Answer to Question #160954 in Trigonometry for Samuel kassapa

Question

A bicycle with 20 inch wheels is travelling down a road at 15mi/h. Find the angular velocity of the wheel in revolutions per minute.

Answer 1

Diameter = 20 in

Radius = 10 in

v = 15 mi/hr

angular speed (ω) = ?

We use the formula:

v = ω r

Substituting,

15 mi/hr = ω * 10 in

Note that 1 mile = 63360 inches, and 1 hour = 60 min:

15 mi * (63360 in / mi) / (1 hr * 60 min / hr) = ω * 10 in

15840 in / min = ω * 10 in

ω = 15840 / 10

ω = 1584 rad/min

rev/min = ?

Note that 1 revolution = 2π. Thus,

(1584 rad/min) * (1 rev / 2π rad) = 252.2 rev/min