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 445-mile trip in a typical midsize car produces about 4.66 x 109 J of energy. How fast would a 19.7-kg flywheel with a radius of 0.351 m have to rotate to store this much energy

Answer 1

`8.37*10^5` rpm

Step-by-step explanation:

Given that rotational kinetic energy =
`4.66*10^9J`

Mass of the fly wheel (m) = 19.7 kg

Radius of the fly wheel (r) = 0.351 m

Moment of inertia (I) =
`(1)/(2) mr ^2`

Rotational K.E is illustrated as
`(K.E)_(rt) = (1)/(2) I \omega^2`

`\omega = \sqrt{(2(K.E)_(rt))/(I) }`

`\omega = \sqrt{(2(KE)_(rt))/(1/2 mr^2) }`

`\omega = \sqrt{(4(K.E)_(rt))/(mr^2) }`

`\omega = \sqrt{(4*4.66*10^9J)/(19.7kg*(0.351)^2) }`

`\omega = 87636.04`

`\omega = 8.76*10^4 rad/s`

Since 1 rpm =
`(2 \pi)/(60) rad/s`

`\omega = 8.76*10^4((60)/(2 \pi))`

`\omega = 836518.38`

`\omega = 8.37 *10^5 rpm`