A disc has mass ' $m$ ' and radius ' $R$ '. How much tangential force should be applied to the rim of the…
A disc has mass ' $m$ ' and radius ' $R$ '. How much tangential force should be applied to the rim of the disc so as to rotate with angular velocity ' $\omega$ ' in time t?
$\frac{\mathrm{mR} \omega}{2 \mathrm{t}}$
$\mathrm{mR} \omega \mathrm{t}$
$\frac{\mathrm{mR} \omega}{4 \mathrm{t}}$
$\frac{\mathrm{mR} \omega}{\mathrm{t}}$
Solution
Angular acceleration, $\alpha=\frac{\omega}{\mathrm{t}}$
And, moment of inertia of disc $\mathrm{I}=\frac{1}{2} \mathrm{MR}^2$
Hence, torque,
$\begin{aligned} & \tau=I \cdot \alpha=\frac{1}{2} M^2 \frac{\omega}{t} c \\ & \tau=F \cdot R \\ & \Rightarrow F=\frac{\tau}{R} \\ & \Rightarrow F=\frac{M R \omega}{2 t}\end{aligned}$