Calculate the rotational inertia of a wheel that has a kinetic energy of 24,400j when rotating at...

Question:

Calculate the rotational inertia of a wheel that has a kinetic energy of 24,400j when rotating at 614rev/min.

Rotational kinetic energy:

When the object rotates about an axis with an angular velocity then it has rotational kinetic energy.

It is given as,

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

where I is the rotational inertia of the object.

Given:

{eq}RKE = 24400\ J\\ \omega = 614\ rev/min = 64.26\ rad/s\\ {/eq}

By the formula of the rotational kinetic energy,

{eq}RKE = 0.5\ I\omega^2\\ 24400= 0.5\times I\times 64.26^2\\ \implies \boxed{I = 5.9\ kg\ m^2}\\ {/eq}