The moment of inertia of a body about a given axis is 12 kg m 2 . Initially the body is at rest. In order to produce a rotational kinetic energy of 15000 J , an angular acceleration of 10 rad s - 2 must be applied about that axis for a duration of________.

Step-by-step solution

The kinetic energy of rotation is, K . E . = 1 2 I ω 2 = 1 2 × 12 × ω 2 = 15000   J ω 2 = 15000   J 1 2 × 12 = 30000 12 ⇒ ω = 30000 12 = 50   rad   s - 1 Using the equation of motion of rotation, ω = ω 0 + α t 50 = 0 + 10 × t t = 5   s