Trigonometry class

Question

A truck with 44-in.-diameter wheels is traveling at 50 mph.

How many revolutions per minute do the wheels make?  rpm 

What is the angular speed of the wheels in radians/min?  rad/min

Answer 1

44"dia

d*pi=circumference=

138.23"

50mph=5/6mpm=5/6*5280=4400fpm*12=52,800"/m

52,800/138.23=381.972rpm

381.972rpm=137,510degrees/m

/ 57.296

=2400rad./m

Answer 2

The distance for one revolution is the circumference of the wheel, which is pi*diameter. In this case, that is approximately 138.23 inches or 11.52 feet.

A car that travels 50 miles per hour travels 5280(50) = 264000 feet per hour.

Divided 264000 feet by 11.52 feet to get the number of revolutions per hour.

264000/11.52 is approximately 22916.67.

Now since there are 60 minutes in an hour, divide 22916.67 by 60 to get revolutions per minute. Therefore the wheel makes 381.9445 or approximately 382 revolutions per minute.

One revolution is 2pi radians. Multiply that by 382 revolutions and the angular speed is approximately 764pi radians/minute