Question

A disc of mass $1$ kg and radius $0.1$ m is rotating with angular velocity $20rad/s$. What is angular velocity (in rad/s) if a mass of $0.5$ kg is put on the circumference of the disc?

• A. $10$
• B. $20$
• C. $40$
• D. $30$

Answer 1

The correct option is A $10$

Initial angular velocity is ${\omega }_1=20$ $rad/s$

Moment of Inertia of disc is $I_1=m{r}^2/2=\frac{1\times 0.01}{2}kg{m}^2=0.005kg{m}^2$

The new moment of inertia when a particle is placed on the circumference i.e $\text{at a distance r from the axis}$ is , $I_2=I_1+M{r}^2=0.005+0.5kg\times (0.1{)}^2=0.01kg{m}^2$

In this process the the angular momentum, $J=I\omega$ will remain conserved so $I_1{\omega }_1=I_2{\omega }_2$

so the new angular velocity, ${\omega }_2=\frac{I_1}{I_2}{\omega }_1=\frac{0.005}{0.01}20=10rad/s$

Option A is correct.