What is his angular​ speed, in revolutions per​ hour?

Question

A rider in a road bike race had an average linear speed of ​39.975 km/hr. The wheel of his bicycle had a diameter of 66cm. What is his angular​ speed, in revolutions per​ hour?

Answer 1

This type of question is approached most easily using a technique called dimensional analysis.

In essence, we will start with the linear speed, expressing it as a fraction, and continue to multiply by conversion fractions = to 1, using the units to decide which fractions to use. Because we are converting from a linear speed to an angular speed, the critical fraction will be 1 revolution / 2πr :

39.975 km / 1 hr · 10,000 cm / 1 km · 1 revolution / 66π cm ≈ 1,928 revs / hr

Answer 2

1) Convert 39.975 to centimeters

2) Divide 1) by 66, This number of revolutions / hr

3) Multily 2) by 360°. This is angular speed / hr