A bicycle is moving at 8.8 m/s. What is the angular speed of its tires if their radius is 39 cm?

Answer 1

You know the radius of the tire, so you can figure out its circumference (C=d*pi=2r*pi). For each revolution of the tire, it moves 1 full circumference along the ground. In this case, the circumference is, C = 2*0.39m*pi = 2.45m

So, to cover the distance of 8.8m in a second, the angular speed is (8.8 m/s) / (2.45 m/rev) or 3.59 rev/s. Since 2pi radians = 1 revolution, you can also express it as 7.2pi rads/s