Conservation of angular momentum is not absolute: it depends on the pole, i.e. the point about which is calculated. The same system may conserve about some poles and not about others. Choosing the right pole is often the only move that makes a problem solvable.
The rule is simple: choose a pole about which the impulsive external forces (the intense ones acting during a collision) have no moment. If a force has zero arm relative to the pole, it produces no external angular impulse, and the angular momentum about that pole is conserved.
How to choose the right pole
To make conserved, look for a pole about which the impulsive external forces produce no moment. Typically:
- a point on the line of action of the constraint force (which has zero arm relative to that point);
- the centre of mass of the system, where the total momentum is “concentrated”;
- a point of fixed rotation, such as a hinge or a pivot.
The guiding example is the hinged rod struck by a projectile. During the collision the hinge exerts a violent impulsive reaction: about any generic pole this force has a non-zero arm and ruins the conservation. But if the hinge itself is chosen as the pole, that reaction has zero arm and drops out of the accounting — and the angular momentum about the hinge is conserved. The rod’s weight does have an arm, but it is not impulsive (it acts weakly during the very short duration of the impact), so it is negligible.
This is the moment physics rewards those who look at the problem from the right perspective: changing the pole does not change the physics, but it can turn an intractable problem into a single equation.
Collegamenti
Argomenti: Dinamica rotazionale Concetti: Conservazione del momento angolare Competenze: Scelta del polo
Esercizi collegati: Problema — La pattinatrice che si stringe · Esercizio svolto — proiettile contro asta incernierata · Problema — Perché il pattinatore ruota più veloce