Back To Course

Physical Science: Help and Review19 chapters | 248 lessons

Watch short & fun videos
**
Start Your Free Trial Today
**

Start Your Free Trial To Continue Watching

As a member, you'll also get unlimited access to over 70,000 lessons in math, English, science, history, and more. Plus, get practice tests, quizzes, and personalized coaching to help you succeed.

Free 5-day trial
Your next lesson will play in
10 seconds

Lesson Transcript

Instructor:
*Erin Monagan*

Erin has been writing and editing for several years and has a degree in fiction writing.

If you need some practice on problems involving angular momentum, then this is the place you need to be! In this lesson, we'll work on conservation of momentum, rotating bodies and moments of inertia.

In linear momentum we use the equation *P = mv*, where *P* is the momentum, *m* is the mass in kilograms, and *v* is the velocity in meters per second. The angular momentum equivalent is:

Where *L* is angular momentum, *I* is the moment of inertia, and omega is the angular velocity. The angular velocity can be related to the linear velocity, *v*, if you know the radius, *r*, from the center of rotation by using the equation *w = v/r*. However, the moment of inertia for any object is determined by three factors: its mass, shape, and axis of rotation.

The moment of inertia *I* of a point mass moving in a circle of radius *r*:

The moment of inertia of a disc:

The moment of inertia of a thin rod about its center:

The moment of inertia of a thin rod about its end:

The easiest types of angular momentum problems are those that involve a **point mass**, or point particle rotating around a center of an axis. Examples of point mass problems can be anything from a ball on a string to planetary sized bodies. Using the linear momentum equation, and substituting in the moment of inertia of a rotating point mass, we get *L* = *mrv*. So, these problems depend on mass, radius, and linear velocity.

What is the angular momentum around the catcher of a baseball thrown at 40 m/s? The weight of the baseball is 145 kilograms and on a wild pitch the catcher has extended his arm 1.25 m from his center of rotation.

*L* = *mrv*

*L* = (.145 kg)(1.25 m)(40 m/s)

*L* = 7.25 kg/m2/s

A ball is rotating on a string 5ft from the end of a hollow pipe with a linear velocity of 10 ft/s. The string continues down the pipe to the other end. What would the new linear velocity of the ball be if you pulled the string 3 ft, thereby shortening the turning radius of the ball?

Since linear momentum is conserved between the two states (as long as we ignore friction, the weight of the string and the diameter of the pipe) the new angular momentum and old angular momentum are going to be equal.

*L*(old) = *L*(new)

*mrv*(old) = *mrv*(new)

*m*(5)(10) = *m*(5-3)(*v*)

The masses cancel out, leaving:

50 = 2*v*

*v* = 25 ft/s

Does the linear velocity of the Earth increase as it moves from its furthest distance away from the sun to its closest approach? Perihelion (when Earth is closest to the Sun) = 91.4 million miles and Aphelion (when Earth is farthest from the Sun) = 94.5 million miles.

Although it seems like a very different problem, we can use the very same approach as the earlier ball on the string problem.

*L*(slow) = *L*(fast)

*mrv*(slow) = *mrv*(fast)

*m*(94.5)(*v*) = *m*(91.4)(*v*)

The masses cancel out, meaning the percentage increase in velocity is determined only by the change in radii of perihelion and aphelion.

% velocity increase = (94.5 - 91.4) / 91.4 = 3.4 %

Cylinder problems end up being fairly similar to the point mass problems because the moment of inertia of a disc spinning about its center is half of a point mass rotating with the same radius. In equation form, the linear momentum of this type of system becomes:

*L* = *mrv*/2

Point A on the perimeter of a disc is moving with a velocity of 10 m/s. If two twin discs of the same material and thickness, but with no spin are placed on top of the first disc, what will be the final linear velocity of point A?

*L*(old) = *L*(new)

*mrv*/2 = *mrv*/2

But, what if the new mass is triple what the old mass was, and the old velocity was 10 m/s?

*mr*(10)/2 = 3*mrv*/2

We see that *m* and *r* both cancel out, leaving:

5 = 1.5(*v*)

*V* = 5/1.5 = 3.33 m/s.

