Is a heavier baseball bat better than a lighter one? Baseball season is coming up and I would like to know which bat is best for me. I think the heaviest bat I can swing good would be the best, but my brother thinks the lightest bat would be the best so you can swing it as fast as you can. I said if you have a bat too light; A, you won't hit the ball far, and B, it will hurt your hand. I think the heavier bat would be better because it has a greater inertia. Who is right? I would like to hit the ball farther and I don't want my hand to hurt.
 A: Well we can look at momentum here, since you essentially transfer momentum from your bat to the ball
p=mv
Where p is the momentum
m is the system mass (In this case we can just consider baseball since your arm's mass don't change I presume)
v is the velocity
Let's just assume that momentum is conserved here. So if you pick a bat that is TOO light, you end up with a small m, and realistically you can say there is a v that you probably won't pass due to air resistance and how fast your arms can move and other factors. So a small m, but not a large increase in v results in a small p, so your momentum will end up being small.
For higher mass however, you are not going to be swinging as fast. But that is made up by the mass of your bat. Too high of a mass however, and you won't be able to swing the bat fast enough to react to the ball.
So there is actually a wee range where the amount of mass and the velocity you'll swing at gives out the maximum momentum. It is capped at the maximum velocity you can swing with a lower mass, and the highest mass to which you can swing the bat sufficiently fast. 
As to how much the bat will hurt your hand, it is usually the vibration of the bat that ends up hurting your hand. And yes, higher mass means less vibration due to inertia. 
So with these two, I would pick the highest mass bat I can swing at a sufficient velocity
A: One physics-like way to think about this is to consider the end cases: what about an incredibly light bat? Incredibly heavy bat? Neither is likely to be great: nobody bats with a soda straw or steel I-beam. 
So “best” must be somewhere in the middle. 
Now we need to narrow it down for you and your muscles, reactions, skills, etc. 
On the heavy end, if you can’t move it fast enough to routinely make contact, it’s too heavy. Find the heaviest you can hit pitches with and set it aside. 
Control also matters, but so does putting power in. Find the lightest that feels like you can control and really get some meet into. 
Now take those two “just barely” bats and compare them. Optimum is likely to be about half-way in between. That’s where you get a mix of power and control. 
