Force is an interaction that can change the motion of an object or deform it. In classical mechanics, force is represented as a vector quantity with magnitude and direction, and the net force acting on an object determines its acceleration through Newton second law. Force is measured in newtons, where one newton is the force required to give a one kilogram mass an acceleration of one metre per second squared.
Forces can arise through contact interactions, such as friction, tension and normal forces, or through interactions that operate across space, such as gravity and electromagnetism. At the fundamental level, many familiar forces can be understood as manifestations of the fundamental interactions. The concept is therefore both a practical tool for analysing macroscopic systems and a bridge to deeper theories of matter and fields.
Newton second law provides the central quantitative relationship between force and motion. For a system of constant mass in classical mechanics, net force equals mass multiplied by acceleration. The word net is essential because several forces can act simultaneously. An object can experience substantial forces while having zero acceleration if those forces cancel vectorially. For example, a stationary book on a table experiences downward gravitational force and upward normal force of approximately equal magnitude.
If one force becomes larger than the other, the object accelerates in the direction of the resulting net force. Force therefore does not mean motion itself. An object can move at constant velocity with zero net force, while an object at rest can have nonzero forces acting on it provided those forces balance.
Forces are vectors, so both magnitude and direction matter. Two forces of equal magnitude acting in opposite directions cancel, while two forces of equal magnitude acting perpendicular to one another produce a resultant whose magnitude is greater than either individual force. Vector addition is therefore essential in mechanics. Components are often resolved along convenient coordinate axes so that equations can be solved independently in each direction. This approach is useful for projectile motion, inclined planes, circular motion and structural analysis. The resultant force determines acceleration, but individual forces can provide important physical information about the interactions within a system. Correctly identifying all relevant forces and their directions is therefore a fundamental skill in mechanics.
Common forces in classical mechanics include gravitational force, normal force, friction, tension, spring force, drag and buoyancy. Gravitational force attracts masses, normal force arises from contact constraints, friction opposes relative motion or the tendency toward relative motion at surfaces, tension acts through flexible connections such as ropes, and spring forces arise from elastic deformation. Drag results from interaction with a fluid and often depends on velocity, shape, fluid density and flow regime.
Buoyant force results from pressure differences in a fluid under gravity. These forces are not all fundamental in the same sense. For example, normal and friction forces ultimately arise from electromagnetic interactions and quantum mechanical properties of matter, while gravity and electromagnetism are fundamental interactions in modern physical theory.
The fundamental interactions are gravity, electromagnetism, the strong interaction and the weak interaction. Electromagnetism governs interactions involving electric charge and accounts for phenomena such as electricity, magnetism and light. The strong interaction binds quarks and is responsible for the stability of atomic nuclei through residual nuclear interactions. The weak interaction is responsible for processes such as beta decay and plays an important role in neutrino interactions and stellar nuclear reactions.
Gravity acts universally on energy and momentum and dominates many astronomical systems because it is always attractive under ordinary conditions. In modern physics, describing these interactions as forces can be useful at macroscopic scales, but quantum field theory describes the other three fundamental interactions through fields and exchange processes, while general relativity describes gravity geometrically.
Force is closely related to momentum. Newton second law can be expressed more generally as net force equals the rate of change of momentum. This formulation remains useful for systems in which mass changes or relativistic effects become important, provided momentum is defined appropriately. Impulse is the change in momentum produced by a force acting over a time interval.
A large force applied for a very short time can produce the same impulse as a smaller force acting for a longer time. This principle explains the design of airbags, helmets and crumple zones, which increase the time over which momentum changes during a collision and thereby reduce peak forces on occupants. Force therefore provides information about how motion changes, while impulse connects force with the cumulative effect of an interaction over time.
Forces also cause deformation. A solid can stretch, compress, bend, twist or shear when forces act upon it. The relationship between applied force and deformation depends on material properties and the magnitude and duration of loading. Hooke law provides an approximation for elastic deformation in springs and other systems within an appropriate range, with force proportional to displacement and directed toward equilibrium. Beyond the elastic limit, materials may undergo permanent deformation or fracture.
Engineering therefore distinguishes stress from force because stress represents force distributed over an area. Strain represents relative deformation. Material mechanics uses these quantities to predict whether structures will remain safe under applied loads. Thus force is important not only for explaining acceleration but also for understanding how physical materials respond to interactions.
Force concepts have limitations when applied outside their appropriate theoretical domain. Newtonian force laws are highly accurate for ordinary macroscopic systems at speeds much lower than light speed and in gravitational fields that are not extremely strong. Relativity is required when relativistic effects become significant, while quantum mechanics is required for microscopic systems where classical trajectories are inadequate. In general relativity, gravity is described fundamentally through spacetime curvature rather than as a Newtonian force.
In quantum field theory, interactions are described through quantum fields rather than classical forces between point objects. Nevertheless, force remains an extraordinarily useful concept because classical mechanics emerges as an accurate approximation across a vast range of everyday phenomena, allowing complex physical systems to be analysed with comparatively simple mathematical relationships.
