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Newton's second law

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Newton's second law of motion, one of the most important in physics, states that the force which, acting on a body, is necessary to produce a change in its motion is proportional to its mass and to the acceleration (the time derivative of its velocity). Thus it can be written as F = kma (where F and a are understood as vector quantities). It may also be stated as F = k(dp/dt, where p represents the momentum vector.

If the units of force, mass, and acceleration (or of force, momentum, and time) are chosen appropriately, the constant k in the above equations may be taken to be 1. Many physicists consider that any system of units in which the constant k has to be taken different from 1 is "incoherent," and refuse to recognize that physical calculations can be made in such systems without any problem, simply choosing the correct value of k. However, this is equivalent to assuming that Newton's second law has a significance greater than all other laws of motion which contain a constant in their formulation. It is perfectly consistent with the laws of physics to give a constant appearing in some other equation a unit value, It is even possible to set k to any value one chooses, without requiring any other constant in a law of physics to be 1, if that is useful, and such a formulation will still be consistent with the laws of physics.

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