The moment of inertia of a body about a certain axis is 1.2 ~kg ~m ^2 . Initially, the body is at rest. In order to produce rotational kinetic energy of 1800 ~J , an angular acceleration of 30 rads ⁻² must be applied about the given axis for a duration of.........s.

Step-by-step solution

Given that, moment of inertia, I=1.2 ~kg - m ^2 Initial angular velocity, ₀=0 Angular acceleration, =30 rad s ⁻² Final rotational kinetic energy, K_f=1800 ~J Let final angular velocity = Using, K_f= 1 2 I ^2 By substituting the values, we get 1800= 1 2 1.2 ^2 =10 30 rad / s We know that, = ₀+ t 10 30 =0+30 tt= 30 3 ~s