Question

A truck with 32-inch diameter wheels is traveling at 60 mi/h. Find the angular speed of the wheels in rad/min. How many revolutions per minute do the wheels make?

Answer 1

Angular Speed = (final angle - initial angle)/(time)
Angular Speed = ω = (ΔФ)/Δ.t [ Ф in Radian and t in second]

To ease calculation let's convert 60 mi/h into in/second

a) 1 mi = 63,360 in   and 1 hour = 3600 seconds
b) 60 mi/h EQUIVALENT to  (60 x 63,360)/3600
c) Speed of the truck in in/s = 1,056 in/s
d) Circumference of wheel = 2π.R = 2π.(16) = 32.π
e) Time need to travel 32.π (=100.53 in) → 100.53/1,056 = 0.095 second
f) Δ.Ф (after one revolution) = 2π - 0 → Ф = 2π
g) Now we can calculate ω, the angular speed:
ω =(ΔΘ)/Δ.t  → 2π/0.095 → w = 66.14 Radian/Second