Kick serves



The racquet head moves diagonally across the back of the ball in a kick serve. The friction force on the back of the ball causes the ball to rotate in the direction of that force, and the spin axis is at right angles to the force. There is only one spin axis, but the spin can be regarded as a combination of sidespin due to the sideways component of the force plus topsin due to the vertical component of the force. Additional spin is generated if (a) the racquet head is tilted forward on impact (b) the racquet head is rotating forward and (c) the ball is falling as a result of the ball toss – since that is equivalent to the racquet head rising to meet the ball. Topspin causes the ball to dive into the court at a steeper angle, so it bounces at a steeper angle and then crosses the baseline at about shoulder height. That makes it more difficult for the receiver to return the ball well. The arrow labelled F shows the direction of the Magnus force on the ball, which is opposite in direction to the friction force. F acts down onto the court but it also acts sideways, causing the ball to curve sideways as well as downward.  Gravity also acts downward but not sideways.



Rolling when ball is spinning


If a ball is projected forward on a horizontal surface while spinning about a near vertical axis then the ball rolls along a small circular path of radius r near the bottom of the ball.


This type of rolling motion occurs in tenpin bowling, when sidespin is used in billiards, when a golfer putts a ball off-center, when a kick serve ball lands on the court and when a top is spinning on the floor. As the ball slows down, the axis can rotate into a vertical position if it is spinning fast enough (a top rights itself in this way, and so does the golf ball and the steel ball in the movie clips), otherwise it rotates into a horizontal position and then rolls in the conventional manner. The latter result is more common in billiards and also occurs when a top is spinning slowly. Rolling occurs when v = rw so r = v/w where v is the speed of the rolling ball and w is its rate of spin (in radians/second). If v decreases faster than w then r decreases so the spin axis rotates to a more vertical position. If w decreases faster than v then r increases and the spin axis rotates into a horizontal position. If v decreases to zero then r = 0 so the ball keeps spinning on the spot until w also drops to zero. For a steel ball on a steel plate, this could take several minutes.