Dynamics of rotational motion about fixed axis

Question

Three objects, *A*: (a solid sphere), *B*: (a thin circular disk) and *C*: (a circular ring), each have the same mass *M* and radius *R*. They all spin with the same angular speed $\omega $ about their own symmetry axes. The amounts of work *(W)* required to bring them to rest, would satisfy the relation

Moderate

Solution

Work done required to bring a object to rest

$\Delta W=\Delta KE$

$\Delta W=\frac{1}{2}I{\omega}^{2};\text{where}I=\text{moment of inertia}$

$\text{For same}\omega ,\Delta W\propto I$

$\text{For a solid sphere,}{I}_{A}=\frac{2}{5}M{R}^{2}$

$\text{For a thin circular disk,}{I}_{B}=\frac{1}{2}M{R}^{2}$

$\text{For a circular ring,}{I}_{C}=M{R}^{2}$

$\therefore {I}_{C}{I}_{B}{I}_{A}$

$\therefore {W}_{C}>{W}_{B}>{W}_{A}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Download Now