Force is an interaction capable of changing an object's momentum, and in classical mechanics the net external force on an object is related to the time rate of change of its momentum. For constant mass, this becomes the familiar relationship between net force, mass and acceleration. Force is a vector quantity, so both magnitude and direction are required to specify it completely. Forces arise from interactions such as gravity, electromagnetic effects, contact interactions, tension, elasticity and friction. In mechanics, it is the net force rather than the existence of an individual force that determines whether an object's velocity changes.
Forces can be classified in several ways. Gravitational and electromagnetic interactions can act without direct mechanical contact, while normal reactions, friction, tension and many applied forces occur through contact or mediated material interactions. In introductory mechanics, gravity is commonly represented as weight near Earth's surface, while the normal force represents a surface's reaction to contact. Tension arises in idealised strings, cables and similar elements, while spring forces can be modelled using Hooke's law within the elastic regime. These categories are modelling descriptions of physical interactions and should not be confused with fundamental interactions in particle physics.
Newton's Second Law provides the principal quantitative treatment of Force in classical particle mechanics. When mass is constant, acceleration is proportional to the net force and inversely proportional to mass. Because the relationship is vectorial, changing the direction of a force can change the direction of acceleration without necessarily changing speed in a simple way. In circular motion, for example, a net inward force produces centripetal acceleration even when the object's speed is constant. The term centripetal force does not describe a new fundamental type of force; it refers to the net inward force required for circular motion, which may be supplied by gravity, tension, friction, a normal reaction or another interaction.
Free-body diagrams are a central practical tool for analysing forces. They isolate one chosen object and represent external forces acting on that object using vectors. The forces must be identified according to actual interactions rather than according to the motion alone. An object moving to the right does not automatically experience a rightward force, and an object stationary on a surface does not necessarily have no forces acting on it. If weight and normal reaction balance vertically while horizontal forces also balance, the net force is zero even though several individual forces are present. Free-body diagrams therefore help distinguish individual interactions from their vector sum.
Force and energy are related but not synonymous. A force can transfer energy when it acts through displacement, with work depending on the force component along the displacement. A force can also act without doing mechanical work if it remains perpendicular to the instantaneous displacement, as in ideal uniform circular motion where the centripetal force changes direction without changing kinetic energy. Similarly, a force can alter momentum even when the associated work is zero. These distinctions prevent the common mistake of treating force, work, power, energy and momentum as interchangeable quantities.
The SI unit of Force is the newton, defined as a kilogram metre per second squared. Dimensional analysis expresses this as mass multiplied by acceleration. Force measurements can be made using devices such as load cells, force plates and calibrated spring systems, although practical measurements include uncertainty and may depend on dynamic response, calibration and environmental conditions. In engineering, force is often analysed alongside stress, pressure and torque, but these quantities represent different physical concepts. Pressure is force distributed over area, while torque describes the rotational effect of a force about a chosen point or axis.
At the fundamental level, known physical interactions are commonly grouped into gravitational, electromagnetic, strong nuclear and weak nuclear interactions. Everyday mechanical forces often emerge from these underlying interactions rather than representing separate fundamental forces. For example, contact forces between ordinary materials are largely electromagnetic in microscopic origin, while friction and normal reactions arise from complex interactions between surfaces. This distinction is important because introductory mechanics classifies forces according to their role in macroscopic modelling, whereas fundamental physics classifies interactions according to their underlying field and particle descriptions.
Force has broad applications in engineering, biomechanics, structural analysis, transportation and machinery. Bridges and buildings must transmit loads safely, vehicles require forces to accelerate and brake, aircraft generate aerodynamic forces, and machines transmit forces through components and joints. In biomechanics, ground reaction forces and muscle forces are used to analyse human movement. In each case, correct system boundaries, reference frames, force directions and constitutive assumptions are essential. A force model is therefore only as useful as the physical interactions it includes and the assumptions under which those interactions are represented.
