Circular Motion 

When discussing the motion of objects which are moving in circular (or nearly circular) paths, we often consider angles measured in radians rather than degrees.

In the diagram above, the angle q, in radians, is defined as follows

So, if s = r the angle is 1 rad and if s is equal to the full circumference of the circle, the angle is 2parad. (In other words, 360° = 2p rad.)

If we consider a small body to be moving round the circle from A to B we say that it has experienced an angular displacement of q radians. The relation between the (linear) distance moved, s, of the body and the angular displacement, q, is given by

Also, if the angle is small, s is very nearly equal to the magnitude of the linear displacement of the body.

Suppose that the body moved from A to B in a time t. The linear speed, v, of the body is given by v = s/t. If we divide equation 1 by t, we have

We now define the angular velocity w as follows

so units of w are rads^-1

Therefore, the relation between v and w is

• Angular Acceleration
• Time Period, T
• Rotational Frequency, f
• Mechanics Chapters Index
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