second_law

Equation #5: law of motion

Newton’s second law, as it was written, states that
the alteration of motion is ever proportional to the motive force impress’d; and is made in the direction of the right line in which that force is impress’d.” 
However, the statement “Force = mass times acceleration” fails if the mass is variable; for example, as in rocket motion. Also, in relativistic terms, the concept of mass as we know it no longer suffices, because relativistic speeds cause objects to “behave” to be more massive than their rest mass. Hence, we should keep in mind that Newton’s second law as he defined it, is only valid if the mass of the object is constant and we are dealing with non-relativistic velocities.

A more robust and “safe” form is to write

F = dp/dt.

here, p=linear momentum
usually, p = mv, where v = velocity and m = mass.

For more equations, see Famous Equations in Physics

Newton’s second law of motion

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