Back To Course

MCAT Prep: Help and Review90 chapters | 1015 lessons | 73 flashcard sets

Are you a student or a teacher?

Try Study.com, risk-free

As a member, you'll also get unlimited access to over 75,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Try it risk-freeWhat teachers are saying about Study.com

Already registered? Login here for access

Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Laura Pennington*

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

Angular velocity applies to objects that move along a circular path. We will explore the definition of angular velocity and learn three different formulas we can use to calculate this type of velocity.

Before we can get to angular velocity, we will first review linear velocity. **Linear velocity** applies to an object or particle that is moving in a straight line. It is the rate of change of the object's position with respect to time.

One of the most common examples of linear velocity is your speed when you are driving down the road. Your speedometer gives your speed, or rate, in miles per hour. This is the rate of change of your position with respect to time, in other words, your speed is your linear velocity.

Linear velocity can be calculated using the formula *v* = *s* / *t*, where *v* = linear velocity, *s* = distance traveled, and *t* = time it takes to travel distance. For example, if I drove 120 miles in 2 hours, then to calculate my linear velocity, I'd plug *s* = 120 miles, and *t* = 2 hours into my linear velocity formula to get *v* = 120 / 2 = 60 miles per hour.

We have one more thing to review before getting to angular velocity, and that is radians. When we deal with angular velocity, we use the radian measure of an angle, so it is important that we are familiar with radian measure. The technical definition of **radian measure** is the length of the arc subtended by the angle, divided by the radius of the circle the angle is a part of, where subtended means to be opposite of the angle and to extend from one point on the circle to the other, both marked off by the angle. This tells us that an angle theta = *s* / *r* radians, where *s* = length of the arc corresponding to theta, and *r* = radius of the circle theta is a part of.

Since most of us are comfortable with the degree measurement of angles, it is convenient that we can easily convert degree measure to radian measure by multiplying the degree measure by pi / 180. For example, a 45 degree angle has a radian measure 45 (pi / 180), which is equal to pi / 4 radians.

**Angular velocity** is less common than linear velocity, because it only applies to objects that are moving along a circular path. For instance, a racecar on a circular track, a roulette ball on a roulette wheel, or a Ferris wheel, all have an angular velocity.

The angular velocity of an object is the object's angular displacement with respect to time. When an object is traveling along a circular path, the central angle corresponding to the object's position on the circle is changing. The angular velocity, represented by *w*, is the rate of change of this angle with respect to time.

For example, a Ferris wheel may be rotating pi / 6 radians every minute. Therefore, the Ferris wheel's angular velocity would be pi / 6 radians per minute.

There are **three formulas** we can use to find angular velocity.

**Option 1**

The first comes straight from the definition. Angular velocity is the rate of change of the position angle of an object with respect to time, so *w* = theta / *t*, where *w* = angular velocity, theta = position angle, and *t* = time.

For example, if a race car is traveling along a circular track, and it travels 1 lap, or 2pi radians in 4 minutes, then we can find the cars angular velocity by plugging theta = 2pi radians and *t* = 4 minutes into our formula to get *w* = 2pi / 4 = pi / 2 radians per minute. The car's angular velocity is pi / 2 radians per minute.

**Option 2**

To get our second formula for angular velocity, we recognize that theta is given in radians, and the definition of radian measure gives theta = *s* / *r*. Thus, we can plug theta = *s* / *r* into our first angular velocity formula. This gives *w* = (*s* / *r*) / *t*. Simplifying gives *w* = *s* / (*r**t*), where *s* = arc length, *r* = radius, and *t* = time.

For example, if a roulette wheel has a radius of 10 inches, and the ball travels 7 inches along its circular path in 2 seconds, then we can find the ball's angular velocity by plugging *s* = 7 inches, *r* = 10 inches, and *t* = 2 seconds into *w* = *s* / (*r**t*) to get *w* = 7 / (10*2) = 0.35 radians per second. The ball's angular velocity is 0.35 radians per second.

**Option 3**

The last formula comes from recognizing that we can rewrite our second angular velocity formula as *w* = *s* / (*r**t*) = (*s* / *t*) (1 / *r*). Recall that *s* / *t* is our linear velocity, so we can rewrite this formula as *w* = *v* (1 / *r*) = *v* / *r*, where *v* = linear velocity and *r* = radius of the circle.

For example, if a race car is traveling along a circular track at 110 miles per hour, and the radius of the race track is 0.2 miles, then we can find the angular velocity of the car by plugging *v* = 110 miles per hour and *r* = 0.2 miles into our formula to get *w* = 110 / 0.2 = 550 radians per hour.

