Question

A solid sphere of diameter 25 cm and mass 25kg rotates about an axis through its centre. Calculate its moment of inertia, if its angular velocity changes from 2 rad/s to 12 rad/s in 5 second. Also calculate the torque applied.

Answer 1

Radius of sphere $R=\frac{d}{2}=12.5cm=0.125m$

Moment of inertia $I=\frac{m{R}^2}{2}=\frac{25\times (0.125{)}^2}{2}=0.195kg{m}^2$

Using $w_f=w_i+\alpha t$

Or $12=2+\alpha \times 5$ $⟹\alpha =2rad/s^2$

Torque applied $\tau =I\alpha$

Or $\tau =0.195\times 2=0.39Nm$