Definition: In table tennis, topspin occurs when the top of the ball is going in the same direction as the ball is moving, and the bottom of the ball is moving in the opposite direction to the motion of the ball.

Assume ping-pong ball is moving with horizontal velocity v, and angular velocity w.

If the radius of the ball is R, topspin occurs when v

The bottom of the ball tends to moving [b]backward[/b] relative to table when the ping-pong ball touch the table. So the friction force is in the [b]same[/b] direction relative to the horizontal velocity.

The friction force will increase the horizontal momentum after the ball bounced off the table (Assume the gain in momentum is ?p)

Torque from the friction force will cause the angular momentum to decrease by R*?p.

Assume energy is conserved (The role of static friction is transfer part of its rotational energy into translation energy).

Expand the last term:

It can be reduced to

So the change in momentum

For thin sphere shell the momentum of inertia I=(2/3)mR[sup]2[/sup].

So .

The ball did not increase it's spin but decrease it's spin. But the ball gain more horizontal velocity, so the top of the ball moving faster after the bounce : (4/5)(w*R-v).

May be that is the reason why the player think the ball is spinning faster.

The above calculation assume the static friction is larger enough so no sliding occurs to keep the energy conserved. It requires strong enough normal force , which is equal to change in vertical momentum divide by impact time.

You can adjust the initial velocity vx and the ratio of angular velocity to velocity (by R*w/vx slider).

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