A bucket is being lowered down into a well through a rope passing over a fixed pulley of radius 10 cm. Assume that the rope does not slip on the pulley. Find the angular velocity and angular acceleration of the pulley at an instant when the bucket is going down at at speed of 20 cm/s and has an acceleration of `4.0 m/s^2`.

Explanation

Since the rope does not slip on the pulley, the linear speed v of therim of the pulley is same as the speed of the bucket.
the anguklar velocity of the pulley is then
`omega=v/r=(20cm/s)/(10cm)=2rad/s`
and the angular acceleration of the pulley is
`alphaa/r(4.0m/s^2)/(10cm)=40rad/s^2`