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

Answer:

$N=285711.106\,rpm$

Explanation:

Given:

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

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:

$KE=\frac{1}{2} I.\omega^2$.................................(1)

&

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

where:

I=moment of inertia

$\omega$= angular velocity in radian per second

putting respective values in eq. (2)

$I=12\times 0.32^2$

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

Now, from eq. (1)

$E=\frac{1}{2} \times I.\omega^2$

$1.1\times 10^9=1.2288\times \omega^2$

$\omega=29919.5971 \,rad.s^{-1}$

∵    $\omega=\frac{ 2\pi.N}{60}$

$N=\frac{29919.5971\times 60}{2\pi}$

$N=285711.106\,rpm$