Baseball physics question: corking the bat versus using a lighter bat vs choking up on the handle?

Question

which one would be the best in terms of delivering power to the ball?

I've always wondered why players who cork their bats don't just use a shorter bat in the first place, since the end of the end bat essentially becomes useless. Also, holding the bat higher up on the handle effectively is the same thing as using a shorter bat.

Answer 1

It has to do with inertia and bat speed.
The longer the bat, the faster the center of mass of the bat will be moving given the same torque. This creates a higher angular momentum since the moment of inertia approx 1/2*m*L^2
the moment increases linearly w/r/t mass, but exponentially w/r/t length. The cork creates a longer L with less mass than pure hardwood.

Choking up on the bat puts the torque closer to the center of mass, and therefore generates less angular momentum.

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