Angular momentum problems all start out with this equation:

This equation reads as angular momentum equals the moment of inertia times omega, or the angular velocity.

The trick to solving angular momentum problems is to set up the equation using the correct rotation shape and axis of rotation.

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

Create
your account

Already a member? Log In

BackDid you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 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
18 in chapter 2 of the course:

Back To Course

Physical Science: Help and Review19 chapters | 248 lessons

- Work: Definition, Characteristics, and Examples 4:38
- Work Done by a Variable Force 7:10
- What is Energy? - Definition and Significance in Nature 9:40
- Kinetic Energy to Potential Energy: Relationship in Different Energy Types 5:59
- Power: Definition and Mathematics 5:24
- Linear Momentum: Definition, Equation, and Examples 4:58
- Work-Energy Theorem: Definition and Application 4:29
- First Law of Thermodynamics: Law of Conservation of Energy 7:42
- Second Law of Thermodynamics: Entropy and Systems 6:21
- What is Mechanical Energy? - Definition & Examples 4:29
- Conservation of Mechanical Energy 6:39
- What is Thermal Energy? - Definition & Examples 6:08
- What is Radiant Energy? - Definition & Examples 7:26
- What is Chemical Energy? - Definition & Examples 6:05
- What is Electrical Energy? - Definition & Examples 7:07
- What is Nuclear Energy? - Definition & Examples 5:17
- Calculating Angular Momentum: Definition, Formula & Examples 6:23
- Angular Momentum Practice Problems 6:16
- Go to Energy and Momentum: Help and Review

- Psychology 315: Psychology of Motivation
- Fraud Examination: Help & Review
- Psychology 314: Psychology of Learning
- Computer Science 201: Data Structures & Algorithms
- Drama 101: Intro to Dramatic Art
- Studying for Philosophy 101
- Motivation & Neuroscience
- Core Data Structures
- Object-Oriented Design Fundamentals
- Analyzing Algorithms
- Study.com FTCE Scholarship: Application Form & Information
- Study.com CLEP Scholarship: Application Form & Information
- List of FTCE Tests
- CLEP Prep Product Comparison
- CLEP Exam vs. AP Test: Difficulty & Differences
- CLEP Tests for the Military
- How to Transfer CLEP Credits

- Dollar Diplomacy: Definition & Examples
- Radio Wave: Definition, Spectrum & Uses
- SQL TRUNCATE String: Tutorial & Overview
- Business Analysis Tools, Techniques & Software
- Interpreting Pulmonary Diagnostics: Normal vs. Abnormal Results
- Health Policy Resources: Financial & Administrative
- Managing Relationships with Employees
- Edward Gibbon's Contributions to History & Historiography
- Quiz & Worksheet - Low Self-Esteem & Bullying
- Quiz & Worksheet - Demand Forecasting Techniques
- Quiz & Worksheet - How to Use Historical Data
- Quiz & Worksheet - Systems Thinking & Environmental Ethics
- Quiz & Worksheet - 4 Sided Polygons
- Political Philosophy & Social Justice Flashcards
- Ethics in Philosophy Flashcards

- MTEL Foundations of Reading: Study Guide & Prep
- MEGA Marketing: Practice & Study Guide
- ScienceFusion Motion, Forces, and Energy: Online Textbook Help
- Great Expectations Study Guide
- STAAR Algebra I: Test Prep & Practice
- Weather and Storms: Homework Help
- AP Chemistry: Nuclear Chemistry: Homework Help
- Quiz & Worksheet - Union Development During WWI
- Quiz & Worksheet - Significance of Employer & Employee Expectations
- Quiz & Worksheet - Deferred Payments
- Quiz & Worksheet - Business Sales Taxes
- Quiz & Worksheet - PR Writing

- Self-Destructive Behavior: Signs, Causes & Effects
- Students with Low-Incidence Exceptionalities: Types & Assessments
- High School Interview Questions & Tips
- Creative Writing Exercises for High School
- College Scholarships for Adults
- How to Pass the Physics Regents Exam
- Preview Personal Finance
- Curriculum Vitae Template
- What Is Continuing Education?
- Natural Selection Lesson Plan
- Do Private Schools Take Standardized Tests?
- How to Pass the GED Test

Browse by subject