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# Chapter 10: Rotations about a Fixed Axis

Many everyday objects undergo motion in a circle including: a spinning compact disk, the wheels (and other components) of a car, and a ceiling fan to name just a few.

While motion in a circle occurs in two dimensions, it turns out that this motion has a lot in common with motion on a line. We will analyze this motion using all of the techniques we have developed in one-dimensional and two-dimensional motion.

# Table of Contents

## Illustrations

- Illustration 10.1: Coordinates for Circular Motion.
- Illustration 10.2: Motion about a Fixed Axis.
- Illustration 10.3: Moment of Inertia, Rotational Energy, and Angular Momentum.

## Explorations

- Exploration 10.1: Constant Angular Velocity Equation.
- Exploration 10.2: Constant Angular Acceleration Equation.
- Exploration 10.3: Torque and Moment of Inertia.
- Exploration 10.4: Torque on Pulley Due to the Tension of Two Strings.

## Problems

- Problem 10.1: Determine angular displacement.
- Problem 10.2: Determine angular and tangential speed and velocity.
- Problem 10.3: A quarter and a penny are on a turntable.
- Problem 10.4: Determine angular acceleration.
- Problem 10.5: Determine tangential acceleration.
- Problem 10.6: Determine angular acceleration of the wheel.
- Problem 10.7: What is the average torque on the turntable?
- Problem 10.8: Which vector represents the acceleration of the object?
- Problem 10.9: What is the ratio of the kinetic energy?
- Problem 10.10: Two identical masses are hung over two different pulleys.
- Problem 10.11: A modified Atwood's machine with a real pulley.
- Problem 10.12: Two masses are attached with a massless string over a pulley.
- Problem 10.13: A red disk is connected by a string to a hanging mass.
- Problem 10.14: Calculate the angular momentum of several rotating objects.