Question

A large vehicle has wheels with

a 2-foot radius. These wheels are turning at 650 rpm. Find the linear velocity in mph.

Answer 1

A wheel with radius 2 ft has circumference 2π(2 ft) = 4π ft, and this is the distance traveled by a fixed point on the edge of the wheel as it completes one revolution. So we have

1 rev = 4π ft

1 mi = 5280 ft

1 h = 60 min

Turning at a rate of 650 rpm (rev/min), the linear velocity would then be

650 rev/min = (650 rev/min) * (4π ft/rev) * (1/5280 mi/ft) * (60 min/h)

650 rev/min = 325π/11 mi/h

650 rpm ≈ 92.82 mph