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=(1)/(2)mr^2\\ \\ I_z=(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=(1)/(2)I\omega^2`

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

`\begin{gathered} 4.25\cdot10^9=(1)/(2)\cdot0.989\cdot w^2\\ \\ w^2=(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(60)/(2\pi)\text{ rev/min}=88.52\cdot10^4\text{ rev/min}`