Undergrad Restoring S.I. units to a Lagrangian in natural units

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Restoring S.I. units to a Lagrangian in natural units involves understanding which quantities were excluded for simplification. The discussion clarifies that fundamental quantities are not omitted but rather quantities that relate different dimensions are. To restore S.I. units, one can either reintroduce the excluded quantities or apply specific scaling factors that align with the dimensions of the Lagrangian density. The choice between these methods depends on the context of the field being analyzed. Ultimately, the approach taken should ensure dimensional consistency in the Lagrangian formulation.
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TL;DR
Restoring the Lagrangian units
If we have a natural unit Lagrangian, where some fundamental quantities have been excluded to ease calculations...and aim to restore it's S.I units back, do we just have to plug back the fundamental quantities that were initially excluded Into the Lagrangian...or we use some specific scaling factors corresponding to that field that has the same S.I units of Lagrangian density, and scale the unitless Lagrangian with it.
 
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"fundamental quantities" are not excluded in using natural units.
Only quantities relating two different dimensions are excluded.
 
I do not have a good working knowledge of physics yet. I tried to piece this together but after researching this, I couldn’t figure out the correct laws of physics to combine to develop a formula to answer this question. Ex. 1 - A moving object impacts a static object at a constant velocity. Ex. 2 - A moving object impacts a static object at the same velocity but is accelerating at the moment of impact. Assuming the mass of the objects is the same and the velocity at the moment of impact...

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