## trivia

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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
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

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.
• 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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