Question

A cockroach is moving with velocity v in anticlockwise direction on the rim of a disc of radius R of mass m. The moment of inertia of the disc about the axis is I and it is rotating in clockwise direction with an angular velocity omega. If the cockroach stops, the angular velocity of the disc will be

Answer 1

Answer:

The direction of angular velocity and angular momentum are perpendicular to the plane of rotation. Using the right hand rule, the direction of both angular velocity and angular momentum is defined as the direction in which the thumb of your right hand points when you curl your fingers in the direction of rotation.

Answer 2

Answer:

w'= (Iw−mvR) / I+mR2

Explanation:

The cockroach is moving with a velocity V in anticlockwise roatation.

Cosnidering clockwise motion to be positive

We can write the  

Angular Momentum at initial = Iw + m(−V) R  (negative sign due to anticlockwise)

= Iw−mVR

When the cockroach stops, its speed gets zero.

Final angular Momentum  = (I+mR2)w' where w' is the final angular velocity of disc.

By,lawa of conservation of angular Momentum ;

Iw−mVR=(I+mR2)w'

w' = (Iw−mvR) / I+mR2