Question

A solid sphere of mass $2kg$ and radius $1m$ is free to rotate about an axis passing through its centre. Find a constant tangential force $F$ required to the sphere with $10rad/s$ in $2s$. Also find the number of rotations made by the sphere in that time interval.

Answer 1

we know that , $\omega ={\omega }_0+\alpha t$

using given values we get, $\alpha =\frac{10}{2}=5rad/s^2$

moment of inertia for solid sphere ,$I=\frac{2}{5}M{R}^2=\frac{4}{5}$

so, torque $\tau =I\alpha =rF$

this gives , $F=\frac{I\alpha }{R}=\frac{4}{5}\times 5=4N$

for no of rotation we use 2nd law of equation for rotation; $\theta ={\omega }_{0}t+\frac{\alpha t^2}{2}$

$=\frac{5\times 2^2}{2}=10rad$