Question

A wheel of moment of inertia $I$ and radius $R$ is rotating about its axis at an angular speed ${\omega }_o.$ If a particle of mass $m$ is gently placed on its edge, find the new angular speed of the wheel.

• A. $\frac{{\omega }_o}{1+m{R}^2}$
• B. $\frac{I{\omega }_o}{I+mR}$
• C. $\frac{I{\omega }_o}{I+m{R}^2}$
• D. $\frac{I}{I+m{R}^2}$

Answer 1

The correct option is C $\frac{I{\omega }_o}{I+m{R}^2}$

Here, the external torque on the system is zero. Therefore, angular momentum will remain conserved.
Thus,
$I_1{\omega }_1=I_2{\omega }_2$
$\Rightarrow {\omega }_2=\frac{I_1{\omega }_1}{I_2}$

Here, $I_1=I$
${\omega }_1={\omega }_o$
$I_2=I+$ Moment of inertia of particle with mass $m=I+m{R}^2$
$\therefore {\omega }_2=\frac{I{\omega }_0}{I+m{R}^2}$