- #1

Quantum55151

- 23

- 6

*Classical Mechanics*), an inertial balance is shown.

Intuitively, I totally understand that unequal masses would cause unequal accelerations and therefore rotational motion of the rod. However, how does one prove this mathematically?

The first thing that came to mind was to look at the situation from the point of view of angular momentum. The system is in rotational equilibrium if and only if the sum of the angular momenta of the two masses is zero, where

*L = r*x

*p.*But since the masses are subject to unequal accelerations, at any instant in time after the force is applied,

*p*

_{1}is not equal to

*p*

_{2}, and so the sum of

*L*cannot possibly zero. However, this explanation seems quite hand-wavy to me, so I'm wondering if anyone could suggest a more rigorous treatment of the problem.