Physics of Baseball


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Finding and understanding the sweet spot on a wooden bat.

When you strike a bat against a ball it sends vibrations, much like the vibrations acting on airplanes or bridges, which travel in waves through the bat. This motion is important to understand because every vibration the bat experiences takes energy away from the ball's speed as it leaves the bat.

If you hit the ball at a bat's "nodes", the frequencies (each bat vibrates at several low and high frequencies at once, which is like the harmonics of stringed instruments) cancel out and since this happens you don't feel the sting in your hands that you experience when you hit the ball at different points on the bat.

There is some discrepency of where the sweet spot is on the bat. Some believe that the sweet spot is 17 inches from the end and others believe that it is 6 inches from the end. For a wooden bat, I tend to believe that the sweet spot is 6 inches from the end of a 34 inch bat (opposite of where your hands are). This is due to the fact that if you were to hit a ball 17 inches from the end, you would be hitting on the bat's emblem. If hit hard enough, the bat would break because this is a weak spot in the bat due to the stamping of the emblem.

It's Basic Physics

When looking at a collision between a baseball bat and ball, three things always apply:
Conservation of linear momentum-

The linear momentum of a particle of mass, m, moving with a velocity, v, is defined to be the product of the mass and velocity: p=mv
Elastic collision-

An elastic collision between two objects is one in which total kinetic energy (as well as total momentum) is the same before and after the collision.
Conservation of energy-

Energy can never be created or destroyed. Energy may be transformed from one form to another, but the total energy of an isolated system is always constant.
Newton's Third Law-

States that for every action there is an opposite and equal reaction.
How hitting the ball works
The Swing

When a person swings a bat, their arms propel the bat to a high velocity which is needed to transfer momentum to the ball and send it sailing. Also, there is a transfer of energy starting with the batter then moving from the batter's arms to the bat and then when contact is being made with the ball the energy in the bat is transferred to the ball which propels the ball forward (hopefully:)) The force that acts on the ball, as contact is being made (contact is about 1/1000sec.

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long), can easily reach a couple thousand pounds.

Equations for Baseball

Some physical properites that occur in baseball are velocity, force, momentum, acceleration, friction, gravity, and waves. These properties help solve baseball problems. Listed below are some equations to do this.
Projectile Motion-

These equations help calculate the range, height and time of objects hit or thrown. Assuming that the air resistance is negligible, and gravity is constant.

1) Vx=Vcos(theta); where Vx=horizontal velocity and (theta) is the angle at which it was launched.

2) Viy=Vsin(theta); where Viy=initial vertical velocity.

3) dymax=.5gt1/22; where dymax=max height and g=gravity.

4) dx=Vxttotal; where dx=range and t=time.
Dynamics-

This is the study of forces and motion. And this is described by Newton's second law.

1) F=ma; where m=mass and a=acceleration.

2) k=Ff/Fn; where k=coefficient of friction and Ff=frictional force and Fn=normal force.
Kinematics-

This is the study of motion. And the following equations help describe linear motion.

1) v=d/t; where v=velocity and d=distance and t-time.

2) average velocity=(Vf + Vi)/2; where Vf=final velocity and Vi=initial velocity.

3) a=Vf-Vi/t; where a=acceleration.

4) d=Vit + .5at



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