Check out this trailer video from OpenStax about the Moment of Inertia.

https://www.youtube.com/watch?v=IpZL-gxTKy4

## Pre-lecture Study Resources

Watch the pre-lecture videos and read through the OpenStax text before doing the pre-lecture homework or attending class.

### BoxSand Videos

## Required Videos

## Suggested Supplemental Videos

### Learning Objectives

## Summary

We have previously studied Newton's laws of motion while only considering what happens to the center-of-mass (COM) of an object, otherwise known as a point particle model. In statics and dynamics, we still work under the framework of Newton's laws of motion, but we extend our consideration from the point particle model to also include the shape and size of the object. The sum of the forces on a object still determine the linear motion of it's COM, but where those forces are applied will tell us something about how and if the object rotates.

## Atomistic Goals

Students will be able to...

Statics and Dynamics

1. Understand the application of Newton's laws of motion to rigid bodies, while also identifying the similarities when compared to the point particle model.

2. Demonstrate the ability to analyze a system in rotational equilibrium using the rotational version of Newton's second law.

3. Define moment of inertia.

4. Understand moment of inertia and its dependence on mass distribution. Also recognize its analogy to the previous working definition of inertia as applied to the point particle model.

5. Connect quantities found from a rotational dynamics analysis to both rotational and linear kinematics.

Stability

6. Be able to calculate the center of mass of an object or a system of objects.

7. Be able to determine if an object or system of objects will be stable based on center of mass location relative to normal forces.

### BoxSand Introduction

## Statics and Dynamics | Dyamics and Moment of Inertia

Dynamics involves applying Newton's 2nd Law for rotation.

In a system that is not in rotational equilibrium, the angular acceleration is not zero. This results in the RHS (right-hand side) of the 2nd law to not be zero. You will need to know the moment of inertia for a mass distribution. Below are the equations for a the moment of inertia for some common mass distributions.

Here are some examples of moments of inertia for various mass distributions.

## Key Equations and Infographics

Now, take a look at the pre-lecture reading and videos below.

### OpenStax Reading

## Additional Study Resources

Use the supplemental resources below to support your post-lecture study.

### YouTube Videos

Moment of inertia explanation. At 12:25 doc begins to derive moments of inertia for various objects, you can ignore this.

https://www.youtube.com/watch?v=PBo7llsc6LA

Doc Schuster talks about rotational dynamics.

### Simulations

PhET simulation on dynamic torque. Note that when you let the wheel rotate without acceleration, it is actually in torsional equilibrium despite the fact that it is in motion.

For additional simulations on this subject, visit the simulations repository.

You need to have Java installed and updated. Download and run the file.

### Demos

A demonstration of the intermediate axis theorem, an application of moment of inertia.

https://www.youtube.com/watch?v=-Si6iRL5Fj8

For additional demos involving this subject, visit the demo repository

### History

Oh no, we haven't been able to write up a history overview for this topic. If you'd like to contribute, contact the director of BoxSand, KC Walsh (walshke@oregonstate.edu).

### Physics Fun

### Other Resources

Read pages 1-10 for static equilibrium.

This links to a set of slides detailing static equilibrium.

## Resource Repository

This link will take you to the repository of other content related resources.

## Problem Solving Guide

Use the Tips and Tricks below to support your post-lecture study.

### Assumptions

### Checklist

### Misconceptions & Mistakes

### Pro Tips

### Multiple Representations

Multiple Representations is the concept that a physical phenomena can be expressed in different ways.

### Physical

### Mathematical

### Graphical

### Descriptive

### Experimental

## Practice

Use the practice problem sets below to strengthen your knowledge of this topic.

### Fundamental examples

Recommended example practice problems

### Practice Problems

- set 1: Problems with solutions, Website Link
- set 2: Static net torque = 0, Website Link
- set 3: PDF of free body diagram problems, Offsite PDF Link

2. There are additional practice problems you can work for credit | Calendar