Physics and Mathematics of Table Tennis

The following is the physics of table tennis in the Newtonian physics

P = W/t

W = Fd

F = ma

a = (v_f-v_i)/t

T = Fr

P is power. It is the strength applied to a shot.

W is work. It is the energy consumed.

t is the length of time power is applied. It is the amount of time the ball is in contact with the paddle.

F is force. It shares some similarity to power but it is more distinct.

d is the displacement of the ball.

m is the mass of the ball. It is about 2.7g.

a is acceleration.

v_f is the final velocity. It refers to the speed of the shot.

v_i is the initial velocity. it refers to the speed of the incoming ball.

T is torque. In table tennis, it is the turning force.

r is radius.

Power
To gain more power, more work or less time is required. Considering that time of contact is practically constant (fixed at 0.003s), work is the variable that generally must be changed.

Work
To do more work, application of force or increased displacement is required. Increasing displacement will not effectively grant more power because the length of the table is fixed. Therefore, force is the variable that must increase.

Force
To increase force, acceleration has to be increased because the mass of the ball is constant.

Acceleration
There are multiple aspects to the acceleration. The most important aspects are the initial and final velocities. Initial velocity cannot be controlled because it is dependent on the opposition. Final velocity can be controlled depending on how hard the ball is hit. To increase acceleration, the ball has to be hit as hard as possible to add ideally the largest v_f as possible. Having the largest v_f possible would ultimately lead to the largest magnitude of power in the shot.

Starting with power and ending with acceleration, physics has determined that in order to hit a shot with a lot of power, you must hit the ball very hard. Though there is some truth to that statement, there are of course some technicalities that make table tennis much more complex. Otherwise, anyone can be an olympic medalist as long as they can hit a hollow celluloid ball hard enough.

These technicalities, of course, refer to spin! In terms of physics, spin can be achieve through the angle and follow-through of the collision between the paddle and the ball. To maximize spin, players have to maximize torque! Maximization of torque doesn't actually doesn't refer to the paddle on the ball. It actually refers to the winding of a players body prior to the execution of the shot. As T = rF, the maximization of force has already been established by just hitting hard, but there is also r, or the radius! This does not refer to the ball as previously explained. It actually refers to the wind-up before the execution of the shot! So, the bigger radius of the spin, the more potential for spin! Of course, technique is important, but that's just another technicality.