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F = ma

  1. Nov 19, 2009 #1
    Does this equation F= ma (Newton's famous second law of motion) actually tell us anything?

    When I was studying physics at college I realised that every time we used this equation, a couple of lines of algebra later it seemed we'd always divide throughout by the object's own mass and find out it's equation of motion. Amazing

    Or is it?
    Weren't we really just adding the all the acceleration vectors together to find out the object's path ? (Not amazing)

    If so, then that F = ma law isn't adding any new information whatsoever to the laws of motion, and the whole thing of Newton's 2nd law is an illusion.

    Aren't Galileo's principle of inertia (1st law), and the conservation of momentum (3rd law) all that we really need to do physics ?
  2. jcsd
  3. Nov 19, 2009 #2
    well first off, F=MA is probably one of the most integrated parts of physics..... EVER. you can derive so many things from it, Momentum is actually derived from F=MA using calculus, so technically you would need F=MA to get your momentum equations. And the reason why you would divide through by the mass was to probably isolate A because once you have A you can derive the formula for its velocity and then the formula for its position all in terms of time
  4. Nov 20, 2009 #3
    I don't think so. Momentum can be defined independently of F=ma.

    "Equations of motion" is pure mathematics involving standards for length and time. You can observe a number of projectiles, plot their positions; find their velocities at different times and conclude that they all have the same and constant acceleration of 9.8m/s/s using the equations of motion. But you can find out why it is so only using The Second Law (introduction of the concept of Force) and Newton's law of gravity. These made Kepler's laws as mere consequences of the Newton's four laws. The contemplation and finding of these two laws are a few of the instances that actually involve the "doing physics" thing. (as a response to the last part of your question)
  5. Nov 20, 2009 #4


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    Hi YellowTaxi! :smile:

    (erm :redface: … technically, it's F = d(mv)/dt :wink:)

    Take the Lorentz force as an example …

    the equation of motion is mx'' = q(E + x' x B) …

    there is no necessity give the RHS a name, but it's convenient to call it "force".

    So F = ma is really only a statement of the general physical principle that acceleration (and not higher derivatives of position) is determined by various inputs, and is proportional to inertial mass.

    Ultimately, it's a consequence of Emmy Noether's famous theorem, that every symmetry has its conservation principle.
    (Newton's third law isn't conservation of momentum, but anyway …)

    How do you get "field" forces (like the Lorentz force) out of conservation of momentum? :wink:

    For non-field physics, I think you can get F = m dv/dt from conservation of momentum and Newton's third law by considering the whole universe, and dividing it into two parts, whose action and reaction are equal and opposite. :wink:
    uhh? written F = d(mv)/dt, momentum is in F=MA (and conservation of momentum comes simply from putting F = 0)
  6. Nov 20, 2009 #5
  7. Nov 20, 2009 #6
    Second law says "Rate of change of momentum is directly proportio--..... [snip]". So defining momentum from the second law doesn't make sense.. Even if its taught in the class by a bearded professor, you can cross-analyze it given the omnipotent existence of both insanity and intelligence.
  8. Nov 20, 2009 #7
    you do know that F=ma can also be written as F= deltaP/deltatime, P being momentum..... so if you multiply your force over a given time acting on an object then your object will have a velocity because it is accelerating, and with velocity comes momentum. Its basically all in one and one in all as far as the classical laws of motion go.
    Im not trying to argue. seriously, im just telling you how it was done
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