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

`\dot n = 748178.306\,rpm`

Step-by-step explanation:

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

`K = (1)/(2)\cdot I \cdot \omega^(2)`

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

`K = (1)/(4)\cdot m\cdot r^(2)\cdot \omega^(2)`

The final speed of the flywheel is:

`\Delta E = (1)/(4)\cdot m \cdot r^(2)\cdot \omega^(2)`

`\omega = \sqrt{(4\cdot \Delta E)/(m\cdot r^(2)) }`

`\omega = (2)/(r)\cdot \sqrt{(\Delta E)/(m) }`

`\omega = (2)/(0.437\,m)\cdot \sqrt{(2.96* 10^(9)\,J)/(10.1\,kg) }`

`\omega \approx 78349.049\,(rad)/(s)`

The final speed in revolutions per minute is:

`\dot n = (60\cdot \omega)/(2\pi)`

`\dot n = (60\cdot (78349.049\,(rad)/(s) ))/(2\pi)`

`\dot n = 748178.306\,rpm`