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
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:
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:
Now I can use conservation of energy: