Question

The moment of inertia of a body about a given axis $1.2\, kg \,m ^{2}$. Initially the body is at rest. In order to produce a rotational kinetic energy of $1500\, J$ and angular acceleration of $25\, rad / s ^{2}$ must be applied about the axis for a duration of:

• A. 10 s
• B. 8 s
• C. 2 s
• D. 4 s

Answer 1

Answer: (C)

2 s

Answer 2

Kinetic energy is given by
$E =\frac{1}{2} I \omega^{2}, \omega^{2}=\frac{2 E}{I}$
$\omega^{2} =\frac{2 \times 1500}{1.2}=2500$
$\omega =\sqrt{2500}=50 \,rad / \sec$
$t =\frac{\omega}{\alpha}=\frac{50}{25}=2 \,\sec$