Question

Precalculus angular speed problem:
A car is moving at a rate of 65 miles per hour and the diameter of its wheels is 2.5 feet.

a) Find the number of revolutions per minute the wheels are rotating.

b) Find the angular speed of the wheels in radians per minute.

Answer 1

a) 732 rpm

b) 4599 radians per minute

65 mph is 105 kph (1 mi = 1.609 km)

Because we have to find the revolutions per minute I changed the speeds to kilometres per minute, so if the speed is per hour, I divide by 60 to find the speed per minute in km.

The car is travelling 1.75 km per minute

For the wheel I needed the circumference, so I multiplied the diameter by pi (3.14) and then by 0.3048 to convert it into metres which was 2.39m

Each time the wheel spins once the car travels 2.39m and the wheel has done 1 revolution.

So if the car travels 1.75 km a minute (1750m) the wheel has had to rotate 1750/2.39 times to cover that distance which is 732, so thats 732 revolutions and since the distance is covered in a minute at that speed it's 732 rpm.

As for the radians per minute, 1 full rotation = 2 x pi (3.14) so all you do is multiply 732 by 2pi.

Hopefully you understand it.

Answer 2

Thanks so much for you help :) One question though, I followed through with your steps, but when I multiplied the diameter by pi and by .3048, I got 4.78, not 2.39. Am I doing something wrong?

Answer 3

Oh, never mind, I thought 2.5 was the radius and not the diameter. You were right.