A device consists of eight balls each of mass 0.7 kg attached to the ends of low

Question

A device consists of eight balls each of mass 0.7 kg attached to the ends of low-mass spokes of length 1.2 m, so the radius of rotation of the balls is 0.6 m. The device is mounted in the vertical plane. The axle is held up by supports that are not shown, and the wheel is free to rotate on the nearly frictionless axle. A lump of clay with mass0.18 kg falls and sticks to one of the balls at the location shown, when the spoke attached to that ball is at 45 degrees to the horizontal. Just before the impact the clay has a speed 7 m/s, and the wheel is rotating counterclockwise with angular speed 0.20 radians/s.

(a) Which of the following statements are true about the device and the clay, for angular momentum relative to the axle of the device?

Explanation / Answer

B.

Ltoti = 8[mball r^2][wi] - mclay vclay r sin 45

As r = 0.6 m, wi = 0.20 rad/s, then

Ltoti = -0.13137 kg m^2/s k^   [into the page]

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C.

Just after the impact,

Ltotf = Ltoti

by conservation of angular momentum.

Thus,

Ltotf = -0.13137 kg m^2/s k^   [into the page]

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D.

Just after the impact,

If = 8 mball r^2 + mclay r^2 = 2.0808 kg m^2

Thus,

wf = Ltotf / If = 0.0631 rad/s, clockwise   [ANSWER]

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