Question

A body rotating at 20 rad/s is acted upon by a constant torque providing it a deceleration of 2 rad/s ² . At what time will the body have kinetic energy same as the initial value if the torque continues to act ?

Answer 1

Initial angular velocity = 20 rad/s
Therefore α = 2 rad/s²
 t₁ = ω/α ₁ = 20/2 = 10 sec
Therefore 10 sec it will come to rest.
Since the same torque continues to act on the body it will produce same angular acceleration and
since the initial kinetic energy = the kinetic energy at an instant.
So initial angular velocity = angular velocity at that instant
Therefore time require to come to that angular velocity,
t₂ = ω₂/α ₂ = 20/2 = 10 sec
therefore time required = t₁ + t₂ = 20 sec.