Question

You (mass m) are riding on the edge of a disc of radius r and also of mass m (I = ½mr2) that is rotating counter-clockwise about an axle with rotational speed ω. You jump off the rotating disc so that you move tangent to the edge of the disc, causing the disc to come to rest. Determine the speed at which you jumped from the disc.

Answer 1

Your mass = m

Mass of the disc = m

Radius of the disc = r

Moment of inertia of the disc = I

I = mr²/2

Initial angular speed of the disc =

You are at the edge of the disc therefore you are at a distance equal to the radius from the center of the disc.

Speed at which you jump from the disc = V

The disk comes to rest after you jump off therefore it has zero angular velocity after you jump off.

By conservation of angular momentum,

(I + mr²) = mVr

(mr²/2 + mr²) = mVr

3mr²/2 = mVr

V = 3r/2

Speed at which you jumped from the disc = 3r/2