Question

A body rotating at $20\text{rad/s}$ is acted upon by a uniform torque providing it an angular deceleration of $2{\text{rad/s}}^2$. After what time will the body have the same kinetic energy as the initial value, if the torque acts continuously?

• A. $5\text{s}$
• B. $10\text{s}$
• C. $15\text{s}$
• D. $20\text{s}$

Answer 1

The correct option is D $20\text{s}$

Given, deceleration $\alpha =2{\text{rad/s}}^2$
and initial angular velocity $w_0=20\text{rad/s}$
Kinetic energy will be the same again when the angular speed of the body will be same as the initial angular speed.
In this case, the body is decelerating. Hence angular speed decreases continuously. It will become zero, then body will start rotating in reverse direction because torque is acting continuously.
Consider at time $t$, angular velocity $=-20\text{rad/s}$
Then, initial kinetic energy will be equal to the final kinetic energy.
From eqn $w=w_0+\alpha t$,
$-20=20-2t$
or $t=20\text{seconds}$