Question

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?

Answer 1

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=(Vf-Vo)/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.