Physics - Rotation Question with Solution | TestHub

Given kinetic energy $K=500$ J and angular frequency $f=5$ Hz.

Angular velocity $\omega =2\pi f=2\pi \times 5=10\pi$ rad/s.

The rotational kinetic energy is given by $K=\frac{1}{2}I{\omega }^2$.

Substituting the values:

$500=\frac{1}{2}I(10\pi {)}^2$

$500=\frac{1}{2}I(100{\pi }^2)$

Given ${\pi }^2=10$:

$500=\frac{1}{2}I(100\times 10)$

$500=500I$

$I=1{\text{ kg m}}^2$

Answer: $1{\text{ kg m}}^2$