An interaction that changes the motion or shape of an object.Force is the fundamental interaction that changes the motion or shape of an object. It is the push or pull that causes a body to accelerate, deform, or alter its trajectory. In physics, force is a vector quantity, meaning it has both magnitude and direction, and is measured in newtons. The concept is central to classical mechanics, where Newton's laws describe how forces affect motion, and extends to modern physics, where forces are understood as exchanges of particles or curvature of spacetime.
The modern concept of force was formalized by Isaac Newton in his 1687 work 'Principia Mathematica', where he stated the three laws of motion. Earlier ideas existed in Aristotelian physics, but Newton's quantitative treatment laid the foundation for classical mechanics.
Forces arise from fundamental interactions: gravitational, electromagnetic, strong nuclear, and weak nuclear. In everyday contexts, forces like friction, tension, and normal reaction are macroscopic manifestations of electromagnetic interactions between atoms. When a force acts on an object, it imparts momentum, changing the object's velocity according to Newton's second law (F = ma). Deformation occurs when internal forces within a material resist external applied forces, leading to stress and strain.
Forces are engineered in countless technologies, from structural engineering (load-bearing beams) to aerospace (thrust and lift) and everyday devices like brakes and springs.
The strongest known force, the strong nuclear force, is about 10^38 times stronger than gravity, yet it operates only over subatomic distances.
| F | variable | Gravitational force magnitude — force newton |
| M | variable | Mass of the central object — mass kilogram |
| m | variable | Mass of the test particle — mass kilogram |
| r | variable | Distance between masses — distance metre |
| ρ | variable | Energy density of the cosmic fluid — energy density joule per cubic metre |
| w | variable | Equation-of-state parameter of the fluid — equation of state parameter |
| G | constant | Universal constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |
| F | variable | Force on the sail — force newton |
| A | variable | Area of the sail — area square metre |
| s | variable | Poynting flux (power per unit area) of incident light — irradiance watt per square metre |
| v | variable | Speed of the sail relative to the light source — velocity metre per second |
| c | constant | Universal constant, speed of light in vacuum — speed of light = 299792458 metre per second |
| \cdot | operator | Product of quantities — multiplication |
| \frac{1 - v/c}{1 + v | operator | Ratio of reflected to incident photon energy and rate — doppler factor squared |
| \mathbf{F} | variable | gravitational force vector — force newton |
| m_1 | variable | mass of first object — mass kilogram |
| m_2 | variable | mass of second object — mass kilogram |
| r | variable | distance between the centers of mass — distance metre |
| \hat{\mathbf{r}} | variable | unit vector pointing from one mass to the other — unit vector |
| G | constant | Newtonian gravitational constant, fundamental constant of gravitation — gravitational constant = 6.67430e-11 cubic metre per kilogram per second squared |







