Question

A flywheel weighing 10 kg and of radius 8cm is revolving at 150rpm. A constant force applied tangentially to its rim reduced its speed to 120 rpm . Find the force

Answer 1

Given,

• $\sf{m=10\ kg}$

• $\sf{r=8\ cm=8\times10^{-2}\ m}$

• $\sf{\omega_0=150\ rpm=5\pi\ rad\ s^{-1}\quad\quad\left[1\ rpm=\dfrac{\pi}{30}\ rad\ s^{-1}\right]}$

• $\sf{\omega=120\ rpm=4\pi\ rad\ s^{-1}}$

Angular retardation is given by,

$\longrightarrow\sf{\omega=\omega_0+\alpha t}$

$\longrightarrow\sf{\alpha=\dfrac{\omega-\omega_0}{t}}$

$\longrightarrow\sf{\alpha=-\dfrac{\pi}{t}\ rad\ s^{-2}}$

where t is the time taken for attaining the angular speed $\sf{\omega.}$

Then the tangential force is,

$\longrightarrow\sf{F=mr\alpha}$

$\longrightarrow\sf{\underline{\underline{F=-\dfrac{0.8\pi}{t}\ N}}}$

If $\sf{\theta}$ is the angular displacement then,

$\longrightarrow\sf{\underline{\underline{F=-\dfrac{3.6\pi^2}{\theta}\ N}}}$

because $\theta$ is given by,

$\longrightarrow\sf{\omega^2=(\omega_0)^2+2\alpha\theta}$

$\longrightarrow\sf{\alpha=\dfrac{(\omega_0)^2-\omega^2}{2\theta}}$

$\longrightarrow\sf{\alpha=-\dfrac{9\pi^2}{2\theta}}$

It is not possible to find the actual answer without time or angular displacement or any more hint.