Question

The radii of the sprocket assemblies and the wheel of the bicycle in the figure are:
4 inches,
2 inches,
and 14 inches respectively.

If the cyclist is pedaling at a rate of 1 revolution per second, find the speed of the bicycle in (a) feet per second and (b) miles per hour.

Any hints on what I should do?

Answer 1

let distance s=r(B), where r=radius,B=angle in rad
velocity v=ds/dt= w(r), where w = angular speed in rad/s
w1 = 1 revolution/sec = 2Pi (rad/s)
by ratio and proportion:
v1=v2 so that:
w1*r1 = w2r2
w2 = w1 * r1/r2 = 2w1 = 4Pi (rad/s)
w2 = w3 (angular velocity of the rear wheel)
v3 = w3 * r3 = 4pi * 14 (inch/s) = 14.66 ft/sec ans.....a)
v3 = 14.66 ft/sec(1 mile/5280 ft)( 3600 sec/h)
= 9.99 mph or approximately 10 mph ........ans......b)