Question

A uniform circular disc of radius $R$ is rotating about its own axis with moment of inertia $I$ at an angular velocity $\omega$. If a dense particle of mass $m$ is gently attached to the rim of disc than its angular velocity is :

• A. $\omega$
• B. $Iw(I+mR)$
• C. $\frac{I+m{R}^2}{Iw}$
• D. $\frac{Iw}{I+m{R}^2}$

Answer 1

The correct option is D $\frac{Iw}{I+m{R}^2}$

Initial moment of inertia $=I$

Final moment of inertia, $I_1=I+m{R}^2$

Using conservation of angular momentum

we have $I\omega =(I+m{R}^2){\omega }_1$

${\omega }_1=\frac{I\omega }{I+m{R}^2}$