Question

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

• A. $4 \, s$
• B. $2s$
• C. $8s$
• D. $10s$

Answer 1

Answer: (B)

$I=1.2 \, kg \, m^{2}$
$\omega _{i}=0$ ; $\alpha =25 \, rad \, s^{- 2}$
Rotational KE $=\frac{1}{2}Iω_{f}^{2}=1500J$
$\Rightarrow \omega _{f}=50rads^{- 1}$
$\Rightarrow t=\frac{\omega _{f} - \omega _{i}}{\alpha }=\frac{50}{25}=2s$