Question

A string is wound tightly around a fixed pulley having a radius of 5.0 cm. As the string is pulled, the pulley rotates without any slipping of the string. What is the angular speed of the pulley when the string is moving at 5.0 m/s?

Answer 1

Expression for the linear velocity of the pulley is given by

$$ \begin{aligned} v &=r \omega \\ r &=\text { Redius of the pulley } \\ \omega &=\text { Angular velocity of the pulley } \\ \omega &=\frac{v}{r} \\ &=\frac{5}{5 \times 10^{-2}} \\ & \omega=100 \mathrm{rad} / \mathrm{s} \end{aligned} $$

Therefore the angular velocity of the pulley is \(\omega=100 \mathrm{rad} / \mathrm{s}\).