Question

A rope is wrapped around the rim of a large uniform solid disk of mass 155 kg and radius 2.30 m. The horizontal disk is made to rotate by pulling on the rope with a constant force of 195 N. If the disk starts from rest, what is its angular speed in rev/s at the end of 2.05 s?

Answer 1

Answer:1.21 rad/s

Explanation:

Given

mass of disk $m=155 kg$

radius $r=2.3 m$

Force applied $F=195 N$

initial angular velocity $\omega =0$

time interval $t=2.05 s$

Moment  of inertia of rim $I=mr^2$

$I=155\times 2.3^2=819.95\ kg-m^2$

$F\cdot r=I\times \alpha$

$195\times 2.3=819.95\times \alpha$

$\alpha =0.546 rad/s^2$

$\omega _2=\omega _1+\alpha t$

$\omega _2=0+0.546\times 2.05$

$\omega _2=1.21 rad/s$