We've reviewed **linear velocity** ,the rate of change of the position of an object traveling on a straight line with respect to time and **radian measure** of an angle (theta = *s* / *r*, where *s* = arc length and *r* = radius). We've seen that both of these play an important role in angular velocity. **Angular velocity** is the angular displacement over time of an object or particle that is moving along a circular path. We have three formulas we use to find angular velocity, and they are displayed on screen.

These formulas and definitions have equipped us with everything we need to work with angular velocity efficiently and effectively.

To unlock this lesson you must be a Study.com Member.

Create your account

Are you a student or a teacher?

Already a member? Log In

BackWhat teachers are saying about Study.com

Already registered? Login here for access

Did you know… We have over 160 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

You are viewing lesson
Lesson
10 in chapter 14 of the course:

Back To Course

MCAT Prep: Help and Review90 chapters | 1015 lessons | 73 flashcard sets

- Implications of Mechanics on Objects 6:53
- Newton's First Law of Motion: Examples of the Effect of Force on Motion 8:25
- Newton's Second Law of Motion: The Relationship Between Force and Acceleration 8:04
- Newton's Third Law of Motion: Examples of the Relationship Between Two Forces 4:24
- Newton's Laws and Weight, Mass & Gravity 8:14
- Friction: Definition and Types 4:15
- Inclined Planes in Physics: Definition, Facts, and Examples 6:56
- Pulleys: Basic Mechanics 7:25
- Mass and Weight: Differences and Calculations 5:44
- Angular Velocity: Definition, Formula & Examples 7:01
- Linear Velocity: Definition & Formula 5:28
- Understanding the Center of Mass & Center of Gravity 4:42
- Newton's Law of Gravitation: Definition & Examples 6:35
- Uniform Circular Motion: Definition & Mathematics 7:00
- The Centripetal Force Requirement: Definition, Examples & Problems
- Go to Force, Motion & Gravitation for the MCAT: Help and Review

- Go to Memory

- Go to Emotion

- Go to Stress

- AFOQT Information Guide
- ACT Information Guide
- Computer Science 335: Mobile Forensics
- Electricity, Physics & Engineering Lesson Plans
- Teaching Economics Lesson Plans
- FTCE Middle Grades Math: Connecting Math Concepts
- Social Justice Goals in Social Work
- Developmental Abnormalities
- Overview of Human Growth & Development
- ACT Informational Resources
- AFOQT Prep Product Comparison
- ACT Prep Product Comparison
- CGAP Prep Product Comparison
- CPCE Prep Product Comparison
- CCXP Prep Product Comparison
- CNE Prep Product Comparison
- IAAP CAP Prep Product Comparison

- Cognition: Theory, Overview
- History of Sparta
- Realistic vs Optimistic Thinking
- How Language Reflects Culture & Affects Meaning
- Overview of Data Types in Java
- Managing Keys in Mobile Ad-Hoc Networks
- Using OpenStack for Building & Managing Clouds
- Quiz & Worksheet - Frontalis Muscle
- Octopus Diet: Quiz & Worksheet for Kids
- Logical Thinking & Reasoning Queries: Quiz & Worksheet for Kids
- Quiz & Worksheet - Fezziwig in A Christmas Carol
- Analytical & Non-Euclidean Geometry Flashcards
- Flashcards - Measurement & Experimental Design
- Algebra 2 Worksheets
- Pronoun Worksheets

- Classroom Management Strategies for Teachers
- High School Physical Science: Tutoring Solution
- Political Science 101: Intro to Political Science
- SAT Prep: Tutoring Solution
- History of the Vietnam War: Certificate Program
- The Internal Structure of the Earth: Homeschool Curriculum
- Geometry Basics: Homeschool Curriculum
- Quiz & Worksheet - How UK Policy is Affected By Class & Race
- Quiz & Worksheet - Chance & Dadaism
- Quiz & Worksheet - Types of Stramenopiles
- Quiz & Worksheet - Straight-Line Depreciation
- Quiz & Worksheet - Adrenergic Receptor Types

- What Is Residual Income? - Definition, Model & Formula
- Nobel Prize in Economics: Winners & Contributions
- Best Online College English Courses
- How to Pass the California Real Estate Exam
- Brain Breaks for Kids in the Classroom
- How to Stop Procrastinating
- Expelled from School: Next Steps
- English Conversation Topics
- Critical Thinking Games for Kids
- What Are the NGSS Cross Cutting Concepts?
- Timeline Lesson Plan
- Next Generation Science Standards for Kindergarten

- Tech and Engineering - Videos
- Tech and Engineering - Quizzes
- Tech and Engineering - Questions & Answers

Browse by subject