The front wheel of a motorcycle has a 16 inch radius. Find the angle in Radion, through which the wheel rotates in four seconds if the motorcycle is traveling at a speed of 45 mph?

Answer 1

First let's convert the linear speed of 45 mph to a the speed that one of the tires is rotating at.

We are using the equation:

v = r ω which is the speed that each of the wheels of the motorcycle is rotating at.

where v = linear velocity in Mil/hr (or mph) , r = radius of one wheel, ω = angular velocity rad/sec

45 Mile 1 hr 1 min 5280 ft 12 in 1 rad

== * == * === * ==== * === * === = 49.5 rad / sec = ω

1 hr 60 min 60 sec 1 Mile 1 ft 16 in

Now we want to know the radians after 4 seconds so we can just multiply ω by 4 seconds

49.5 rad / sec * 4 sec = 198 radians

Hope this helps

Answer 2

4 seconds * 1 minute 1 hour 45 miles 5280 feet 12 inches

=========== * =========== * ============== * ============== * ===========

60 seconds 60 min 1 hour 1 mile 1 foot

which is 3168 inches

The perimeter (a.k.a. circumference) of the wheel is pi*32 inches

3168 inches in terms of ROTATIONS,by dividing by this perimeter, is 3168/(pi*32) = 99/pi

So in 4 seconds, the wheel makes 99/pi rotations which is 3168 inches

Note that (99/pi)(32*pi) = 3168

Each rotation is 2*pi radians , so 2*pi * (99/pi) = 198 radians