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 310-mile trip in a typical midsize car produces about 1.10 109 J of energy. How fast would a 12-kg flywheel with a radius of 0.32 m have to rotate to store this much energy? Give your answer in rev/min.

Answer 1

`N=285711.106\,rpm`

Step-by-step explanation:

Given:

energy to be stored in a flywheel,
`E=1.1* 10^9\,J`

mass of the flywheel,
`m=12\,kg`

radius of the flywheel,
`r=0.32\,m`

To find:

rotational speed, N=?

We know that kinetic energy of a flywheel can be given by:

`KE=(1)/(2) I.\omega^2`.................................(1)

&

`I=m.r^2`......................................(2)

where:

I=moment of inertia

`\omega`= angular velocity in radian per second

putting respective values in eq. (2)

`I=12* 0.32^2`

`I=1.2288 \,kg.m^2`

Now, from eq. (1)

`E=(1)/(2) * I.\omega^2`

`1.1* 10^9=1.2288* \omega^2`

`\omega=29919.5971 \,rad.s^(-1)`

∵
`\omega=( 2\pi.N)/(60)`

`N=(29919.5971* 60)/(2\pi)`

`N=285711.106\,rpm`