Question

A wheel is rotating at a rate of $1000rpm$ and its kinetic energy is ${10}^{6}J$. Determine the moment of inertia of the wheel about its axis of rotation.

• A. $180kg{m}^2$
• B. $1800kg{m}^2$
• C. $18kg{m}^2$
• D. $0.180kg{m}^2$

Answer 1

The correct option is A $180kg{m}^2$

Given the rate of rotating of wheel $=1000rpm=1000\times \frac{2\pi }{60}rad/sec$

$=\frac{100\pi }{3}rad\sec$

also, kinetic energy of the wheel $=\frac{1}{2}I{\omega }^2={10}^6$

$\Rightarrow \frac{1}{2}\left(I\right)(\frac{100\pi }{3}{)}^2={10}^6$

$\Rightarrow \frac{1}{2}\left(I\right)\left(\frac{{10}^4\times {\pi }^2}{9}\right)={10}^6$

$\Rightarrow I=180kg{m}^2$