# Describing the second law of motion using linear momentum

Trying2Learn
Hi! This is a very simple question regarding terms of expressions.

1. One law of motion is: F=ma
2. Another, using L as the linear momentum, is: F = dL/dt

If the first equation can be characterized (ignoring reference frames) as a "coordinate-based equation" (since is concerned with the second derivative of the position coordinate) (also ignoring moving reference frames, etc.)...

Then, how would one characterizes the second equation? Yes, I can see it is different, but would one say "more general?"

How would one state the difference in the formulation? "?-based equation"

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Summary:: Describing the second law of motion using linear momentum

Hi! This is a very simple question regarding terms of expressions.

1. One law of motion is: F=ma
2. Another, using L as the linear momentum, is: F = dL/dt

If the first equation can be characterized (ignoring reference frames) as a "coordinate-based equation" (since is concerned with the second derivative of the position coordinate) (also ignoring moving reference frames, etc.)...

Then, how would one characterizes the second equation? Yes, I can see it is different, but would one say "more general?"

How would one state the difference in the formulation? "?-based equation"

There is one important difference. ##F = ma## explicitly assumes a fixed mass. Whereas ##F = \frac{dL}{dt}## can be written as ##F = \frac{d}{dt}(mv)## and then you can have an argument about whether this includes the case where mass varies with time. I.e. whether you can write ##F = ma + \frac{dm}{dt}v## and what this means.

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