1. ## Angular Velocity?

I need to determine how many revolutions a 215/45 R18 tire makes in 1 second. I have determined that the diameter of the tire is roughly 22 inches. I'm not sure which conversions to use for this. Is angular velocity w=theta/time? I'm so confused on how to start this one

2. Angular velocity is measured in revolutions per some unit of time. For instance, your car's tachometer may measure your engine's angular velocity in RPMs, or revolutions per minute.

Take the diameter, and use this to find the circumference. Then take the speed (not provided) of the vehicle, and convert to comparable units. (You've probably been given kilometers per hour or miles per hour. You'd want to convert to inches per minute or inches per second, probably.)

Divide the linear distance covered, per time unit, by the circumference value. This will give you the number of circumferences which fit into that linear distance. Since one circumference corresponds to one revolution, this gives you the number of revolutions per time unit.

3. Hello captaintoast87
Originally Posted by captaintoast87
I need to determine how many revolutions a 215/45 R18 tire makes in 1 second. I have determined that the diameter of the tire is roughly 22 inches. I'm not sure which conversions to use for this. Is angular velocity w=theta/time? I'm so confused on how to start this one
Angular velocity is the rate of change of the angle turned, so, yes it is theta/time.

But if you want the number of revolutions per second, work it out by finding the (linear) distance travelled by the car (or whatever) per second, and dividing this by the circumference of the tyre ( $=\pi d = 69.12$ inches for a $22$ inch diameter wheel).

For example, $60$ mph = $88$ fps = $88\times12$ inches per second. So the angular speed $= \frac{88\times 12}{69.12} = 15.3$ revs per second.