Circular Motion continued

In the previous section we assumed that the body moved from A to B with constant speed. If the linear speed of the body changes then, obviously, the angular speed (velocity) also changes.

We will now define the angular acceleration, a, to be the rate of change of angular velocity.

So, if the angular velocity changes uniformly from w₁ to w₂ in time t, then we can write:

Now, linear acceleration, a, is given by

Thus the relation between linear acceleration and angular acceleration can be found by substituting from equation 2 in the equation for linear acceleration.

We therefore have

The time period of a circular motion is the time taken for one revolution.

The rotational frequency of a circular motion is the number of revolutions per unit time.

Thus the relation between time period and frequency is

and two other useful equations (relating w to T and f) are

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© David Hoult 2009