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## Homework Statement

A 75 g, 30-cm-long rod hangs vertically on a frictionless, horizontal axle passing through its center. A 10 g ball of clay traveling horizontally at 2.5 m/s hits and sticks to the very bottom tip of the rod. To what maximum angle, measured from vertical, does the rod (with the attached ball of clay) rotate?

I know the answer should be 67 degrees but I'm not getting that.

m=mass of clay M=Mass of rod

L=length of rod v=initial velocity of clay ball

## Homework Equations

Conservation of Angular momentum: mv(L/2)=Iw

Conservation of Energy: 1/2 Iw^2=mgh

## The Attempt at a Solution

Using center of mass I can determine that the center of mass of the rod+clay system is:

[(0.15)(0.075)+(0.01)(0.3)]/0.085=0.1676

The moment of inertia should equal the moment of inertia of the rod plus the moment of inertia of the ball of clay:

ML^2/12 + m(L/2)^2=0.0007875

Now I can solver for w:

mv(L/2)=Iw

4.76=w

Now I can use conservation of energy:

1/2 Iw^2=(M+m)gh

1/2 Iw^2=(M+m)g(0.1676-0.1676coso)

20.6=o