Everything about Classical Mechanics totally explained
Classical mechanics (commonly confused with
Newtonian mechanics, which is a subfield thereof) is used for describing the motion of macroscopic objects, from
projectiles to parts of
machinery, as well as
astronomical objects, such as
spacecraft,
planets,
stars, and
galaxies. It produces very accurate results within these domains, and is one of the oldest and largest subjects in
science and
technology.
Besides this, many related specialties exist, dealing with
gases,
liquids, and
solids, and so on. Classical mechanics is enhanced by
special relativity for objects moving with high
velocity, approaching the
speed of light. Furthermore,
general relativity is employed to handle
gravitation at a deeper level.
In
physics,
classical mechanics is one of the two major sub-fields of study in the science of
mechanics, which is concerned with the set of
physical laws governing and mathematically describing the motions of
bodies and aggregates of bodies. The other sub-field is
quantum mechanics.
The term
classical mechanics was coined in the early 20th century to describe the system of mathematical physics begun by
Isaac Newton and many contemporary 17th century workers, building upon the earlier astronomical theories of
Johannes Kepler, which in turn were based on the precise observations of
Tycho Brahe and the studies of terrestrial
projectile motion of
Galileo, but before the development of quantum physics and relativity. Therefore, some sources exclude so-called "
relativistic physics" from that category. However, a number of modern sources
do include
Einstein's mechanics, which in their view represents
classical mechanics in its most developed and most accurate form.
The initial stage in the development of classical mechanics is often referred to as
Newtonian mechanics, and is associated with the physical concepts employed by and the mathematical methods invented by
Newton himself, in parallel with
Leibniz, and others. This is further described in the following sections. More abstract and general methods include
Lagrangian mechanics and
Hamiltonian mechanics. While the terms
classical mechanics and
Newtonian mechanics are usually considered equivalent (if relativity is excluded), much of the content of classical mechanics was created in the 18th and 19th centuries and extends considerably beyond (particularly in its use of analytical mathematics) the work of
Newton.
Description of the theory
The following introduces the basic concepts of classical mechanics. For simplicity, it often models real-world objects as
point particles, objects with
negligible size. The motion of a point particle is characterized by a small number of
parameters: its
position,
mass, and the
forces applied to it. Each of these parameters is discussed in turn.
In reality, the kind of objects which classical mechanics can describe always have a non-zero size. (The physics of
very small particles, such as the
electron, is more accurately described by
quantum mechanics). Objects with non-zero size have more complicated behavior than hypothetical point particles, because of the additional
degrees of freedom—for example, a
baseball can
spin while it's moving. However, the results for point particles can be used to study such objects by treating them as objects, made up of a large number of interacting point particles. The
center of mass of a composite object behaves like a point particle.
Displacement and its derivatives
The
displacement, or
position, of a point particle is defined with respect to an arbitrary fixed reference point,
O, in
space, usually accompanied by a coordinate system, with the reference point located at the
origin of the coordinate system. It is defined as the
vector r from
O to the particle. In general, the point particle need not be stationary relative to
O, so
r is a function of
t, the
time elapsed since an arbitrary initial time. In pre-Einstein relativity (known as
Galilean relativity), time is considered an absolute, for example, the time interval between any given pair of events is the same for all observers. In addition to relying on
absolute time, classical mechanics assumes
Euclidean geometry for the structure of space.
Velocity and speed
The
velocity, or the
rate of change of position with time, is defined as the
derivative of the position with respect to time or
»
where
h is
Planck's constant and
p is the momentum.
Again, this happens with
electrons before it happens with heavier particles. For example, the electrons used by
Clinton Davisson and
Lester Germer in 1927, accelerated by 54 volts, had a wave length of 0.167 nm, which was long enough to exhibit a single
diffraction side lobe when reflecting from the face of a nickel
crystal with atomic spacing of 0.215 nm.
With a larger
vacuum chamber, it would seem relatively easy to increase the
angular resolution from around a radian to a milliradian and see quantum diffraction from the periodic patterns of
integrated circuit computer memory.
More practical examples of the failure of classical mechanics on an engineering scale are conduction by
quantum tunneling in
tunnel diodes and very narrow
transistor gates in
integrated circuits.
Classical mechanics is the same extreme
high frequency approximation as
geometric optics. It is more often accurate because it describes particles and bodies with
rest mass. These have more momentum and therefore shorter De Broglie wavelengths than massless particles, such as light, with the same kinetic energies.
Further Information
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