Question

The moment of inertia and rotational kinetic energy of a fly wheel are $20kg-m^2$ and $1000joule$ respectively. Its angular frequency per minute would be

• A. $\frac{600}{\pi }$
• B. $\frac{25}{{\pi }^2}$
• C. $\frac{5}{\pi }$
• D. $\frac{300}{\pi }$

Answer 1

Answer: (D)

$\frac{300}{\pi }$

Given,

$I=20kh{m}^2$

$K_r=1000J$

The rotational kinetic energy is given by

$K_r=\frac{1}{2}I{\omega }^2$

$1000=\frac{1}{2}\times 20\times {\omega }^2$

${\omega }^2=100$

$\omega =10rad/sec$

$2\pi f=10rad/sec$

$f=\frac{10}{2\pi }rad/s$

We know that $1min=60sec$

$1sec=\frac{1}{60}min$

So, the angular frequency per minute is

$f=\frac{10}{2\pi /60}=\frac{10\times 60}{2\pi }=\frac{300}{\pi }rad/min$

The correct option is D.