# The bicycle wheel has a radius of 40 cm. How fast does the cyclist travel if the wheel

March 28, 2021 | education

| **The bicycle wheel has a radius of 40 cm. How fast does the cyclist travel if the wheel is making 120 rpm? What is the period of rotation of the wheel?**

Given:

r = 40 centimeters = 0.4 meters – the radius of the bicycle wheel;

n = 120 rpm – wheel speed.

It is required to determine the speed of the cyclist v (m / s) and the period of rotation T.

For the circumference of the wheel is equal to:

C = 2 * pi * r = 2 * 3.14 * 0.4 = 2.5 meters.

In 1 minute, the wheel travels a distance equal to:

S = n * C = 2.5 * 120 = 300 meters.

Then its speed is equal to:

v = S / t = 300/60 = 5 m / s.

The period is:

T = 60 / n = 60/120 = 0.5 s.

Answer: the speed of the cyclist is 5 m / s, the period of rotation of the wheel is 0.5 seconds.