Question

A rotating heavy wheel is used to store energy as kinetic energy. If it is designed to store 1.00 x 106 J of kinetic energy when rotating at 64 revolutions per second, find the moment of inertia (rotational inertia) of the wheel. (Hint: Start with the expression for rotational kinetic energy.)

Answer 1

We know,
`1\ rpm = (2\pi)/(60) \ rad/s` .

`64\ rpm\ is = (2\pi)/(60)* 64\ rad/s\\\\= (32\pi)/(15)\ rad/s`

We know, kinetic energy is given by :

`K.E = (I\omega^2)/(2)\\\\I = (2(K.E))/(\omega^2)\\\\I = (2* 10^6)/((32)/(15)* \pi)\\\\I = 298415.52 \ kg \ m^2`

Hence, this is the required solution.