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  4. Moment of inertia of a body about a given axis is 1.5 kg m2. Initially the body is at rest. In order to produce a rotational kinetic energy of 1200 J, the angular acceleration of 20 rad/s2 must be applied about the axis for a duration of seconds.

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Q. Moment of inertia of a body about a given axis is $1.5\, kg\, m^2$. Initially the body is at rest. In order to produce a rotational kinetic energy of $1200 \,J$, the angular acceleration of $20 \,rad/s^2$ must be applied about the axis for a duration of _______ seconds.

System of Particles and Rotational Motion

Solution:

$\omega = \alpha t = 20t$
Given, $\frac{1}{2} I\omega^2 = 1200$
or $\frac{1}{2} \times 1.5 \times (20t)^2 = 1200$
or $ t = 2\,s$