Question

The moment of inertia of a body about a given axis is $1.2 \,kg - m ^{2}$. To produce a rotational kinetic energy of $1500\, J$ an angular acceleration of $25\, rad / s ^{2}$ must be applied for :

• A. 8.5 s
• B. 5 s
• C. 2 s
• D. 1 s

Answer 1

Answer: (C)

2 s

Answer 2

Key Idea : Kinetic energy of rotation is half the product of the moment of inertia (I) of the body and the square of the angular velocity $(\omega)$ of the body.
Kinetic energy of rotation $=\frac{1}{2} \times$ moment of inertia $\times$ angular velocity.
i.e. $K =\frac{1}{2} I \omega^{2}$
$\Rightarrow \omega^{2} =\frac{2 K}{I}$
Given, $I= 1.2\, kgm ^{2} ,$
$K=1500\, J$
$\therefore \omega^{2} =\frac{2 \times 1500}{1.2}$
$\omega^{2} =2500$
$\Rightarrow \omega =50 \,rad / s$
From the equation of angular motion, we have
$\omega=\omega_{0}+\alpha t$
where $\omega_{0}$ is initial angular velocity,
$\alpha$ is angular acceleration and $t$ is time.
Given, $\omega_{0}=0,$
$\omega=50 \,rad / s ,$
$\alpha=25 \,rad / s ^{2}$
$\therefore t=\frac{\omega}{\alpha}=\frac{50}{25}=2 s$
Note : The equation of kinetic energy of rotation is similar to kinetic energy expression in linear form $\left(\frac{1}{2} m v^{2}\right)$ and equation of angular motion is similar to Newton's equation of motion $(v=u+a t)$