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Momentum vs. acceleration

Q: A lot of tennis experts talk about acceleration on your swing, but I thought the whole point was to have more momentum. Since when did acceleration become more important?

A: You are correct in thinking that momentum is important. It is baffling why so many professional tennis instructors focus on acceleration, some even going so far as to imply that you should wait until you feel the ball on the strings before accelerating your racquet. Considering the fact that the ball is on the strings for only 4 to 10 milliseconds — far less time than the 30 milliseconds or more your body needs to recruit the muscles in such a way as to react to the impact — this is clearly impossible. Furthermore, the rate of racquet acceleration before impact has virtually nothing to do with what happens during impact.

Before proceeding, let’s define our terms. Momentum is “mass times velocity.” Mass can be thought of as the weight of the object, although for a tennis racquet, not all the mass is available at the point of impact. Velocity is the speed of the object. Acceleration is the change in velocity over a period of time (in tennis, this period of time is usually the 4 to 10 milliseconds the ball is on the strings, also known as the time of impact). Using these definitions, you can see that a heavier racquet traveling the same speed as a lighter racquet will have more momentum, as will any racquet the faster it is swung. Tennis balls are supposed to be about the same weight, but even here, a faster-moving tennis ball will have greater momentum than a slower-moving one.

It’s possible the confusion arises because when two objects having momentum (such as a tennis ball and a racquet) collide, the impact creates impact-momentum change. This change is best described by a different equation, which is also known as Newton’s Second Law of Motion: Force equals mass times acceleration. Because most so-called tennis experts misunderstand the terms involved in this seemingly simple equation, you will find some wacky recommendations that misuse these terms. For example, at least one noted tennis expert advises players to put more force on the ball by accelerating the tennis racquet through the swing.

As stated above, however, “acceleration” in the equation does not refer to any acceleration that you impart to the racquet prior to impact. It refers only to the changes in the velocities of the ball and racquet during the 4 to 10 millisecond impact: The racquet (which is heavy relative to the ball) decelerates a little, while the ball changes directions completely (on a groundstroke, it decelerates to zero, and then accelerates in another direction entirely). In a straight-on impact, only the speed and mass at impact bear on the result, which clearly shows that momentum should be the center of any such discussion, not acceleration.

The “force” in the equation is a calculated amount, which you determine by looking at the mass of each object in the collision (in our case, the mass of the racquet at the point of impact, and the ball), and the change of velocity during the impact (also known as acceleration). Thus, it is also incorrect to advise players to use more “force,” as one industry-leading expert repeatedly advises.

Another way of looking at this is that before and after the impact, the ball exerts no force on the racquet, and neither does the racquet exert any force on the ball, regardless of wind-up, follow-through, or how quickly you are accelerating the racquet. Therefore, unless you are dealing in-depth with the physics of the collision between the ball and racquet, “momentum” is the better term to use with your students.

For thorough examinations of this and other tennis-related physics, see The Physics and Technology of Tennis, by Howard Brody, Rod Cross, and Crawford Lindsey (published by Racquet Tech Publishing).

From the March 2006 issue
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