Conceptual Physics

10.13 - Summary

Torque is a force that causes rotation. Torque is a vector quantity with units N·m.

An object's moment of inertia is a measure of its resistance to angular acceleration,

just as an object's mass is a measure of its resistance to linear acceleration. The

moment of inertia is measured in kg·m^2 and depends not only upon an object’s

mass, but also on the distribution of that mass around the axis of rotation. The

farther the distribution of the mass from the axis, the greater the moment of inertia.

Another linear analogy applies: Just as Newton's second law states that net force

equals mass times linear acceleration, the net torque on an object equals its

moment of inertia times its angular acceleration.

Rotational kinetic energy depends upon the moment of inertia and the angular

velocity. Mechanical devices called flywheels can store rotational kinetic energy.

Angular momentum is the rotational analog to linear momentum. Its units are

kg·m^2 /s. The magnitude of the angular momentum of an object in circular motion is

the product of its mass, tangential velocity, and the radius of its path. The angular

momentum of a rigid rotating body equals its moment of inertia multiplied by its

angular velocity.

Just as a change in linear momentum (impulse) is equal to a force times its

duration, a change in angular momentum is equal to a torque times its duration.

Angular momentum is conserved in the absence of a net torque on the system.

Torque

IJ = rF

Newton's second law for rotation

ȈIJ = IĮ

Moment of inertia

I = Ȉmr^2

Angular momentum

L = IȦ

IJǻt = ǻL

Conservation of angular momentum

Li = Lf

IiȦi = IfȦf

(^200) Copyright 2007 Kinetic Books Co. Chapter 10