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, , to be the rate of change of angular velocity.

So, if the angular velocity changes uniformly from ₁ to ₂ 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 to T and f) are

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