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?

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  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.

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