Momentum in sports is often associated with some undefinable, inertia-in-motion that is transferred back and forth between teams, affecting the flow of the game. While this mental concept of momentum may be debatable, physical momentum is very real in sports. In baseball and softball, it is extremely important to the act of hitting.

Imagine that you just put your best swing of the season on the ball – highest bat speed ever, squared up to the ball, good launch angle - this will definitely have a home run trajectory, right? But it is a shallow fly ball to centerfield. What happened? Everything about the swing was good, but the problem is that the tee-ball bat you were using didn’t have enough momentum to generate the necessary exit velocity for a home run.

Obviously this is an exaggerated scenario, but one that clarifies the importance of momentum. There has been a lot of interest lately in ball exit velocity, for good reason, because the distance a ball travels is directly related to exit velocity.

Exit velocity is an outcome, and a key ingredient of exit velocity is bat momentum at impact. In an impact problem, like the ball-bat collision, the velocities of the bodies after impact are dependent on the momentums of the bodies before impact, as dictated by the principle of “Conservation of Momentum” (the type of impact and the coefficient of restitution also matter, but we’ll save those for another day).

Momentum is mass times velocity. We have intuition about how it applies from everyday examples. If we roll two balls of equal mass toward each other at equal speeds, they will collide then bounce off at roughly equal speeds. However, if one ball is twice as heavy as the other (or moving twice as fast), the heavier (or faster) ball dominates the collision and the other ball bounces off at a higher speed than in the first scenario.

The ball-bat collision is like that, but much more extreme. Let’s imagine a ball-bat collision in which the bat weighs 20 oz. and moves 60 mph while the ball weighs 5 oz. and also moves 60 mph. In this instance, the bat’s momentum is greater than that of the ball (for now we’ll ignore the fact that the bat’s mass is distributed along its length).

Typical of ball-bat collisions, the bat momentum dominates and the ball flies off in the opposite direction from which it came. If we increase the bat weight to 25 oz. and swing it at the same speed, then we get a substantial increase in bat momentum that results in higher ball exit velocity.

In theory the trend would continue with ever-increasing bat weight, but in practice the hitter’s biomechanics come into play. As the bat gets heavier a player can no longer swing it at the same speed, so the extra bat mass doesn’t translate to a momentum increase (in fact, if the speed falls off enough then momentum will decrease).

If we try a lighter-weight bat, we may see an increase in bat speed. However, momentum will go up only if the combined mass-speed product is higher. Eventually we run into the body’s physical speed limit, and no matter how light we make the bat, it just can’t be swung faster.

Going back to the lead-in example at the top, we might get very high bat speed with a tee-ball bat, but it may not have enough mass for us to generate home run momentum, and therefore home run exit velocity. The key for a batter is to find the bat that is just right for him or her.

So, is there momentum in baseball? There is in the swing. And by maximizing it – with a bat that provides plenty of weight without overly compromising speed – one can maximize ball exit velocity.

**Dr. William Clark is the co-founder of Diamond Kinetics and has been an active researcher and innovator in the field of dynamic systems and control for over 25 years. He is currently Professor of Mechanical Engineering and Materials Science at the University of Pittsburgh.**

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