Question

A flywheel is a solid disk that rotates about an axis that is perpendicular to the disk at its center. Rotating flywheels provide a means for storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electric cars. The gasoline burned in a 309-mile trip in a typical midsize car produces about 2.96 x 109 J of energy. How fast would a 10.1-kg flywheel with a radius of 0.437 m have to rotate to store this much energy? Give your answer in rev/min.

Answer 1

Answer:

$\dot n = 748178.306\,rpm$

Explanation:

A flywheel stores mechanical energy in the form of rotational kinetic energy:

$K = \frac{1}{2}\cdot I \cdot \omega^{2}$

The expression is simplified by considering the flywheel as a solid disk:

$K = \frac{1}{4}\cdot m\cdot r^{2}\cdot \omega^{2}$

The final speed of the flywheel is:

$\Delta E = \frac{1}{4}\cdot m \cdot r^{2}\cdot \omega^{2}$

$\omega = \sqrt{\frac{4\cdot \Delta E}{m\cdot r^{2}} }$

$\omega = \frac{2}{r}\cdot \sqrt{\frac{\Delta E}{m} }$

$\omega = \frac{2}{0.437\,m}\cdot \sqrt{\frac{2.96\times 10^{9}\,J}{10.1\,kg} }$

$\omega \approx 78349.049\,\frac{rad}{s}$

The final speed in revolutions per minute is:

$\dot n = \frac{60\cdot \omega}{2\pi}$

$\dot n = \frac{60\cdot (78349.049\,\frac{rad}{s} )}{2\pi}$

$\dot n = 748178.306\,rpm$