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 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. (Wink)