Question

A scooterist is racing at a speed of 72 km/h. If the radius of the wheel is 20 cm, find the angular speed of the wheels.

Answer 1

Step 1: Given data

Speed of the scooter, v = 72 km/h $=\frac{72\times 1000}{3600}=20\mathrm{m}/\mathrm{s}$.

Radius of wheel, r = 20 centimeters = 0.2 meter.

Let the angular speed be ω.

Step 2: Finding the value of ω

Linear speed = Angular speed × Radius

$$\begin{gathered} \mathrm{v}=\mathrm{\omega r} \\ 20\mathrm{m}/\mathrm{s}=\mathrm{\omega }\times 0.2 \\ \mathrm{\omega }=\frac{20}{0.2}=100\mathrm{rad}/\mathrm{s}. \end{gathered}$$

Therefore, the angular speed of the wheels is 100 rad/s.