Answer to Question #122404 in Mechanics | Relativity for jacob

Question

Some European trucks run on energy stored in a rotating flywheel, with an electric motor getting the flywheel up to its top speed of 350 π rad/s. One such flywheel is a solid, uniform cylinder with a mass of 640 kg and a radius of 0.914 m. (a) What is the kinetic energy of the flywheel after charging? (b) If the truck uses an average power of 7.0 kW, for how many minutes can it operate between chargings?

Answer 1

(a) The kinetic energy of the flywheel after charging is

$$E_K=\frac{I\omega^2}{2}=\frac{(mr^2/2)\omega^2}{2}=\frac{m(r\omega)^2}{4}=162\text{ MJ}.$$

(b) If the truck uses an average power of 7.0 kW, this energy will be enough for

$$t=\frac{E_K}{P}=23100\text{ s},$$

or 6.43 hours.