The Rotational Variables

We wish to examine the rotation of a rigid body about a fixed axis. A rigid body is a body that can rotate with all its parts locked together and without any change in its shape. A fixed axismeans that the rotation occurs about an axis that does not move. Thus, we shall not examine an object like the Sun, because the parts of the Sun (a ball of gas) are not locked together. We also shall not examine an object like a bowling ball rolling along a bowling alley, because the ball rotates about an axis that moves (the ball's motion is a mixture of rotation and translation).

Figure 11-2 shows a rigid body of arbitrary shape in rotation about a fixed axis, called the axis of rotationor the rotation axis.Every point of the body moves in a circle whose center lies on the axis of rotation, and every point moves through the same angle during a particular time interval. In pure translation, every point of the body moves in a straight line, and every point moves through the same linear distance during a particular time interval. (Comparisons between angular and linear motion will appear throughout this chapter.)

We deal now - one at a time - with the angular equivalents of the linear quantities position, displacement, velocity, and acceleration.