Question

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

• A. $2\text{rad/s}$
• B. $0.2\text{rad/s}$
• C. $0.02\text{rad/s}$
• D. $20\text{rad/s}$

Answer 1

The correct option is A $2\text{rad/s}$

Since the rope does not slip on the pulley, the linear speed $v$ of the point of contact on pulley is same as the speed of the bucket.

The angular velocity of the pulley is then given by

$\omega =\frac{v}{r}=\frac{20\text{cm/s}}{10\text{cm}}=2\text{rad/s}$

Hence option A is the correct answer.