Foundations of Momentum in Non-Inertial Systems

Foundations of Momentum in Non-Inertial Systems establishes a rigorous correction to a long-standing conceptual error in classical mechanics: the mistaken use of inertial linear momentum formulations inside non-inertial rotating systems.

 

The work clarifies that:

1. Momentum expressed as p = m v is valid only in inertial frames.

2. Inside a rotating, non-inertial frame, the appropriate quantity is

p_{\tau} = m\,\omega\,r,

a tangential momentum, fully dependent on angular velocity and geometric confinement. This is not linear momentum, because the velocity vector is constantly redirected by constraint forces.

3. Applying the inertial formula p = mv to a constrained curved trajectory leads to false interpretations of recoil, impulse, and conservation laws—especially in systems where curvature is intentionally removed during release events.

4. The analysis restores the strict separation between:

• inertial linear momentum (straight-line, unconstrained),

• angular/tangential momentum (curved, constrained),

• and constraint forces (centripetal).

5. This correction enables consistent treatment of closed-cycle momentum engines, captive-mass accelerators, propulsion architectures, orbital analogues, and the broader framework of MIND — Momentum in Non-Inertial Dynamics.

 

The document formalizes the physical distinctions required to avoid conceptual collapse between inertial and non-inertial regimes, and provides a foundation for studying momentum transition, constraint removal, and the emergence of true inertial linear momentum at the instant a mass exits a rotating frame.