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Question

A cyclist is riding a bicycle whose wheels have a diameter of 24 inches. Suppose he is traveling at 26 miles per hour. (A useful fact: =1mi5280ft.)

(a) Find the angular speed of the wheels in radians per minute.

(b) Find the number of revolutions the wheels make per minute.

Answer 1

theta =Θ=s/r

The basic equation for this problem is relatively simple. Using dimensional analysis, we convert the linear speed in mi/hr. to radians /min. and finally to revolutions/sec.

›dΘ/dt = (1/r)ds/dt =(1/12 in)*26 mi./hr.*5280 ft./mi.*12 in./1 ft.*1 hr./60 min. = 2288 radians / min.

2288 rad./min * 1 rev./2∏ rad. = 364.15 rev./min = 364.15 rev/min * 1 min/60 sec. = 6.07 rev per second

Answer 2

Speed = 26mi/hr

=2288 ft/min

Diameter = 24 in

Radius = 12 in = 1 ft

(a)

ω=V/r

= 2288/(1) = 2288 rad/min

(b) ω = 2288/(2π) = 364.15 rev/min