An object whose size and shape don’t change as it moves is called a rigid body. A rigid body is characterized by its moment of inertia I, which is the rotational equivalent of mass. We’ll consider

• Rotation about an axle.

• Rolling without slipping.

《 LOOKING BACK Section 6.1 Equilibrium

Torque is the tendency or ability of a force to rotate an object about a pivot point. You’ll learn that torque depends on both the force and where the force is applied. A longer wrench provides a larger torque.

Torque is to rotation what force is to linear motion. Torque $\tau$ causes an object to have angular acceleration. Newton’s second law for rotation is $\alpha =\tau /I$. Much of rotational dynamics will look familiar because it is analogous to linear dynamics.

《 LOOKING BACK Section 6.2 Newton’s second law

Angular momentum is to rotation what momentum is to linear motion. Angular momentum is an object’s tendency to “keep rotating.” Angular momentum $\vec{L}$ is a vector pointing along the rotation axis. You’ll use angular momentum to understand the precession of a spinning top or gyroscope.

The mechanical energy of a rotating object includes its rotational kinetic energy $\frac{1}{2}I{\omega }^2$. This is analogous to linear kinetic energy.

• Mechanical energy is conserved for frictionless, rotating systems.

• Angular momentum is conserved for isolated systems.

《 LOOKING BACK Section 10.4 Conservation of energy; Section 11.2 Conservation of momentum

The world is full of rotating objects, from windmill turbines to the gyroscopes used in navigation. The wheels on your bicycle or car roll without slipping. Scientists investigate rotating molecules and rotating galaxies. No understanding of motion is complete without understanding rotational motion, and this chapter will develop the tools you need. We’ll also expand our understanding of equilibrium by exploring the conditions under which objects don’t rotate.