The moment of inertia of a body about a given axis is 1.2 ~kg - m ^2 . To produce a rotational kinetic energy of 1500 J an angular acceleration of 25 rad / s ^2 must be applied for

Step-by-step solution

Kinetic energy of rotation is half the product of the moment of inertia (l) of the body and the square of the angular velocity ( ) of the body. Kinetic energy of rotation = 1 2 moment of inertia angular velocity i.e., K= 1 2 / ^2 ^2= 2 K 1 Given l=1.2 ~kg ~m ^2, K=1500 ~J ^2= 2 1500 1.2 =50 rad / s From the equation of angular motion, we have = ₀+ t where ₀ is initial angular velocity, is angular acceleration and t is time given ₀=0 aligned & =50 rad / s & =25 rad / s ^2 & t= = 50 25 =2 ~s aligned