My name is Mike. I am a big baseball fan (Go Washington Nationals!) so thank you for your great question "How much harder an aluminum bat would hit a ball compared to a wooden bat?"

Aluminum bats allow baseball player to hit the ball farther and faster than with a wooden bat for a few different reasons. The first reason is that a player can swing an aluminum bat about 5 to 10 miles per hour faster than a wooden bat.

The reason for this that the "balance point" of an aluminum bat is closer to the handle than for a wooden bat. The closer the balance point of a bat is to the handle, the faster a player can swing the bat. Since the player can swing the aluminum bat faster, the ball will travel farther when the player hits with an aluminum bat.

The second reason is that when an aluminum bat hits a ball, the aluminum bat will very quickly bend and compress in response to the hard ball, and then very quickly the bat will spring back to its original shape. This compress-and-spring motion causes the ball to shoot off the bat faster and travel farther than if it is hit with a wood bat. The motion is similar to jumping on a trampoline: when you land on a trampoline, the bottom of the trampoline bends against your weight, and then springs you quickly back high into the air. Wooden bats are too hard and dense to have this "trampoline motion."

And lastly, aluminum bats have a larger "sweet spot" than wooden bats do. The sweet spot is the area of the bat that causes the ball to travel the fastest and farthest. Since aluminum bats have this larger sweet spot, it is easier to hit balls that go farther and faster than it is with a wooden bat. And finally, I have attached a website that further explains a lot of what I have said. Hope this answers your question!

The amount of momentum transferred to the ball is the same; what may depend on material is the force per unit time. However, I don't know the material properties of aluminum relative to those of wood (or what kind of wood).