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# Chapter 11: General Rotations

In the last chapter we studied rotational kinematics, rotational energy, and moment of inertia for objects rotating about a fixed axis. In this chapter we will begin by discussing the mathematical description of torque as a vector or cross product. We will also focus on general rotations such as when objects roll (rotate and translate).

# Table of Contents

## Illustrations

- Illustration 11.1: Torque as a Vector Product.
- Illustration 11.2: Rolling Motion.
- Illustration 11.3: Translational and Rotational Kinetic Energy.
- Illustration 11.4: Angular Momentum and Area.
- Illustration 11.5: Conservation of Angular Momentum.

## Explorations

- Exploration 11.1: Torque.
- Exploration 11.2: Nonuniform Circular Motion.
- Exploration 11.3: Rolling Down an Incline.
- Exploration 11.4: Moment of Inertia and Angular Momentum.
- Exploration 11.5: Conservation of Angular Momentum.

## Problems

- Problem 11.1: Velocity of a rolling wheel.
- Problem 11.2: A wheel rolls without slipping while pulled by a string wrapped around its circumference.
- Problem 11.3: Determine whether an object rolls without slipping or slides down an incline.
- Problem 11.4: Determine whether an object rolls without slipping or slides down an incline.
- Problem 11.5: Determine the torque on a yo-yo.
- Problem 11.6: A rolling wheel is attached via a string to a hanging mass.
- Problem 11.7: Calculate the angular momentum of several systems.
- Problem 11.8: A red disk is dropped onto a rotating yellow disk.
- Problem 11.9: A puck sliding on an air table collides with another puck.
- Problem 11.10: A puck sliding on an air table collides with another puck.