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Angular Velocity & Speed of Tip

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A long, thin rod of mass M and length L is standing straight up on a table. Its lower end rotates on a frictionless pivot. A very slight push causes the rod to fall over.

(A) As it hits the table, what is the angular velocity of the tip of the rod?

(B) What is the speed of the tip of the rod?

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RESPONSE:
PART (A)
Step 1. The rod rotates about the fixed end from vertical to horizontal. Conservation of energy requires that PE lost = KE gained

Step 2. In this transfer, the c.g. moves downward a distance .5L. Therefore:
(1) PE lost = .5 M g L

Step 3. The moment of inertia about an axis at the end is:
(2) I = M ...

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