientific notation also gives us the ability to show the information that we have measured for sure, but there might be some hash to just the zero.0338

So let us not multiply out to say the scientific notation and then find the sig figures, you find the sig figs before you multiply the scientific notation.0347

So this one would have three significant digits.0355

Here we have 1,2 and all of these are zeroes, so it just has two significant digits.0358

Here we have 1,2,3,4,5, so it has five significant digits because these ones don't count, but these ones do count because they are to the right0365

It means that you have measured something precisely.0375

There is a difference if I say, I weigh about 75 kilos. I weigh about 75 kilograms, or if I say I weigh 75.000 kilograms.0377

That means I have managed to get a really precise reading.0388

I am down to within a grams certainty of my weight.0391

So, it is a very precise reading of my weight, very precise reading of my mass.0394

So, that 000 at the end matters, but in the front once again there is no extra information there.0398

Finally, if we had 4.700, we would have 1,2,3,4.0404

We count from the right end, or the left in this case because there is no zeroes to the left.0410

So, we count zeroes on the right, here we would have four.0415

How do significant figures interact with one another?0420

If you add, subtract, multiply or divide numbers, we have to pay attention to how the significant figures interact.0423

The resulting numbers are only going to have as many significant figures as the lesser of the two numbers of significant figures.0429

The smallest number of sig figs in the number you start with becomes the number of sig figs the result has. And this makes sense.0434

If I know I weigh precisely, I have the mass of 75.000 kilograms but then I get on a boat with somebody else who weigh about 80 kilograms, I can't say, together we weigh precisely 80 plus 75, precisely 155.000.0440

I cannot do that because, I don't know, maybe they weigh 83 kilograms.0458

They were unsure when they told me their mass.0462

So, I cannot be certain of that.0464

It means we have to go to the least significant digits we have, which is two, which is those two digits of 80 kilograms.0466

We only got two significant figures.0475

That is the case, we wind up actually having two, round up because we have 155, it could become 160.0479

Here is some great examples: We have two 2 kilograms here, and 0.0803 kilograms here.0487

Mathematically if we add them together, we get the number 2.0803 kilograms.0492

But, this guy has one significant figure.0497

This guy has 1,2, THREE significant figures.0500

It does not matter, he is the smaller one, so we have to cut off after just one, and we round here, we wind up getting just two kilograms, because we only had that significant figure of 2 kilograms in the first one.0503

Over here, we know that we are going 6.083 metre per second so we got 1,2,3,FOUR.0516

Here we got 1,TWO.0523

So just two significant figures over here. It is the smaller one, it wins out.0524

So we have to round to here. This guy will manage to cause it to round up, and we will wind up going to 13 metres.0529

Just a quick trig review, if you do not remember your trig, that is going to really matter with time.0539

So brush up on that.0541

Pythagorean theorem, a2 + b2, the two smaller sides of a right triangle, equals the other side, the hypotenuse squared.0544

a2 + b2 = c2.0553

Then we have also got the trigonometric functions to relate those sides together.0555

The sine of θ is equal to the side opposite over the hypotenuse.0558

So, this would equal 'b' over 'c'.0563

Cosine of θ is equal to the side adjacent over the hypotenuse.0566

So this would be 'a' over 'c', and finally tan θ is equal to the side opposite divided by the side adjacent.0573

So this would be 'b' over 'a'.0584

Definitely important thing to remember.0587

Inverse trigonometric functions. What if we know what the sides of the triangle is, and we want to find the angle.0590

Then we use an inverse trigonometric function.0594

The arcsine or the sin-1, however you want to say it, because it is measuring what is the arc of that, right?0597

The arc that goes along with a given ratio. arcsine of sin θ equals θ.0603

Allows us to reverse it.0611

If we look this up, if we use a calculator, it gives us an answer. If we look it up in a big book, with just a look up table, it gives us an answer.0612

Same basic idea.0619

We are able to figure out all of those ratios beforehand through clever thought, and then at any time if you want to figure out what the angles are being, we just look at the book we created, look at the table, look at the calculator.0621

If sin θ = b/c, we could find θ with sin-1.0631

So θ would be sin-1(b/c), the arcsin(b/c).0635

We plug in numbers, and we get what the angle is.0641

Vectors: Vectors are a way to think about movement.0645

In another sense, they are a way to simultaneously consider the distance and the angle.0647

'v' here has gone some distance and it is up some angle.0651

'u' has managed to go some distance and it is up some angle.0657

But alternatively we could think of it as 'v' went over to the right by 4 and it went up by 5.0660

