With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel

Question

With axle and spokes of negligible mass and a thin rim, a certain bicycle wheel has a radius of 0.31 m and weighs 32 N. It can turn on its axle with negligible friction. A woman holds the wheel with the axle vertical while she stands on a turntable that is free to rotate without friction. The wheel initially rotates with an angular speed of 51.8 rad/s, and the turntable is initially at rest. The rotational inertia of wheel + woman + turntable about the common axis of rotation is 2.1 kg·m2. angularmomentum (a) When the woman flips the wheel 180 degrees, what will be her resulting angular speed and direction? (Up is +) (b) How much work does the woman do to flip the wheel? (c) How many times would she have to flip the wheel to burn off one Snickers candy bar? (We are assuming the human body is 100% efficient.) (250 calories) (d) How many minutes would this take if she made one flip each second?

Explanation / Answer

part A :

Weight W = mg = 32 N

mass m = 32 /9.81 = 3.26 kgs

law of conservation of momentum

I1 W1 = I2 W2

W2 = mr ^2 W1/(I2)

W2 = (3.26 * 0.31^2)* 51.8/(2.1)

W2 = 7.72 rad/s

directon is CW

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Work Done W = 0.5 I W2^2

W = 0.5 * 2.1 * 7.72^2

W = 62.57 J

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n = W1/w2 = 51.8/7.72

n = nearly 7 times

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W = 2pi/T

t = 7 * 2pi/7.72

t = 5.69 secs

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