Question

A bucket of water with total mass 23 kg is attached to a rope, which in turn is wound around a 0.050-m radius cylinder at the top of a well. the bucket is raised to the top of the well and released. the bucket is moving with a speed of 8.0 m/s upon hitting the water surface in the well. what is the angular speed of the cylinder at this instant?

Answer 1

As we know the relation between linear speed and angular speed as

$v = R\omega$

we will say

$v = 8 m/s$

$R = 0.05 m$

so here we can say that angular speed will be given as

$\omega = \frac{8}{0.05}$

$\omega = 160 rad/s$

so it is rotating at angular speed 160 rad/s