Question

If a point moves along a circle. Prove that its angular velocity about any point on the circumference of the circle is half of that about the centre?

Answer 1

Let particle move from point A to B on the circumference of the circle in time t. As shown in fig. arc AB makes angle AOB=theta+ beta. From the figure theta=2(phi) and beta=2(alpha).

The angular velocity about center O is

w=(theta+beta)/t…………………..(1)

Thus, w=2(alpha+phi)………………(2)

But, angular velocity about P is

w’=(alpha+phi)………………………..(3)

From (2) and (3),

w=2w’