'u' went to the left, so it went negative two (-2), and it went up by 2.0668

That is the idea of a vector. We can expand this. We can do a vector addition.0675

If we got two vectors we can add them, we can put them head to tail, numerically you will add their components.0679

So, you have got 'v' and you have got 'u', v+u is just the sum of the numbers involved.0684

This one is 4 and -2. 4 and -2 becomes 2.0690

5+2 becomes 7.0695

There you go. As simple as that.0701

Subtraction is just adding by the negative version of the number.0703

If you want to know what the negative version of 'u' was, -u, we just put a negative sign in front of what it was originally.0707

We apply that in, we get (2,-2). We add 'v' to the negative version of 'u'.0713

2 plus, it was 4 before, we get 6.0720

-2 plus, it was 5 before, we get 3. Simple as that.0725

Scalar: Vector is a distance and a direction.0731

Scalars in a way, are just a number. It is a way to scale a vector.0735

It is a multiplication thing. You scale the vector, you change how much it grows or shrinks.0740

You can the length, and even flip the direction of a vector by using scalar.0745

You just multiply each element of a vector with it. Vectors are multi-dimensional, scalars are just one dimensional.0750

If s=3, then if we had 'v' as (4,5), what we have been using so far, then 3 would just be 1,...2, ...3 out.0755

So, 'sv' is just 3 v's stacked on top of one another.0767

Makes sense. v+v+v. 3 × v.0771

If we had -2, then we have to flip to the negative version. Here is where -v would show up.0775

We stack it twice, and we have got -2v.0780

If we want to do it numerically, we just wind up multiplying it by each component involved.0783

3 times (4,5) becomes (12,15), -2 times (4,5) becomes (-8,-10).0790

If we want to break a vector in to its components, we just do it.0798

We know what each of the components are, so we can see how much should we move in the 'x', how much should we move in the 'y'.0801

So, vx and vy.0807

If v = (4,5), then we see that the x side must be length 4, and the y side must be length 5.0809

Also, if we wanted to, we can say, v = (4,5), which is the same thing as (4,0) plus (0,5), which is basically what we see right here.0817

We added here, to here, and we get to the same spot.0830

If we want to find the length of a vector, we use the Pythagorean theorem.0839

We know what those sides are, because we know what the x-component is, we know what the y-component is.0842

How does the Pythagorean theorem work?0846

Square root of the two smaller sides, 42 + 52 equals the square of the other side.0850

We call it the absolute value, the magnitude, that is how we denote it.0860

In this case, square root of (16+25), does not wind up coming out to be a nice round number, we get the square root of 41, that is as simple as it is going to be.0864

But that is what its length is. If you want, you can change it into decimal using a calculator.0879

There is a relationship between length, angle and coordinates.0886

In general, if we wanted to know what arc, what it was if we knew that our vector had a length 5 and an angle 0f 36.87 degrees above the horizontal, what would be the vector, let's just make a triangle.0889

Our angle here is 36.87 degrees, and this here is 5, this look like a perfect time to use sin θ.0904

This side over here, let's call it 'y'.0916

So, sin θ equals y/5.0918

We multiply both sides by 5, so we get 5sin θ equals y.0927

We plug in what that θ was, 5sin(36.87).0932

Punch that into a calculator, multiply by 5, and we are going to wind up getting 3.0938

So, that side is equal to 3. Same basic idea over here.0944

We call this side x, and any time we are doing this, it is going to be the hypotenuse divided by the other.0948

Cosine equals adjacent divided by hypotenuse.0954

So, any time we want to know the adjacent side, it is just going to be hypotenuse times cosine of the angle.0957

Or if we want to know the opposite side, it is going to be hypotenuse times sine of angle. Simple as that.0960

'x' is going to be 5cosine(36.87),0966

Toss that into a calculator, and we get 4.0975

The vector 'v' would be its two components put together, (4,3).0977

If you want to check that out, 42 + 32 = 25, which is the square of 5.0985

Checks out by the Pythagorean theorem. We got the answer.0991

That is basically all the Math that we got to have under our belt if we want to get started in this Physics course.0994

Hope all that made sense. If it did not make sense, go back, check some of the stuff that you do not remember from trigonometry.0999

Just get back up to speak, because we are going to wind up using a lot of this, especially when we are talking about multi-dimensional stuff.1003

Alright, see you at the next...1010

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