In physics, motion is the change in position of an object or fluid with respect to a reference frame over a given time. Motion is mathematically described in terms of vector quantities such as displacement (with direction and distance), velocity (direction and speed), acceleration, etc. The relative motion of an object with respect to an observer is the object's motion described in the observer's comoving frame, quantified in terms of relative position, relative velocity, etc. The branch of physics describing the motion of objects without reference to their cause is called kinematics, while the branch studying forces and their effect on motion is called dynamics. If an object is not in motion relative to a given frame of reference, it is said to be at rest, motionless, immobile, stationary, or to have a constant or time-invariant position with reference to its surroundings. Modern physics holds that, as there is no absolute frame of reference, Isaac Newton's concept of absolute motion cannot be determined. Everything in the universe can be considered to be in motion. Motion applies to various physical systems: objects, bodies, matter particles, matter fields, radiation, radiation fields, radiation particles, curvature, and space-time. The concept of motion also applies to images, shapes, and boundaries. In general, the term motion signifies a continuous change in the position or configuration of a physical system in space. For example, one can talk about the motion of a wave or the motion of a quantum particle, where the configuration consists of the probabilities of the wave or particle occupying specific positions.
Equations of motion
Laws of motion In physics, the motion of massive bodies is described through two related sets of laws of mechanics. Classical mechanics for super atomic (larger than an atom) objects (such as cars, projectiles, planets, cells, and humans) and quantum mechanics for atomic and sub-atomic objects (such as helium, protons, and electrons). Historically, Newton and Euler formulated three laws of classical mechanics:
Classical mechanics
Classical mechanics is used for describing the motion of macroscopic objects moving at speeds significantly slower than the speed of light, 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 scientific descriptions 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, which was first published on July 5, 1687. Newton's three laws are:
A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force. (This is known as the law of inertia.) Force ( F → {\displaystyle {\vec {F}}} ) is equal to the change in momentum per change in time ( Δ m v → Δ t {\displaystyle {\frac {\Delta m{\vec {v}}}{\Delta t}}} ). For a constant mass, force equals mass times acceleration ( F → = m a → {\displaystyle {\vec {F}}=m{\vec {a}}} ). For every action, there is an equal and opposite reaction. (In other words, whenever one body exerts a force F → {\displaystyle {\vec {F}}} onto a second body, (in some cases, which is standing still) the second body exerts the force − F → {\displaystyle -{\vec {F}}} back onto the first body. F → {\displaystyle {\vec {F}}} and − F → {\displaystyle -{\vec {F}}} are equal in magnitude and opposite in direction. So, the body that exerts F → {\displaystyle {\vec {F}}} will be pushed backward.) 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 the motion of objects on Earth.
Relativistic mechanics Modern kinematics developed with study of electromagnetism and refers all velocities v {\displaystyle v} to their ratio to speed of light c {\displaystyle c} . Velocity is then interpreted as rapidity, the hyperbolic angle φ {\displaystyle \varphi } for which the hyperbolic tangent function tanh φ = v ÷ c {\displaystyle \tanh \varphi =v\div c} . Acceleration, the change of velocity over time, 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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