Everything about Linear Momentum totally explained
In
classical mechanics,
momentum (
pl. momenta;
SI unit
kg·
m/s, or, equivalently,
N·
s) is the product of the
mass and
velocity of an object (p=mv). For more accurate measures of momentum, see the section
"modern definitions of momentum" on this page. It is sometimes referred to as
linear momentum to distinguish it from the related subject of
angular momentum. Linear momentum is a
vector quantity, since it has a direction as well as a magnitude. Angular momentum is a
pseudovector quantity because it gains an additional sign flip under an
improper rotation. The total momentum of any group of objects remains the same unless outside forces act on the objects.
Momentum is a
conserved quantity, meaning that the total momentum of any
closed system (one not affected by external forces) can't change.
History of the concept
The word for the general concept of
mōmentum was used in the
Roman Republic primarily to mean "a movement, motion (as an indwelling force ...)." A fish was able to change velocity (
velocitas) through the
mōmentum of its tail. The word is formed by an accretion of
suffices on the stem of
Latin movēre, "to move." A
movi-men- is the result of the
movēre just as
frag-men- is the result of
frangere, "to break." Extension by -to- obtains
mōvimentum and
fragmentum, the former contracting to
mōmentum.
The
mōmentum wasn't merely the motion, which was
mōtus, but was the power residing in a moving object, captured by today's mathematical definitions. A
mōtus, "movement", was a stage in any sort of change, while
velocitas, "swiftness", captured only
speed. The Romans, due to limitations inherent in the
Roman numeral system, were unable to go further with the perception.
The concept of momentum in classical mechanics was originated by a number of great thinkers and experimentalists. The first of these was
Ibn Sina (Avicenna)
circa 1000, who referred to
impetus as proportional to
weight times
velocity.
René Descartes later referred to
mass times velocity as the
fundamental force of motion.
Galileo in his
Two New Sciences used the
Italian word "impeto."
The question has been much debated as to what Sir
Isaac Newton's contribution to the concept was. Apparently nothing, except to state more fully and with better mathematics what was already known. The first and second of
Newton's Laws of Motion had already been stated by
John Wallis in his 1670 work,
Mechanica slive De Motu, Tractatus Geometricus: "the initial state of the body, either of rest or of motion, will persist" and "If the force is greater than the resistance, motion will result...." Wallis uses
momentum and
vis for force.
Newton's "Mathematical Principles of Natural History" when it first came out in 1686 showed a similar casting around for words to use for the mathematical momentum. His Definition II defines
quantitas motus, "quantity of motion," as "arising from the velocity and quantity of matter conjointly", which identifies it as momentum. Thus when in Law II he refers to
mutatio motus, "change of motion," being proportional to the force impressed, he's generally taken to mean momentum and not motion.
It remained only to assign a standard term to the quantity of motion. The first use of "momentum" in its proper mathematical sense isn't clear but by the time of Jenning's
Miscellanea in 1721, four years before the final edition of Newton's
Principia Mathematica, momentum M or "quantity of motion" was being defined for students as "a rectangle", the product of Q and V where Q is "quantity of material" and V is "velocity", s/t.
Linear momentum of a particle
If an object is moving in any
reference frame, then it has momentum in that frame. It is important to note that momentum is
frame dependent. That is, the same object may have a certain momentum in one frame of reference, but a different amount in another frame. For example, a moving object has momentum in a reference frame fixed to a spot on the ground, while at the same time having 0 momentum in a reference frame attached to the object's
center of mass.
The amount of momentum that an object has depends on two physical quantities: the
mass and the
velocity of the moving object in the
frame of reference. In physics, the usual symbol for momentum is a small bold
p (bold because it's a
vector); so this can be written:
» may be sufficiently high to explode capacity.
Thus electric and magnetic fields do carry momentum.
Light (visible, UV, radio) is an electromagnetic wave and also has momentum. Even though
photons (the particle aspect of light) have no mass, they still carry momentum. This leads to applications such as the
solar sail.
Momentum is conserved in an electrodynamic system (it may change from momentum in the fields to mechanical momentum of moving parts). The treatment of the momentum of a field is usually accomplished by considering the so-called
energy-momentum tensor and the change in time of the
Poynting vector integrated over some volume. This is a tensor field which has components related to the energy density and the momentum density.
The definition canonical momentum corresponding to the momentum operator of quantum mechanics when it interacts with the electromagnetic field is, using the
principle of least coupling:
» ,
instead of the customary
» ,
where:
» is the electromagnetic vector potential
the charged particle's invariant mass
» its velocity
its charge.
Further Information
Get more info on 'Linear Momentum'.
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