Question

A bus is designed to draw its power from a rotating flywheel that is brought up to 3000 rpm by an electric motor. The flywheel is a solid cylinder of mass 2000 kg and diameter 1 m. If the bus requires an average power of 20 kilowatts, how long will the flywheel rotate?
620 s

830 s

980 s

1,200 s

2,500 s

Answer 1

To solve this problem we will apply the concept of rotational kinetic energy. Once this energy is found we will proceed to find the time from the definition of the power, which indicates the change of energy over time. Let's start with the kinetic energy of the rotating flywheel is

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

Here

I = moment of inertia

$\omega =$ Angular velocity

Here we have that,

$\omega = 3000\frac{rev}{min}(\frac{2\pi rad}{1rev})(\frac{1min}{60s})$

$\omega = 314.159rad/s$

Replacing the value of the moment of inertia for this object we have,

$E_r = \frac{1}{2} (\frac{MR^2}{2})\omega^2$

$E_r = \frac{1}{2} (\frac{2000(0.5)^2}{2})(314.159)^2$

$E_r = 1.233698*10^7J$

The expression for average power is

$P = \frac{E_r}{\Delta t}$

$\Delta t = \frac{E_r}{P}$

$\Delta t = \frac{1.233698*10^7}{20*10^3}$

$\Delta t = 616.8s \approx 620s$

Therefore the correct answer is 620s.