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a) The arm is treated as an ideal pendulum, with all of its mass concentrated as a point mass at the free end.

b) The arm is treated as a thin rigid rod, with its mass evenly distributed along its length.

**Relevant equations:**

mvL = (I

_{rod}+ I

_{proj})ω

_{f}

E

_{i}= E

_{f}

There might be a simpler equation, though.

Here's how I tried to solve it:

First, I solved for ω

_{f}by substituting the moments of inertia. I ended up with this:

ω

_{f}= mvL / [(1/3)mL

^{2}+ mL

^{2}] , which became:

3mv/(mL+3m).

Then, I used energy conservation, resulting in this equation:

1/2(I

_{rod}+ I

_{proj})ω

_{f}

^{2}+ mg(L/2) = mg(L-L cos θ) + mg{L/2 + [(L/2) - (L/2 cos θ)]}

I cancelled the masses, yet I still got it wrong. I can't seem to find a way to simplify the equation! All the above is for part B. If I can get part B, I can get A, since it's the same, but with one less moment of inertia to worry about. All help is appreciated.

I'm sorry if this post isn't perfect. This is my first post here.