Question

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 a $5\, rad / s ^{2}$ must be applied about that axis for:

• A. 3 s
• B. 4 s
• C. 5 s
• D. 6 s

Answer 1

Answer: (C)

Kinetic energy of rotation is half the product of the moment of inertia $(I)$ of the body and square of the angular velocity $(\omega)$ of the body.
$\therefore d K=\frac{1}{2} I \omega^{2}$
Given, $I=2.4 \,kg - m ^{2}, $
$K=750\, J$
$\Rightarrow \omega^{2}=\frac{2 K}{I}$
$=\frac{2 \times 750}{2.4}=625$
$\Rightarrow \omega=25 \,rad / s .$
Also angular acceleration $(\alpha) \times$ time $(t)=$ angular velocity $(\omega)$
$\Rightarrow t=\frac{\omega}{\alpha}=\frac{25}{5}=5 \,s .$