If you balance a pencil of length $d$ on its tip, and let it fall, how do you compute the final velocity of its other end just before it touches the ground?
(Assume the pencil is a uniform one dimensional rod)
Answer
The amount of kinetic energy in the pencil just before it touches the ground is equal to the gravitational potential energy it lost while falling. That quantity is easy to compute, being simply m*g*h, where h=d/2 (the center of mass of the pencil started at height d/2 and ends at height 0). If we assume the tip of the pencil hasn't moved (this becomes a much more complex problem if there is friction between the tip and the table, etc) then all of that energy is now rotational kinetic energy, which is equal to 1/2*I*ω. I is the moment of inertia (1/12*m*d^2) and ω is the angular velocity. You know d, the mass terms cancel out, and once you solve for angular velocity you can determine linear velocity of the end.
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