Question

A 2kg pulley with a 0.25m radius with a rotational inertia of (1/2)(mr^2) is connected to a 16kg bucket of water. The pulley has an initial clockwise angular velocity of 12rad/s. Calculate the maximum height that the bucket will reach. Calculate the angular acceleration on the bucket.

Answer 1

$\frac{I\omega^2}2=m_2gh,$

$h=\frac{m_1r^2\omega^2}{4m_2g}=2.9~cm,$

$\varepsilon=\frac{\omega^2}{2h}=2500~\frac{rad}{s^2}.$