Motion

Part of a series on
Classical mechanics
${\displaystyle {\textbf {F}}={\frac {d}{dt}}(m{\textbf {v}})}$ Second law of motion
History Timeline Textbooks
Branches Applied Celestial Continuum Dynamics Kinematics Kinetics Statics Statistical
Fundamentals Acceleration Angular momentum Couple D'Alembert's principle Energy kinetic potential Force Frame of reference Inertial frame of reference Impulse Inertia / Moment of inertia Mass Mechanical power Mechanical work Moment Momentum Space Speed Time Torque Velocity Virtual work
Formulations Newton's laws of motion Analytical mechanics Lagrangian mechanics Hamiltonian mechanics Routhian mechanics Hamilton–Jacobi equation Appell's equation of motion Koopman–von Neumann mechanics
Core topics Damping ratio Displacement Equations of motion Euler's laws of motion Fictitious force Friction Harmonic oscillator Inertial / Non-inertial reference frame Mechanics of planar particle motion Motion (linear) Newton's law of universal gravitation Newton's laws of motion Relative velocity Rigid body dynamics Euler's equations Simple harmonic motion Vibration
Rotation Circular motion Rotating reference frame Centripetal force Centrifugal force reactive Coriolis force Pendulum Tangential speed Rotational speed Angular acceleration / displacement / frequency / velocity
Scientists Kepler Galileo Huygens Newton Horrocks Halley Daniel Bernoulli Johann Bernoulli Euler d'Alembert Clairaut Lagrange Laplace Hamilton Poisson Cauchy Routh Liouville Appell Gibbs Koopman von Neumann
Categories ► Classical mechanics

Classical mechanics 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 in science, engineering, and technology.

Classical mechanics is fundamentally based on Newton's laws of motion. These laws describe the relationship between the forces acting on a body and the motion of that body. They were first compiled by Sir Isaac Newton in his work Philosophiæ Naturalis Principia Mathematica, first published on July 5, 1687. Newton's three laws are:

1. A body either is at rest or moves with constant velocity, until and unless an outer force is applied to it.
2. An object will travel in one direction forever or until an outer force changes its direction.
3. Whenever one body exerts a force F onto a second body, (in some cases, which is standing still) the second body exerts the force −F on the first body. F and −F are equal in magnitude and opposite in sense. So, the body which exerts F will go backwards.[3] Newton's 3rd law of motion is summarised by the statement: "For every action, there is an equal but opposite reaction".

Newton's three laws of motion were the first to accurately provide a mathematical model for understanding orbiting bodies in outer space. This explanation unified the motion of celestial bodies and motion of objects on earth.

Uniform Motion:

When an object moves with a constant speed at a particular direction at regular intervals of time it is known as the uniform motion. For example: a bike moving in a straight line with a constant speed.

Equations of Uniform Motion:

If ${\displaystyle \mathbf {v} }$ = final and initial velocity, ${\displaystyle t}$ = time, and ${\displaystyle \mathbf {s} }$ = displacement, then:

Modern kinematics developed with study of electromagnetism and refers all velocities v to their ratio to speed of light c. Velocity is then interpreted as rapidity, the hyperbolic angle φ for which the hyperbolic tangent function tanh φ = v/c. Acceleration, the change of velocity, then changes rapidity according to Lorentz transformations. This part of mechanics is special relativity. Efforts to incorporate gravity into relativistic mechanics were made by W. K. Clifford and Albert Einstein. The development used differential geometry to describe a curved universe with gravity; the study is called general relativity.

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Quantum mechanics
${\displaystyle i\hbar {\frac {\partial }{\partial t}}|\psi (t)\rangle ={\hat {H}}|\psi (t)\rangle }$ Schrödinger equation
Introduction Glossary History Textbooks
Background Classical mechanics Old quantum theory Bra–ket notation Hamiltonian Interference
Fundamentals Coherence Decoherence Complementarity Energy level Entanglement Hamiltonian Uncertainty principle Ground state Interference Measurement Nonlocality Observable Operator Quantum Quantum fluctuation Quantum number Quantum noise Quantum realm Quantum state Quantum system Quantum teleportation Qubit Spin Superposition Quantum vacuum state Symmetry (Spontaneous) symmetry breaking Vacuum state Wave propagation Wave function Wave function collapse Wave–particle duality Matter wave Rectangular potential barrier
Effects Zeeman effect Stark effect Aharonov–Bohm effect Landau quantization Quantum Hall effect Quantum Zeno effect Quantum tunnelling Photoelectric effect Casimir effect
Experiments Bell's inequality Davisson–Germer Double-slit Elitzur–Vaidman Franck–Hertz Leggett–Garg inequality Mach–Zehnder Popper Quantum eraser (delayed-choice) Schrödinger's cat Stern–Gerlach Wheeler's delayed-choice
Formulations Overview Dynamical pictures (Heisenberg; Interaction; Schrödinger) Matrix Phase-space Sum-over-histories (path-integral)
Equations Dirac Hellmann–Feynman Klein–Gordon Lippmann–Schwinger Pauli Rydberg Schrödinger
Interpretations Overview Bayesian Consistent histories Copenhagen de Broglie–Bohm Ensemble Hidden-variable Many-worlds Objective collapse Quantum logic Relational Stochastic Transactional
Advanced topics Quantum annealing Quantum chaos Quantum computing Quantum geometry Density matrix Quantum field theory Fractional quantum mechanics Quantum gravity Quantum information science Quantum machine learning Perturbation theory (quantum mechanics) Relativistic quantum mechanics Scattering theory Superfluid vacuum theory Spontaneous parametric down-conversion Quantum statistical mechanics
Scientists Aharonov Bell Blackett Bloch Bohm Bohr Born Bose de Broglie Candlin Compton Dirac Davisson Debye Ehrenfest Einstein Everett Fock Fermi Feynman Glauber Gutzwiller Heisenberg Hilbert Jordan Kramers Pauli Lamb Landau Laue Moseley Millikan Onnes Planck Rabi Raman Rydberg Schrödinger Sommerfeld von Neumann Weyl Wien Wigner Zeeman Zeilinger Goudsmit Uhlenbeck Yang
Categories ► Quantum mechanics

