Question

A wheel having moment of inertia 2 kgm? about its Axis rotates at 50 RPM about the axis find the torque that can stop the wheel in one minute

Answer 1

Dear student,


$$\begin{gathered} Givenmomentofinertia,I=2kg{m}^2 \\ Initialangularvelocity={\omega }_0=50rpm=\frac{50}{60}\times 2\pi radians/sec=\frac{5\pi }{3}radians/sec \\ Finalangularvelocity=\omega =0rad/sec \\ Time,t=60sec \\ \Rightarrow Torquerequiredtostopthewheel,\tau =I\alpha =I\left(\frac{({\omega }_0-\omega )}{t}\right)=2\left(\frac{\left(\frac{5\pi }{3}-0\right)}{60}\right)=\frac{10\pi }{180}=\frac{\mathbf{\pi }}{\mathbf{18}}\mathit{N}\mathbf{-}\mathit{m} \end{gathered}$$

Regards