December 2005 -- Question: Can you tell my why the laws of momentum aren’t discussed more? All I ever hear about is acceleration, and I’m not convinced it is even a factor. I mean, if my racquet is traveling at 20 mph, it is going to exert a force on the tennis ball, and if the velocity of the racquet head is 40 mph, it will exert more force. Can you help me understand this?
Answer: This is one of those questions that would usually require much more space than we have in this column. Having said that, however, it is a sound question and it should be addressed.
First, you are obviously correct in saying that a racquet traveling at 40 mph will impart more velocity to a ball than a racquet traveling at 20 mph. For the purposes of my answer, I have to begin with the concept of laws, principles and preferences. A law you cannot violate, a principle could help you or hurt you depending on how it is used, and a preference is simply how you prefer to teach a movement. For example, Newton’s second law is the
law of acceleration. It says that force equals mass times acceleration. Since mass stays fairly constant during a tennis swing, this law says that the more force you apply, the more you will accelerate; force is directly proportional to acceleration and this law is fact. Moment of inertia is a
principle that concerns itself with the mass of an object and its resistance to rotation. In general, the farther the mass is from the center of rotation, the slower the rotation will be. If a figure skater begins spinning on the ice with her arms in, the skater rotates faster and then slows down as she extends her arms or lengthens the radius of rotation. If a tennis player tries to swing (or rotate the trunk) with the arm totally extended, it is going to be difficult to rotate quickly due to the lengthened radius. A
preference might be that you like to create acceleration with a high loop backswing or a small loop backswing. Both could be effective and one is not necessarily better than the other.
An object’s momentum equals its mass multiplied by its velocity, or speed. A primary law of physics is the law of momentum conservation. It basically states that for a collision occurring between two objects, the total momentum of the two objects before the collision is equal to the total momentum of the two objects after the collision. That is, the momentum lost by object one is equal to the momentum gained by object two. In a perfectly isolated system, this law holds true. However, there is other energy given off in the situation of a tennis impact. There are sounds, heat and other possible forms of mechanical energy given off.
The person who contributed so much in studying this phenomenon in sport and particularly tennis was the late Dr. Stanley Plagenhoef. If you can find his two books (both are out of print), you will be fascinated by his work. His books are
Fundamentals of Tennis (1970) and
Patterns of Human Motion: A Cinematographical Analysis (1971). He examined the “striking mass” of tennis impact by using the law of momentum conservation. Basically, Plagenhoef’s discussion goes like this: Any impact concerns itself with the mass and velocity of one object, the mass and velocity of the second object, and how the two objects interact (this is called the coefficient of restitution). The mass of the tennis racquet is larger than the ball and the transfer of momentum as the ball is hit remains large, sending the ball with high velocity back over the net. Where this gets sticky is trying to understand that, if you simply throw a ball at a racquet that is standing still on its end, the ball will still rebound and the racquet will fly backward. Now, put the racquet in a vise grip, throw the ball against it and the ball comes off with negligibly different velocity. Now, add to the system a human being swinging the racquet with high velocity toward the impact zone and you add tremendous momentum to the system. There is so much more that could be discussed (the role of grip firmness, a two-handed grip, adding weight to the racquet, off-center hits, etc.) but, for the purposes of your question, I will not go into that detail (perhaps another question).
So, why don’t we discuss momentum more if it is so important? I do not believe it is because we want to shy away from it or that it is so hard to understand, employ, teach, etc. I actually believe it is because physical principles sometimes get very complex when you are working with a biological system like a human being. You see, if a human being were capable of going from zero to maximum velocity instantaneously, I believe we would have to debate your question more. However, a biological system cannot do this. Velocity has to build through muscle contraction, use of the larger body parts and so on. This rate of change of velocity is called acceleration. So, velocity and acceleration are directly related. Acceleration, by definition, equals the change in velocity over a period of time. It may be that many teachers choose to focus on acceleration rather than momentum because an object that accelerates quickly is likely to have more velocity (and more momentum) than an object that does not accelerate as rapidly.
How the body accelerates has been discussed for years. The key method is using the body as a linked system or a kinetic chain, as it is sometimes called. The body, when used as a series of chain links, one building upon the other, creates huge racquet head velocity. Force is created first as a ground reaction force by the legs pushing against the ground, then the hips rotate and add to what was created by the ground reaction force, trunk rotation then contributes, the arm swings from the shoulder, there is likely some elbow and wrist movement to add, and you end up with a high-velocity racquet head. But, all parts must add to the velocity of the previous part and it is this rate of change of velocity that, I believe, leads us to discuss the term acceleration more.
Send questions to jgroppel@LGEPerformance.com.
