Motion is a change in the position of an object or physical system with respect to a chosen reference frame as time passes. Motion is therefore not an absolute property in classical mechanics but a relationship between an object and an observer or coordinate system. A passenger sitting in a moving train is approximately stationary relative to the train but moving relative to the ground. Describing motion requires specifying a reference frame, position, time and usually a coordinate system.
Physics distinguishes several quantities used to characterise motion, including distance, displacement, speed, velocity and acceleration. Motion can be translational, rotational, oscillatory, orbital or a combination of these forms. The study of motion is central to mechanics and provides the basis for analysing everything from falling objects and vehicles to planets, molecules and particles.
Kinematics is the branch of mechanics that describes motion without necessarily explaining its causes. It uses position, displacement, velocity, speed and acceleration as principal quantities. If an object's position changes with time, its trajectory can be described mathematically. Displacement is the vector difference between final and initial positions, while distance is the total path length travelled. Velocity is the rate of change of position with respect to time, and acceleration is the rate of change of velocity.
These quantities are related through calculus in continuous motion. If velocity is known as a function of time, position can be determined by integration, while acceleration can be integrated to obtain velocity. This mathematical framework allows motion to be described precisely even before the forces responsible for it are analysed.
Dynamics explains motion by considering forces and interactions. Newton laws provide the classical framework for connecting force with acceleration, although other formulations such as Lagrangian and Hamiltonian mechanics can be more convenient for complex systems. If the net force on an object is zero, its velocity remains constant in an inertial reference frame. If the net force is nonzero, the object accelerates in the direction of the net force. Gravity produces orbital motion, electromagnetic forces influence charged particles, and contact forces determine the motion of many terrestrial objects. The same kinematic description can therefore arise from different physical causes. Dynamics asks why the motion changes, while kinematics primarily describes what the motion does.
Motion can occur in one, two or three spatial dimensions. One dimensional motion includes idealised situations such as an object moving along a straight track. Two dimensional motion includes projectile trajectories and circular motion in a plane. Three dimensional motion occurs in aircraft, spacecraft, molecules and complex mechanical systems. Coordinate systems can be selected to simplify particular problems.
Cartesian coordinates are useful for many linear systems, polar coordinates are useful for radial and angular motion, and spherical or cylindrical coordinates are useful for systems with corresponding symmetries. The choice of coordinates does not alter the physical motion but can greatly simplify the mathematical representation. More complicated systems may require configuration spaces with many degrees of freedom rather than simple three dimensional position coordinates.
Motion is relative to a reference frame. Inertial frames are reference frames in which Newton first law holds without introducing fictitious forces, while accelerating or rotating frames require additional terms in classical mechanics. Examples of apparent forces in non inertial frames include centrifugal and Coriolis effects. The Coriolis effect is important for large scale atmospheric and oceanic motion because Earth rotates. General relativity extends the concept of reference frames through curved spacetime and local inertial frames.
Relativity also shows that measurements of time, distance and velocity can depend on the observer's state of motion, although all inertial observers agree on the invariant speed of light. The choice of reference frame is therefore fundamental rather than merely a matter of descriptive convenience.
Different types of motion reveal different physical mechanisms. Uniform motion occurs when velocity remains constant. Accelerated motion occurs when velocity changes in magnitude, direction or both. Circular motion involves continuous changes in velocity direction even if speed remains constant, meaning that an inward acceleration is present. Oscillatory motion repeatedly moves around an equilibrium configuration and can be approximately harmonic under suitable conditions. Rotational motion concerns changes in orientation around an axis, while translational motion concerns changes in position. Real systems frequently combine translation and rotation, such as rolling wheels, spinning planets and moving rigid bodies. The mathematical description of such systems may require both linear and angular quantities, including angular velocity, angular acceleration, torque and angular momentum.
Conservation laws provide powerful methods for analysing motion. Conservation of linear momentum applies to isolated systems when the net external impulse is zero. Conservation of angular momentum applies under appropriate conditions when external torque is absent. Conservation of mechanical energy can simplify motion problems when nonconservative energy transfers such as friction are absent or separately accounted for. These principles can describe collisions, planetary motion, scattering processes and many mechanical systems without solving every instantaneous force equation. Motion can also be studied statistically when dealing with huge numbers of particles. Statistical mechanics replaces detailed tracking of every molecule with probability distributions and macroscopic quantities such as temperature and pressure.
Motion is not restricted to visible objects. Molecules move continuously due to thermal energy, atoms undergo quantum mechanical dynamics, electromagnetic fields propagate through space and astronomical bodies move through gravitational fields. At microscopic scales, classical trajectories may cease to provide an adequate description because quantum states and probability amplitudes become fundamental. At relativistic speeds, classical time and space relationships must also be replaced by relativistic kinematics.
Nevertheless, everyday motion remains exceptionally well described by classical mechanics because quantum and relativistic corrections are usually negligible at ordinary scales and speeds. The concept of motion therefore provides a unifying framework across physics while requiring different mathematical theories depending on the scale, speed and physical environment involved.
