Question

a rider in a road bike race had an average linear speed of 40.253 km/hr. the wheel of his bicycle had a diameter of 67 cm. what is his angular speed, in revolutions per hour?
the angular speed is approximately □ revolutions per hour.
(do not round until the final answer. then round to the nearest integer as needed.)

Explanation:

Step1: Convert linear speed to centimeters per hour

Given linear speed \(v = 40.253\) km/h.
Since \(1\) km \(= 100000\) cm, then \(v=40.253\times100000 = 4025300\) cm/h.

Step2: Find the circumference of the wheel

The diameter of the wheel \(d = 67\) cm. The circumference \(C=\pi d\). Using \(\pi\approx3.1416\), \(C = 3.1416\times67=210.4872\) cm.

Step3: Calculate the angular speed (in revolutions per hour)

The formula for angular speed \(\omega\) (in revolutions per hour) is \(\omega=\frac{v}{C}\).
Substitute \(v = 4025300\) cm/h and \(C = 210.4872\) cm.
\(\omega=\frac{4025300}{210.4872}\approx19123.7\)

Answer:

\(19124\)