Abstract
The analysis of the conditions that determine the motion of a billiard ball being tapped by a rod is presented in several textbooks of classical mechanics (for instance Sommerfeld 1977). But they disregard the effect of friction on the kinematic state of the ball after the hit. This induces the student to think that friction reactions do not occur, which is not the case. Besides, there is no justified method to obtain the impulsive reaction forces appearing in a system of solids in contact with friction in a three-dimensional problem. This article deals with the effects of friction on the final kinematic state of the ball, for any orientation of the cue. A method is given to obtain the impulsive friction reactions. The arguments used can be applied also to study other problems of solids in contact. The results presented here show that even very small friction induces important changes in the qualitative properties of the resulting motion. The conditions the shot must fulfil to obtain either the slipping or the rolling of the ball are also given.
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