A truck with 20 inch diameter wheels is traveling at 45mi/hr Find the angular speed of the wheels in rad/min,*hint* convert miles to inches & hours to minutes:
rad/min

How many revolutions per minute do the wheels make?
rpm

Show your work pl

A wheel with a 20 in diameter has a circumference of 2π*(20 in) = 40π in.

For every 40π in traveled, a wheel makes one complete revolution, or turns an angle of 2π rad.

We need to convert from in to mi: there are 12 in to 1 ft, and 5280 ft to 1 mi, and so there are 12*5280 = 63,360 in to 1 mi.

We also need to convert h to min: there are 60 min to 1 h.

So we have an angular speed of

(45 mi/h) * ((2π)/(40π) rad/in) * (63,360 in/mi) * (1/60 h/min) = 2376 rad/min

As mentioned before, there are 2π rad to 1 rev, so

(2376 rad/min) * (1/(2π) rev/rad) ≈ 378.152 rev/min

(where rev/min is equivalent to rpm)

1

step-by-step explanation:

it's the only multiple of both and the least