What is his angular speed, in revolutions per hour?

Question

A rider in a road bike race had an average linear speed of 39.388 km/hr. The wheel of his bicycle had a diameter of 68 cm.

Answer 1

2 x pi x r = distance travelled by wheel in one revolution

 

n x 2 x pi x (68/100000) = 39.388

 

n = 627197.5

 

revolution per hr = 627197.5

:)

Answer 2

One revolution on a circular path is the same as traveling the circumference in distance. With a diameter of 68 cm, the bicycle wheel has a circumference of

1 revolution = C = πd = π(68 cm) = 213.628 cm

 

The speed is given in km, and the circumference in cm, so you need to convert to a common unit. Meters (m) is a good compromise here.

(39.388 km/hr) * (1000 m/1 km) = 39,388 m/hr

(213.628 cm/rev) * (1 m/100 cm) = 2.13628 m/rev

 

Now you can divide to find the rev/hr

(39,388 m/hr) * (1 rev/2.13628 m) = your answer.