Q. The moment of inertia of a body about a given axis is $2.4\ kg - m^{2}$. To produce a rotational kinetic energy of $750\ J$, an angular acceleration of $5\ rad/s^{2}$ must be applied about that axis for
A) $6\ sec$
B) $5\ sec$
C) $4\ sec$
D) $3\ sec$
Explanation
(b) $\frac{1}{2}I\omega^{2} = 750J \Rightarrow \omega^{2} = \frac{750 \times 2}{2.4} = 625 \Rightarrow \omega = 25rad/s$
$\alpha = \frac{\omega_{2} - \omega_{1}}{t} \Rightarrow 5 = \frac{25 - 0}{t} \Rightarrow t = 5s$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.