Question

If a point move along a circle with constant speed. If w1 be its angular speed about any point on the circle and w2 be its angular speed about the center, then :

Answer 1

Answer:

Your question is incomplete. Your question should be like that,,,

If a point move along a circle with constant speed. If w1 be its angular speed about any point on the circle and w2 be its angular speed about the center, then prove that the angular speed about any point on the circle is half of that about the centre.

Now the answer,

Let w1 is the angular speed of the point on circle and w2 is the angular speed of centre.

Let, O be a point on a circle and P be the position of the particle at any time t, such that ∠POA=θ

Then ∠PCA=2θ

Here in the figure, C is the centre of the circle. Angular velocity of P about O is w2=dθ/dt and the angular velocity of P about C is

w1=d(2θ)/dt=2(dθ/dt)

=>w1=2(w2)

=>w2=1/2(w1)..........................PROVED