Posted by monic on Thursday, November 29, 2012 at 12:11am.
angular velocity:
1 rotation = 2π radians
45 rotations = 90π radians
angular velocity = 90π radians/minute
Since circumference is linear and we are told the radius of the pedal sprocket is twice that of the wheel sprocket, for every turn of the pedal, the wheel will make 2 rotations
So in 1 minute the wheel turns 90 times
circumference of wheel = 2π(13) = 26π inches
distance covered in 1 minute = 90(26π) = 2340π inches
speed = 2340π inches/min
there are 12(5280) inches in 1 mile
and 60 minutes in 1 hour
speed = 2340π(60/(12(5280)) miles/hr
= appr 7.0 mph
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