Posted by Samantha on Thursday, June 2, 2011 at 10:57pm.
A penny farthing is a bicylce that was popular between 1870 and 1890. As the drawing shows, this type of bicycle has a large front wheel (R=1.20m) and a smaller rear wheel (r=.34m). A bicyclist, riding at a linear velocity of 12.5 m/s, applies the brake and produces an angular deceleration of 2.0 rad/s^2 in the front wheel. a)What is the angular displacement of the front and rear wheels? b)What is the average angular deceleration of the rear wheel during this motion?

Physics  Henry, Friday, June 3, 2011 at 9:12pm
a. Cf = pi*D = 3.14 * (2*1.2) = 7.54m =
Circumference of front wheel.
Vf=12.5m/s * 6.28rad / 7.54m=10.4rad/s.
= Angular velocity of front wheel.
Vf^2 = Vo^2 + 2ad = 0,
d = (Vo)^2 / 2a = (10.4)^2 / 4 = 27.04m = displacement of front wheel.
V = Vo + at = 0,
t = Vo / a = 10.4 / 2 = 5.2s = time
required to stop.
a=(VfVo)/t = 36.7 / 5.2 = 7.06m/s^2.
d = (Vo)^2 / 2a = (36.7)^2/14.12 =
95.4m = displqcemnt of rear wheel.
Cr = 3.14 * (2*0.34) = 2.14m = circumference of rear wheel.
Vr=12.5m/s * 6.28rad/2.14m = 36.7rad/s
= Angular velocity of rear wheel.
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