Also why do they usually only allow aluminum bats in children's organized play.
Aluminum bats (not actually made of aluminum) are used for youth play because wood bats are usually too heavy for most kids to swing. The lighter weight metal makes the bat easier to swing and kids can hit the ball much harder and farther. They do pose a problem because as they are made better and better to hit the ball harder and faster, there is less reaction time for the fielders, and many kids have been killed/injured by balls hit from aluminum bats. They actually use aluminum bats all the way up through college, although I'm fairly certain that wood bats are allowed in college and high school. The main problems with wood bats are that they're heavy and they can break fairly easily. I usually play with a metal bat, but I hit with a wood bat a lot too, because wood is the traditional bat of the game.
Goodness! Sometimes I wonder if the people answering these questions have ever played baseball. WOOD BATS IN THE PROS ARE NOT NEARLY AS GOOD AS ALUMINUM BATS AND THAT IS WHY THE PROS CAN'T USE THEM!! Sorry, alright, aluminum bats are much lighter than wood bats (someone got that part right). Aluminum bats have a much larger sweet spot than wood bats do. In an aluminum bat, the sweet spot is sometimes up to 5-7 inches or so while on a wooden bat, the sweet spot is maybe 2-3 inches. In an aluminum bat, the elastic properties allow much more give in the wall and then the wall bounces back into place giving the bat a TON more pop. Children use aluminum bats because of the reasons above. They are lighter, easier to hit the sweet spot, and more pop. It takes a lot of skill to use a wooden bat as aluminum bats are much more livlier than wood. If pros used aluminum, you would see a ton more home runs and the balls would be flying off of the bats at a much, much greater speed.
Aluminum bats are more durable and cost effective since they don't break like wood. But, they can be dangerous as they have a higher exit speed. There is a controversy as to whether aluminum is more dangerous than wood. I believe aluminum is more dangerous after reading a study by some researchers at Brown University. So, I encourage my son to use wood and will encourage other boys to use wood when I coach this year (9-10 year olds). Even if it's not conclusive, I don't see why we should risk it.
The ball will go equally as far if hit in the sweet spot on either bat. Aluminum bats have larger sweet spots so the chances of hitting a ball well are increased. That is why they are outlawed in MLB, some's D1's and a few juco conferences. This is to include all of professional baseball as well as most collegiate summer leagues. The fact of the matter is determined by bat speed. The can hit a baseball witha concrete bat and it will go just as far as an aluminum one if you generated the same bat speed with both.
Aluminum bats are lighter, and thus easier to swing. Aluminum lasts longer than wood since they don't break, except in extreme conditions. A youth league will use aluminum because its more cost effective. Two or three aluminum bats can last a whole team an entire season. Wood bats, especially inexpensive ones will break quickly. Aluminum would be too dangerous for pros to use since their strength is so much greater than other players. Pitchers and third basemen would get injured much more often if balls were hit with aluminum. I play adult baseball and love the sound of the wood, but unless all the other players are willing to give up their aluminum, I can't give up the advantage that it gives compared to wood.