Limitations on Newton's 2nd Law

One of the best known relationships in physics is Newton's 2nd Law

but, though extremely useful, it is not a fundamental principle like the conservation laws. F must be the net external force, and even then a more fundamental relationship is

The net force should be defined as the rate of change of momentum; this becomes

only if the mass is constant. Since the mass changes as the speed approaches the speed of light, F=ma is seen to be strictly a non-relativistic relationship which applies to the acceleration of constant mass objects. Despite these limitations, it is extremely useful for the prediction of motion under these constraints.

Limitations on Newton's 2nd Law

One of the best known relationships in physics is Newton's 2nd Law

but, though extremely useful, it is not a fundamental principle like the conservation laws. F must be the net external force, and even then a more fundamental relationship is

The net force should be defined as the rate of change of momentum; this becomes

Variable Mass Applications

The generalization of Newton's 2nd Law to apply to variable mass systems takes the form

The term involving the derivative of the mass is responsible for the thrust in rocket propulsion and must be included in any problem where the mass changes.