A point on the rim of a 6-inch diameter wheel is traveling at 88 ft/sec. What is the angular velocity of the wheel in radian per second?

Answer 1

First we should convert everything into the same units, as inches and feet don't compute well together. The diameter is 6 inches and the linear speed is 1056 inches/sec.

Now, the formula for linear speed is radius times angular speed:

v = rw

So the angular speed is linear speed divided by radius:

w = v/r

So our angular speed is 1056 / 3, or 352 radians/sec.