Question

You are biking down a hill at 24mi/hr. What is the angular speed in radians per second, of your 27-inch-diameter bicycle wheel?

Answer 1

Given :

The speed of bike = 24 mi/hr

The diameter of bicycle wheel = d = 27 inches

                                                   = d = 0.000426 mile

To Find :

The angular speed of bicycle in rad per sec

Solution :

∵  linear speed = 24 mi/hr

                         = 0.00667 mi/sec

Radius of wheel = $\dfrac{Diameter}{2}$

                        r = $\dfrac{d}{2}$

                          =  $\dfrac{ 0.000426}{2}$ = 0.000213 mile

So, Angular speed = $\dfrac{linear speed}{radius of wheel}$

                               = $\dfrac{l}{r}$

                              = $\dfrac{0.00667}{0.000426}$

                              = 15.65 rad per sec

Hence, The angular speed of bicycle is 15.65 rad per sec   Answer