Answer to Question #87156 in Classical Mechanics for Rinku Rai

Question

A wheel having a moment of inertia of 1.0 kg m2
, is rotating about an axis through its centre and perpendicular to its plane, at a speed of 30 rad s−1. Due to friction on its axis, it comes to rest in 10 minutes. Calculate i) the total work done by friction, ii) average torque exerted by the force of friction and iii) the angular momentum of the wheel 2 minutes before it stops rotating.

Answer 1

i)

$$W=0.5I\omega^2=0.5(1)(30)^2=450 J$$

ii)

$$T=I\alpha=\frac{I\omega}{t}=\frac{1(30)}{600}=0.05 Nm$$

iii)

$$L=I\alpha t_1=\frac{1(30)480}{600}=24 kgm^2/s$$