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  • khim.manlangit
    Newton s second law: law of acceleration Lex II: Mutationem motus proportionalem esse vi motrici impressae, et fieri secundum lineam rectam qua vis illa
    Message 1 of 20305 , Nov 30, 2008
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      Newton's second law: law of acceleration

      Lex II: Mutationem motus proportionalem esse vi motrici impressae,
      et fieri secundum lineam rectam qua vis illa imprimitur. The change of
      momentum of a body is proportional to the impulse impressed on the
      body, and happens along the straight line on which that impulse is
      impressed.

      In Motte's 1729 translation (from Newton's Latin), the second law of
      motion reads:[15]

      LAW II: The alteration of motion is ever proportional to the
      motive force impressed; and is made in the direction of the right line
      in which that force is impressed. — If a force generates a motion, a
      double force will generate double the motion, a triple force triple
      the motion, whether that force be impressed altogether and at once, or
      gradually and successively. And this motion (being always directed the
      same way with the generating force), if the body moved before, is
      added to or subtracted from the former motion, according as they
      directly conspire with or are directly contrary to each other; or
      obliquely joined, when they are oblique, so as to produce a new motion
      compounded from the determination of both.

      Using modern symbolic notation, Newton's second law can be written as
      a vector differential equation:

      \mathbf F_{\text{net}} = {\mathrm{d}(m \mathbf v) \over \mathrm{d}t}

      where F is the force vector, m is the mass of the body, v is the
      velocity vector and t is time.

      The product of the mass and velocity is the momentum of the object
      (which Newton himself called "quantity of motion"). Therefore, this
      equation expresses the physical relationship between force and
      momentum for systems of constant mass. The equation implies that,
      under zero net force, the momentum of a system is constant; however,
      any mass that enters or leaves the system will cause a change in
      system momentum that is not the result of an external force. This
      equation does not hold in such cases. See open systems.

      It should be noted that, as is consistent with the law of inertia, the
      time derivative of the momentum is non-zero when the momentum changes
      direction, even if there is no change in its magnitude. See time
      derivative.[16]

      Since the mass of the system is constant, this differential equation
      can be rewritten in its simpler and more familiar form:

      \mathbf F = m \mathbf a

      where

      \mathbf a = \frac{\mathrm{d} \mathbf v}{\mathrm{d}t}

      is the acceleration.

      A verbal equivalent of this is "the acceleration of an object is
      proportional to the force applied, and inversely proportional to the
      mass of the object". In general, at slow speeds (slow relative to the
      speed of light), the relationship between momentum and velocity is
      approximately linear. Nearly all speeds within the human experience
      fall within this category. At higher speeds, however, this
      approximation becomes increasingly inaccurate and the theory of
      special relativity must be applied.
    • lixous_funkghurl
      Did you know that the greater the difference between the number of windings in the respective coils, the greater is the difference between their voltages?
      Message 20305 of 20305 , Oct 4, 2012
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        Did you know that the greater the difference between the number of windings in the respective coils, the greater is the difference between their voltages?
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