Quantum mechanics is a set of principles describing physical reality at the atomic level of matter (molecules and atoms) and the subatomic particles (electrons, protons, neutrons, and even smaller elementary particles such as quarks). These descriptions include the simultaneous wave-like and particle-like behavior of both matter and radiation energy as described in the wave–particle duality:/[4]

In classical mechanics, accurate measurements and predictions of the state of objects can be calculated, such as location and velocity. In quantum mechanics, due to the Heisenberg uncertainty principle, the complete state of a subatomic particle, such as its location and velocity, cannot be simultaneously determined.

In addition to describing the motion of atomic level phenomena, quantum mechanics is useful in understanding some large-scale phenomenon such as superfluidity, superconductivity, and biological systems, including the function of smell receptors and the structures of protein.

Spacetime (the fabric of the universe) is expanding meaning everything in the universe is stretching like a rubber band. This motion is the most obscure as it is not physical motion as such, but rather a change in the very nature of the universe. The primary source of verification of this expansion was provided by Edwin Hubble who demonstrated that all galaxies and distant astronomical objects were moving away from Earth, known as Hubble's law, predicted by a universal expansion.[6]

The Milky Way Galaxy is moving through space and many astronomers believe the velocity of this motion to be approximately 600 kilometres per second (1,340,000 mph) relative to the observed locations of other nearby galaxies. Another reference frame is provided by the Cosmic microwave background. This frame of reference indicates that the Milky Way is moving at around 582 kilometres per second (1,300,000 mph).[7]

The Milky Way is rotating around its dense galactic center, thus the sun is moving in a circle within the galaxy's gravity. Away from the central bulge, or outer rim, the typical stellar velocity is between 210 and 240 kilometres per second (470,000 and 540,000 mph).[8] All planets and their moons move with the sun. Thus, the solar system is moving.

The Earth is rotating or spinning around its axis. This is evidenced by day and night, at the equator the earth has an eastward velocity of 0.4651 kilometres per second (1,040 mph).[9] The Earth is also orbiting around the Sun in an orbital revolution. A complete orbit around the sun takes one year, or about 365 days; it averages a speed of about 30 kilometres per second (67,000 mph).[10]

The Theory of Plate tectonics tells us that the continents are drifting on convection currents within the mantle causing them to move across the surface of the planet at the slow speed of approximately 2.54 centimetres (1 in) per year.[11][12] However, the velocities of plates range widely. The fastest-moving plates are the oceanic plates, with the Cocos Plate advancing at a rate of 75 millimetres (3.0 in) per year[13] and the Pacific Plate moving 52–69 millimetres (2.0–2.7 in) per year. At the other extreme, the slowest-moving plate is the Eurasian Plate, progressing at a typical rate of about 21 millimetres (0.83 in) per year.

The human heart is constantly contracting to move blood throughout the body. Through larger veins and arteries in the body, blood has been found to travel at approximately 0.33 m/s. Though considerable variation exists, and peak flows in the venae cavae have been found between 0.1 and 0.45 metres per second (0.33 and 1.48 ft/s).[14] additionally, the smooth muscles of hollow internal organs are moving. The most familiar would be the occurrence of peristalsis which is where digested food is forced throughout the digestive tract. Though different foods travel through the body at different rates, an average speed through the human small intestine is 3.48 kilometres per hour (2.16 mph).[15] The human lymphatic system is also constantly causing movements of excess fluids, lipids, and immune system related products around the body. The lymph fluid has been found to move through a lymph capillary of the skin at approximately 0.0000097 m/s.[16]

The cells of the human body have many structures which move throughout them. Cytoplasmic streaming is a way which cells move molecular substances throughout the cytoplasm,[17] various motor proteins work as molecular motors within a cell and move along the surface of various cellular substrates such as microtubules, and motor proteins are typically powered by the hydrolysis of adenosine triphosphate (ATP), and convert chemical energy into mechanical work.[18] Vesicles propelled by motor proteins have been found to have a velocity of approximately 0.00000152 m/s.[19]

According to the laws of thermodynamics, all particles of matter are in constant random motion as long as the temperature is above absolute zero. Thus the molecules and atoms which make up the human body are vibrating, colliding, and moving. This motion can be detected as temperature; higher temperatures, which represent greater kinetic energy in the particles, feel warm to humans who sense the thermal energy transferring from the object being touched to their nerves. Similarly, when lower temperature objects are touched, the senses perceive the transfer of heat away from the body as feeling cold.[20]

Within each atom, electrons exist in a region around the nucleus. This region is called the electron cloud. According to Bohr's model of the atom, electrons have a high velocity, and the larger the nucleus they are orbiting the faster they would need to move. If electrons 'move' about the electron cloud in strict paths the same way planets orbit the sun, then electrons would be required to do so at speeds which far exceed the speed of light. However, there is no reason that one must confine one's self to this strict conceptualization, that electrons move in paths the same way macroscopic objects do. Rather one can conceptualize electrons to be 'particles' that capriciously exist within the bounds of the electron cloud.[21] Inside the atomic nucleus, the protons and neutrons are also probably moving around due to the electrical repulsion of the protons and the presence of angular momentum of both particles.[22]