A body of mass 5 ~kg at rest is rotated for 25 ~s with a constant moment of force 10 ~Nm . Find the work done if the moment of inertia of the body is 5 ~kg ~m ^2 .

Step-by-step solution

Given the moment of force (torque) = 10 Nm , moment of inertia I = 5 kg m ^2 , and time t = 25 s . The angular acceleration is given by = I . = I = 10 5 = 2 rad/s ^2 . Since the body starts from rest, the initial angular velocity ₀ = 0 . The angular velocity after time t is = ₀ + t = 0 + 2 25 = 50 rad/s . The work done is equal to the change in rotational kinetic energy W = K = 1 2 I ^2 - 1 2 I ₀^2 . W = 1 2 5 (50)^2 - 0 = 1 2 5 2500 = 5 1250 = 6250 J . Answer: 6250 J