Question

A disc of moment of inertia 1.8 k g.m2 is rotating at a constant angular velocity of 3.2 rad.s−1. A second disc of moment of inertia 0.6 kg.m2, initailly at rest, falls on the first disc and the two rotate as a system. What is the angular velocity of the system?

Answer 1

Answer:

2.4 rad/s

Explanation:

$\omega_1$ = Initial angular velocity = 3.2 rad/s

$\omega_2$ = Final angular velocity of the system

$I_1$ = Initial angular momentum = 1.8 kgm²

$I_2$ = Final angular momentum = 0.6 kgm²

As there is no external torque then the angular momentum in the system is conserved

$I_1\omega_1=(I_1+I_2)\omega_2\\\Rightarrow \omega_2=\frac{I_1\omega_1}{I_1+I_2}\\\Rightarrow \omega_2=\frac{1.8\times 3.2}{1.8+0.6}\\\Rightarrow \omega_2=2.4\ rad/s$

The angular velocity of the system is 2.4 rad/s