Re: Torque and a Baseball Bat

There are several torques involved in swinging a baseball bat. To frame the discussion a little, I need to de fine a few terms.

1) The center of mass of the bat is the usual imaginary point at which the bat will balance and it is sometimes useful to think of all the mass as being located in that one point.

2) The moment of inertia of the bat (usually denoted I) is the effective distribution of the mass for use in torque or angular momentum computation.

3) Torque only comes about from the perpendicular component of force applied to a lever arm.

Let's break the swing down to 3 time frames: BEFORE CONTACT, DURING CONTACT, AFTER CONTACT.

BEFORE CONTACT: The batter's ability to accelerate the bat up to a good hitting speed is the key to power hitting and also can be helpful in hitting for average because the batter can wait longer to judge a pitch and thus increase the likel ihood of swinging at a "good" pitch. The initial motion of the swing is typically a slight lean back toward the cat cher and then a step forward -- this produces little if any torque on the bat. The arms and hands begin to move to produce a torque on the bat to move the bat into the hitting zone. Once the arms have placed the bat into the desired hitting orientation they pretty much just act as part of the lever arm.

DURING CONTACT: The batter applies a force through his hands and arms to the handle of the bat but the actual torque at impact with the ball comes from a force with a perpendicular component to the motion of the bat's center of mass. Th e force that produces this torque comes from the twisting of the body and is therefore generated mostly by the shoulders, b ack, and legs. Typically a batter steps into the pitch when swinging which adds momentum to the bat during contact , but this fact can be mostly ignored to understand the effect of striking the ball.

The ball produces a torque upon the bat. An overpowering pitcher can actually make the bat move backwards (i. e. stronger and opposite torque on the bat than the torque applied by the batter.

AFTER CONTACT: Once the ball is hit and off the bat nothing more about the swing will affect the trajectory of the ball. Typ ically, one hears a coach say "follow through" but the follow through is not important except that a poor follow throu gh starts before the actual contact with the ball!!! The body turns and stops but the bat continues to move thro ugh the hitting zone. The body produces a torque (again mostly shoulders, back, and legs) to stop the motion of the b at.

For a deeper discussion I recommend the The Physics of Baseball by Addair or The Physics of Sports edited by Armenti.

Sincerely, Tom "Big Hack" Cull