Question

A particle p is moving in a circle of radius r with a uniform speed v, C is the centre of the circle and AB is the diameter. The angular velocity of p about A and C is in the ratio:

• A. \(1:1\)
• B. \(1:2\)
• C. \(2:1\)
• D. \(4:1\)

Hint:

Angular velocity depends on the reference point. For points on diameter, distance becomes \(2r\), reducing angular velocity.

Answer 1

The Correct Option is B

Concept: Angular velocity about a point: \[ \omega = \frac{v_{\perp}}{r} \] where \(r\) is the distance from the point and \(v_{\perp}\) is perpendicular component of velocity.

Step 1: Angular velocity about centre \(C\).
\[ \omega_C = \frac{v}{r} \]

Step 2: Angular velocity about point \(A\).
Distance from A to particle varies, but for circular motion: \[ \omega_A = \frac{v}{2r} \] (since diameter \(AB = 2r\))

Step 3: Ratio.
\[ \omega_A : \omega_C = \frac{v}{2r} : \frac{v}{r} = 1:2 \]