For other uses see Force (disambiguation).
In physics, a force is that which can cause an object with mass to change its velocity. Force has both magnitude and direction, making it a vector quantity. Newton's second law states that an object with a constant mass will accelerate in proportion to the net force acting upon and in inverse proportion to its mass. Equivalently, the net force on an object equals the rate at which its momentum changes.
Forces acting on three-dimensional objects may also cause them to rotate or deform, or result in a change in pressure or even change volume in some cases. The tendency of a force to cause changes in rotational speed about an axis is called torque. Deformation and pressure are the result of stress forces within an object. 
Since antiquity, scientists have used the concept of force in the study of stationary and moving objects. The study of forces advanced with descriptions made by the third century BC philosopher Archimedes of how forces interact in simple machines. Prior to this, descriptions of forces by Aristotle incorporated fundamental misunderstandings. By the seventeenth century, Sir Issac Newton corrected these misunderstandings with mathematical insight that remained unchanged for nearly three hundred years. By the early 20th century, Einstein in his theory of general relativity successfully predicted the failure of Newton's model for gravity by ushering in the concept of a space-time continuum.
The recent theory of particle physics known as the Standard Model associate forces at the level of quantum mechanics. The Standard Model predicts that exchange particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational. High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.
Since antiquity, the concept of force has been recognized as integral to the functioning of each of the simple machines. The mechanical advantage given by a simple machine allowed for less force to be used in exchange for that force acting over a greater distance. Analysis of the characteristics of forces ultimately culminated in the work of Archimedes who was especially famous for formulating a treatment of buoyant forces inherent in fluids.
Aristotle provided a philosophical discussion of the concept of a force as an integral part of Aristotelian cosmology. In Aristotle's view, the natural world held four elements that existed in "natural states". Aristotle believed that it was the natural state of objects with mass on Earth, such as the elements water and earth, to be motionless on the ground and that they tended towards that state if left alone. He distinguished between the innate tendency of objects to find their "natural place" (e.g., for heavy bodies to fall), which led to "natural motion", and unnatural or forced motion, which required continued application of a force. This theory, based on the everyday experience of how objects move, such as the constant application of a force needed to keep a cart moving, had conceptual trouble accounting for the behavior of projectiles, such as the flight of arrows. The place where forces were applied to projectiles was only at the start of the flight, and while the projectile sailed through the air, no discernible force acts on it. Aristotle was aware of this problem and proposed that the air displaced through the projectile's path provided the needed force to continue the projectile moving. This explanation demands that air is needed for projectiles and that, for example, in a vacuum, no projectile would move after the initial push. Additional problems with the explanation include the fact that air resists the motion of the projectiles.
These shortcomings would not be fully explained and corrected until the seventeenth century work of Galileo Galilei, who was influenced by the late medieval idea that objects in forced motion carried an innate force of impetus. Galileo constructed an experiment in which stones and cannonballs were both rolled down an incline to disprove the Aristotelian theory of motion early in the seventeenth century. He showed that the bodies were accelerated by gravity to an extent which was independent of their mass and argued that objects retain their velocity unless acted on by a force, for example friction.
See main article: Newton's laws of motion.
Sir Isaac Newton sought to describe the motion of all objects using the concepts of inertia and force, and in doing so, he found that they obey certain conservation laws. In 1687, Newton went on to publish his thesis Philosophiae Naturalis Principia Mathematica.  In this work, Newton set out three laws of motion that to this day are the way forces are described in physics. The general definition of net force can be found in Newton's second law of motion, and it is equal to rate of change of momentum: