a cyclist is ridi g a bicycle whose wheels have a radius of

a cyclist is ridi g a bicycle whose wheels have a radius of 10 inches. suppose the wheels turn at a rate of 190 revolutions per minute.

a) find the angular speed of the wheels in radians per minute

b) find the speed of the cyclist in miles per hour. (use the fact that 1mi=5280ft)

Solution

190 rpm

=190*2pi radians/1 minute (1 rotation = 2pi radians)
so, angular speed is 380pi radians/minute=1194.29 radians/minute


b)
V=rw
V=10*380pi=3800pi=11932 *1/5280*1/12*1/60=3.14*10^-3 miles/hour