gravitational forces (Section 2.6)

Newton's second law: force and acceleration (Sections 3.3 and 3.4)

velocity and acceleration (Sections 3.2 and 3.3)

apparent weight (Section 4.5)

normal and frictional forces (Section 2.7)

The angular displacement Dq is the angle through which an object has turned. Positive and negative angular displacements indicate rotation in different directions. Conventionally, positive represents counterclockwise motion.

Average angular velocity:

Average angular acceleration:

The instantaneous angular velocity and acceleration are the limits of the average quantities as _{<a onClick="window.open('/olcweb/cgi/pluginpop.cgi?it=jpg::::/sites/dl/free/0073512141/663813/ch5_3.JPG','popWin', 'width=NaN,height=NaN,resizable,scrollbars');" href="#"><img valign="absmiddle" height="16" width="16" border="0" src="/olcweb/styles/shared/linkicons/image.gif"> (1.0K)</a>}

A useful measure of angle is the radian:

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Using radian measure for w, the speed of an object in circular motion (including a point on a rotating object) is

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Using radian measure for a, the tangential acceleration component is related to the angular acceleration by

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An object moving in a circle has a radial acceleration component given by

The tangential and radial acceleration components are two perpendicular components of the acceleration vector. The radial acceleration component changes the direction of the velocity and the tangential acceleration component changes the speed.

Uniform circular motion means that u and w are constant. In uniform circular motion, the time to complete one revolution is constant and is called the period T. The frequency f is the number of revolutions completed per second.

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A rolling object is both rotating and translating. If the object rolls without skidding or slipping, then

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Kepler's third law says that the square of the period of a planetary orbit is proportional to the cube of the orbital radius:

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For constant angular acceleration, we can use equations analogous to those we developed for constant acceleration a_x:

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