Final answer:
In billiards and pool, semi-circle, rollover, and long spine massage share a commonality in demonstrating the conservation of momentum and, to some extent, angular momentum during two-dimensional elastic collisions.
Step-by-step explanation:
The common similarity between semi-circle, rollover, and long spine massage in billiards and pool is that all three involve the principles of momentum and angular momentum, particularly in the context of two-dimensional collisions. When playing pool, these occurrences illustrate the conservation of momentum and to some extent, the conservation of angular momentum, especially when spin is applied to the balls. The assumption made in these situations is that the collisions are elastic, which means that the total kinetic energy before and after the collision is conserved, thus maintaining the momentum of the system comprising the two colliding billiard balls.