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# Finding the "Sweet Spot" on a Baseball Bat

Describing a Bat-Ball Collision with Two Mathematical Models
by

## Yachuan Yu

on 20 April 2010

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#### Transcript of Finding the "Sweet Spot" on a Baseball Bat

Introduction

What is "Sweet Spot"?

Why using corked or metal bat?
Is "Sweet Spot" Sweet?
Initial Assumptions
Shayne Smith, Yachuan Yu and Qiang Zheng
1. All motions in one plane
2. Conservation of Angular Momentum
3. Bat is a segament
4. Circular motion
5. All collisions centered
6. Seperating collision to two parts (for simplified model only)
7. Constant coefficient of restitution
8. "Right" and "left" Table of Contents Simplified Model Modeling Conservation of angular momentum Modeling Conservation of Energy Exact Model Results 1. Sweet Spot does exist
2. Metal bats are sweet but corked ones are not Strengths Weaknesses Conclusion Q & A The results of our model supports that we can locate the sweet spot of the bat
However we have discover based on the speeds of the bat and ball
Our model explains that corking a bat with lighter materials are actually inneffective
However corking with a heavier material would result in a better overall velocity of the ball if the velocity of the bat and the ball are kept constant. This being said our model says that aluminum bats create a better overall final velocity of the ball due to the bat having stiffer material and a lower moment of inertia. The model gives an inaccurate measure of the final velocity of the ball with pitched speeds under 75 and a swing speed of 71
Our model does not take into account the human factor involved with control over a bat
Vibrations nodes seem to be very important in determining the sweet spot however we did not take this into account.
We do not model realistic hits (not in the 3d plane).
We dont take temperature or weather into consideration. Our model is very good at predicting the final velocity of the ball with speeds faster than a pitched ball of 71 mph
and a bat speed of 71 mph
We also take a great deal of factors into consideration such as the mass of the ball and bat, the coeficent of restitution, center of mass of the ball, the speeds of the bat and the ball, and the moment of inertia of the bat.
We also determined that our model shows that the speeds of the bat and the ball play a role in determining where the sweet spot on the bat is.
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