Question

A wheel of mass of 30 kg and radius 1.5 m is rotating with an angular velocity of 280 rpm.
Calculate the work that must be done to bring the wheel to rest in 15 seconds. What is the
required average power?

Answer 1

A wheel of mass of $30\,\mathrm{kg}$ and radius $1.5\,\mathrm{m}$ is rotating with an angular velocity of 280 rpm. Calculate the work that must be done to bring the wheel to rest in 15 seconds. What is the required average power?

$w = 280\, \text{rpm} = 280$ revolutions per minute

Angular velocity is measured in International System of Units (SI) in $\frac{\text{rad}}{\text{second}}$:

$$w = 280\, \text{rpm} = 280\,\frac{1}{\text{minute}} \times \frac{2\pi}{60} \frac{\text{rad}}{\text{second}} \times 60\,\text{seconds} = 2\pi \times \frac{280}{60} \frac{\text{rad}}{\text{second}}$$

The energy conservation law:

$$\frac{Iw^2}{2} = A$$

I – moment of inertia of wheel

A – work that must be done to bring the wheel

For wheel

$$I = m r^2$$

m – mass of wheel

r – radius

Therefore:

$$A = \frac{m r^2 w^2}{2} = \frac{30\,\mathrm{kg} (1.5\,\mathrm{m})^2 \left(280 \frac{2\pi}{60}\right)^2}{2} = 29017\,\mathrm{J}$$

The average power equals:

$$P = \frac{A}{t} = \frac{29017\,\mathrm{J}}{15\,\mathrm{s}} = 1934\,\mathrm{W}$$