Question

A body is moving down into a well through a rope passing over a fixed pulley of radius 10 cm. Assume that there is no slipping between rope & pulley, calculate the angular velocity and angular acceleration of the pulley at an instant when the body is going down at a speed of 20 cm/s and has an acceleration of 4.0 $m/s^2$

Answer 1

Radius, $r=10$ $cm=10\times {10}^{-2}$ $m$

Linear velocity, $V=20$ $cm/s=20\times {10}^{-2}$ $m/s$

Angular acceleration, $\omega =\frac{V}{r}$

$⟹\omega =\frac{20\times {10}^{-2}}{10\times {10}^{-2}}$

$⟹\omega =2$ $rad/s$

Angular acceleration, $a=\frac{V^2}{r}$

$⟹a=\frac{400\times {10}^{-4}}{10\times {10}^{-2}}$

$⟹a=40\times {10}^{-2}$ $rad/s^2$