A body rotating at 20 rad/s is subjected to a constant torque that provides a deceleration of 2 rad/s ^2 . If the torque continues to act, at what time will the body possess a kinetic energy equal to its initial value?

Step-by-step solution

The initial kinetic energy of the rotating body is given by K_i = 1 2 I ₀^2 . For the body to possess a kinetic energy equal to its initial value at a later time t > 0 , its final angular velocity must be = - ₀ . Given ₀ = 20 rad/s and angular deceleration = -2 rad/s ^2 , we have = -20 rad/s . Using the first equation of rotational kinematics: = ₀ + t -20 = 20 - 2t 2t = 40 t = 20 s