Question

A body rotating with $20rad/s$ is acted upon by a uniform torque providing it an angular deceleration of $2rad/s^2$. At which time will the body have kinetic energy same as the initial value if the torque acts continuously?

Answer 1

Given,

Equal kinetic energy

$\frac{1}{2}I{\omega }_1^2=\frac{1}{2}I{\omega }_2^2$

${\omega }_2=\pm {\omega }_1$

Possible value is ${\omega }_2=-{\omega }_1$

Initial angular velocity, ${\omega }_1=20rad/s$

Final velocity, ${\omega }_2=-20rad/s$

Angular acceleration $\alpha =-2rad/s^2$

${\omega }_2={\omega }_1+\alpha t$

$t=\frac{{\omega }_2-{\omega }_1}{\alpha }=\frac{-20-20}{-2}=20\sec$

After 20sec, it again achieves equal kinetic energy.