# Calculate the rotational inertia of a wheel that has a kinetic energy of 11.7 kJ when rotating at...

## Question:

Calculate the rotational inertia of a wheel that has a kinetic energy of 11.7 kJ when rotating at 459 rev/min.

## Rotational kinetic energy:

The rotational kinetic energy is the energy of a rotating body. The rotational kinetic energy is given as,

{eq}RKE = 0.5\ I\omega^2 {/eq}

This energy is rotational equivalent to the kinetic energy of the object in the linear motion.

Given:

{eq}E = 11.7\ kJ\\ \omega = 459\ rev/min = 48\ rad/s\\ {/eq}

Let the inertia be I

Then by the formula of the rotational kinetic energy,

{eq}E = 0.5\ I\omega^2\\ 11700 = 0.5\times I\times 48^2\\ \boxed{\implies I = 10.15\ kgm^2}\\ {/eq}