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 meansfor storing energy in the form of rotational kinetic energy and are being considered as a possible alternative to batteries in electriccars. The gasoline burned in a 207-mile trip in a typical midsize car produces about 4.25 x 10^9 J of energy. How fast would a 40.5-kgflywheel with a radius of 0.221 m have to rotate to store this much energy? Give your answer in rev/min.

Answer 1

First, let's calculate the moment of inertia of the disk:

$\begin{gathered} I_z=\frac{1}{2}mr^2\\ \\ I_z=\frac{1}{2}\cdot40.5\cdot0.221^2\\ \\ I_z=0.989 \end{gathered}$

Now, we can use the formula below for the rotational kinetic energy:

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

Using the given energy, let's solve for the angular velocity:

$\begin{gathered} 4.25\cdot10^9=\frac{1}{2}\cdot0.989\cdot w^2\\ \\ w^2=\frac{4.25\cdot10^9}{0.4945}\\ \\ w^2=8.5945\cdot10^9\\ \\ w=9.27\cdot10^4\text{ rad/s} \end{gathered}$

Converting this velocity to rev/min, we have:

$w=9.27\cdot10^4\text{ rad/s}=9.27\cdot10^4\cdot\frac{60}{2\pi}\text{ rev/min}=88.52\cdot10^4\text{ rev/min}$