Math CentralQuandaries & Queries


Subject: Angular Speed
Name: Cristina
Who are you: Student

A car is moving at a rate of 50 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.

Hi Christina.

Every time the wheel turns once around, the car has moved ahead by the circumference of the tire. You know the diameter of the tire, so you can calculate the circumference from that. Let's say the circumference is C feet. The rest of the problem is really just unit conversion:

50 miles / hour = 50 x 5280 / 60 feet / minute = 4400 feet / minute

If one revolution is C feet, then 4400 feet per minute is how many revolutions per minute?

For part B, you just need to remember that each revolution is 2π radians and multiply this by the answer for part A.

Hope this helps,
Stephen La Rocque.

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