Module 8: Rotational Motion and Equilibrium


Module 8: Rotational Inertia

Introduction 

Does a horse near the outside rail of a merry-go-round go faster than a horse near the inside rail? Assuming we are talking about linear speed then yes it does. But if we are talking about angular velocity, then no it doesn't. For every linear quantity there is an angular quantity that is similar, but different. This module has 10 lessons that will introduce the complex principles of rotational motion and equilibrium, be sure to work the practice problems for each module. 

Students have reported that this module is the most demanding of the entire course, so don't wait to the last minute before working through it!

Learning Objectives

Upon completion of this module, students will be able to: 

  • Differentiate between angular speed and linear speed.
  • Define angular velocity.
  • Define angular acceleration.
  • Define torque and be able to calculate the torque applied to a body.
  • Solve problems related to balancing object, using torque.
  • Explain the rotational analogs of linear motion, including rotational inertia, rotational kinetic energy, and angular momentum.
  • Provide examples of rotational motion and equilibrium.
  • Relate the center of mass to balance.
  • Differentiate between the center of mass and the center of gravity.
  • Identify what is the center of mass of a collection of point particles.
  • Determine what factors affect whether an object's stability, whether it stays upright or falls over
  • Define statics.
  • Use the basic laws of statics to calculate the various forces involved in a static system.
  • Define rotational inertia, and know how to calculate the rotational inertia of point-like object
  • Describe the kinetic energy of rotating objects.
  • Define angular momentum and know in what circumstances it is conserved.
  • Identify and solve problems where angular momentum conservation is applicable.

To Do List

1. Watch the Video Lectures (links below)
2. Complete the Practice Problems (links below)
3. Take the Module 8 Quiz
4. Complete the Exam Practice Problems for Module 8

Lessons

Lesson 8.1 Radians

In this lesson, radians will be introduced and defined. 

Lesson 8.2 Angular Speed and Velocity

Angular speed is defined and the relationship between angular speed and linear speed investigated.

Lesson 8.3 Angular Acceleration 

We extend the discussion of rotational motion to include angular acceleration.

Lesson 8.4 Torque

Torque is introduced and problems of balancing see-saws discussed.

Lesson 8.5 Center of Mass

The center-of-mass of an object is introduced and it is shown how this must be used in problems concerning balance.

Lesson 8.6 Object Stability

Here we learn what determines if an object stays upright or falls over

Lesson 8.7 Statics

The subject of "statics" is an entire course in engineering. Here we review the two basic tenets of statics and show how many problems can be solved with just them.

Lesson 8.8 Rotational Inertia

The concept of rotational inertia as "resistance to rotation" is introduced, first for point-like objects and then for extended objects.

Lesson 8.9 Rotational Kinetic Energy

We learn that rolling objects such as balls have kinetic energy because of the motion of the center of mass as well as the motion of the mass of the ball around the center of mass.

Lesson 8.10 Angular Momentum 

The lesson concentrates on angular momentum. We look at the similarities of angular and linear momentum and at some surprising consequences of angular momentum conservation.

Quiz

Once you have watched the lectures and completed the practice problems, you should demonstrate your understanding by taking the Module 8 Quiz. Be sure to submit the quiz before its deadline.

Survey

We ask you to take this Mid-Course Survey. Completing the survey will add an extra 2% to your overall course score (consider it extra credit). We want to have your feedback about how to make the course better!

Coming Up

In the next Module we will learn about Structure of Matter.