The Moment of Inertia is a quantity expressing a body's tendency to resist angular acceleration. In a tennis racket, the axis we analyze, directly related to the techniques of ground strokes, is the grip axis, used to define the swing weight. It is the sum of the product of the mass of each particle in the body with the square of its distance from the axis of rotation. The variations on the Moment of Inertia are the most important factors in the analyses to choose a tennis racket. Moment of Inertia (I) = mass (M) x centroid distance to the axis squared (R²).
I = M x R²
Quite simple to understand. The farther the centroid to the axis of rotation, the bigger will be the Moment of Inertia. The more difficult it will be to move the racket and to control its head. As it is with mass. With a greater mass, there is a bigger Moment of Inertia. We have to realize that the distance from the axis to the centroid is squared, which means that when you move the centroid by any small amount, it has a great influence on the racket moment of inertia. That is why professionals have such a terrible time to find the perfect balance. It means a lot depending on each chosen style. As this calculation is based on the swing weight, other factors that can influence on the racket control are commonly despised.
One important factor in the control of the racket after analyzing the Moment of Inertia is the shape of the racket frame. The frames with flat faces resist a lot more to the air than those with an airplane wing shape. When the friction with the air is reduced, in the airplane wing shape, it allows the racket head to move faster. Moreover, it plays-act as an increase in the Moment of Inertia. It has the same effect on the athlete´s control of the racket. With a greater Moment of Inertia, it is more difficult to control the racket head and the resultant on the ball. The shape factor is responsible for enormous changes in the way the tennis players perform his strokes. Even though they cannot realize that change, brain perception is accurate. It makes all the adaptations so that the player can still have control of the ball. Every time I have seen a player change to an airplane wing shape of the frame, he loses power and essential qualities on his techniques.
With the best player ever, Roger Federer, even though he had a huge technical crew, they failed to produce a racket that would make his strokes stronger. They reduced the racket weight, reducing the Moment of Inertia, but altered the centroid getting it farther from the axis of rotation. As a result, they increased the Moment of Inertia with a lighter racket that produced more power, but unfortunately, taking away from him his incredible capacity to control the ball. During the period he used this racket he did not win a single tournament.
To his next racket project, Federer got involved in the process so that he would get a lighter racket with a smaller Moment of Inertia or swing weight. That allowed him to control the racket head. And, he got back to winning tournaments, including Grand Slams. The swing weight has to be appropriate to each players´ technic, as said. If the player, professional or not, does not use a big backswing, he cannot use a racket with high swing weight. He won´t have the capacity to produce enough power so that his game can be effective.
Among professionals, the best examples are Adrian Mannarino, from France, and Michael Zverev from Germany. Both play without preparing for the ground strokes, with no backswing. They need rackets with very little swing weight. Another French player, even though he is skinny and light, Gilles Simon, that uses a big backswing, needs a racket with bigger swing weight. Does it sound incoherent? The player has a bigger backswing and uses a bigger swing weight? Not at all, a bigger backswing means a bigger preparation using potential energy from gravity, and kinetic accumulated energy to produce the power of the stroke. But that is a subject to another post.