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 1.8 m, so the radius of rotation of the balls is 0.9 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 mass 0.14 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 6 m/s, and the wheel is rotating counterclockwise with angular speed 0.08 radians/s.

5.33

radians/s

Explanation / Answer

b)

Iballs= 8*mr^2 =8*0.7*0.9^2 = 4.54 kg*m^2

balls= 0.08rad/s

R=rsin45 = 0.9sin45 = 0.6364m

M=0.14kg

clay= V/R = 6.0/0.6364= 9.43 rad/s

Li = Iballs*iballs + Iclay* iclay = 4.54*0.08 + MR^2*clay2= 0.3632kg*m^2/s +0.14*0.6364^2*(9.43rad/s)^2 = 0.8979 kg*m^2/s

c)

By law of conservation of angular momentum

Lf=Li

Lf= 0.8979kg*m^2/s

d)

Lf=Li

Iballs*fballs + Iclay* fclay = 0.8979

(Iballs+ Iclay)*f(balls+clay) = 0.8979

(4.54kg*m^2+0.14*0.6364^2)*f(balls+clay) = 0.8979

f(balls+clay) =0.195rad/s

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