Question

A uniform 3.0 kg disk of radius 30 cm is rotating around its central axis at an angular speed of 72 rad/s. At time t = 0, a man begins to slow it at a uniform rate until it stops at t = 20 s. (a) Find its angular acceleration. (b) By time t- 10 s, how much work had the man done? (c) For full 20 s, at what average rate did the man do work?

Answer 1

$I=\frac 12 mr^2=0.135~kg\cdot m^2,$

$E=\frac{I\omega^2}2=350~J,$

$\varepsilon=\frac{\omega}{t_{20}}=3.6~\frac{rad}{s^2},$

$\omega_{10}=\omega-\varepsilon t_{10}=36~\frac{rad}s,$

$E_{10}=\frac{I\omega_{10}^2}2=87.5~J,$

$W=E-E_{10}=263~J,$

$P=\frac E{t_{20}}=17.5~W.$