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Exact meaning of F=dp/dt

  1. Oct 31, 2015 #1

    Force was introduced to me as "what a force meter in an inertial frame measures". I'm a bit confused about the interpretation of Newton's second law$$F=\frac{dp}{dt}\enspace.$$
    Is it a definition? Is it an empirical finding? Can it be derived theoretically?

    Or do we need to make the "definition" "what a force meter in an inertial frame measures" more rigorous? How could we formulate this more mathematically?
  2. jcsd
  3. Oct 31, 2015 #2
    F=ma, like the concept of frames, is purely empirical from the beginning. Force and momentum are circularly defined.
  4. Nov 1, 2015 #3
    It is part of a definition. All three laws of motion together define force.
  5. Nov 1, 2015 #4


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    I think the original formula was [itex]F=\frac{d}{dt}(mv) [/itex]. As long as the mass is constant, this reduces to [itex] F=m\frac{dv}{dt}=m\cdot a[/itex]. In a rocket, where an appreciable amount of mass is fuel which is used up during the flight, the formula becomes [itex]F=m\frac{dv}{dt}+\frac{dm}{dt}v=m\cdot a+\frac{dm}{dt}v [/itex].
  6. Nov 2, 2015 #5
    The second law states that the force on a body is proportional to the rate of change of linear momentum. We work in units where the proportionality constant is 1. You could in principle, define force to be that quantity which is say, twice the rate of change of linear momentum. You would ofcourse, accordingly have to change your other definitions such as work done, energy.
  7. Nov 2, 2015 #6


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    According to the authors in Knudsen & Hjorth, Elements of Newtonian Mechanics, 3rd ed., section 2.1:

    "The whole concept of force has been the subject of much debate since it was introduced by Newton. Let us here note the following: the second law [ref. to eq. for 2nd law] should not be considered as the definition of the concept of force. An essential feature of the law is that the force acting on the particle is supplied by a force law separate from [ref. to eq. for 2nd law]. One example of such a force law is the law of gravity. (...)"
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