The Cue

The cue ball moves only because we typed its velocity into the scene file.

Where the tip lands

A cue tip meets the ball for about a millisecond, so the strike is one impulse J along the shot. Landing at height h above the centre, it gives the ball a speed of J/m and a spin of J·h/I, where I = 2/5·m·R² says how hard a ball is to turn. At h = 2/5·R that spin is exactly v/R, so the ball rolls from the first instant. Below the centre is backspin, called draw. Above it is topspin, called follow. A lone ball, struck at 2 m/s:

tip      spin        then
+0.4 R   69.99 rad/s rolls at once, at 2 m/s
 0       0           slides 0.28 s, then rolls at 1.43 m/s
-0.5 R   87.49 back  slides forward spinning backward for 0.65 s, then rolls on forward at 0.71 m/s

A lone ball never comes back. It would need a tip a whole radius below centre, so draw needs a ball to hit.