Force

Force is the action that accelerates a body having mass. A force is a vector quantity, having a magnitude and a direction that corresponds exactly to the direction of its resulting acceleration. Forces from different sources acting on the same body sum as vectors to form a net force or resultant force on the body. A body's acceleration is proportional to the net force exerted it and, according to Newton's second law of motion, the proportionality constant is the mass of the body. There are two useful expressions for the second law:

${\overrightarrow {F}}=m{\frac {d{\overrightarrow {v}}}{dt}}=m{\overrightarrow {a}}$ and ${\overrightarrow {F}}={\frac {d{\overrightarrow {p}}}{dt}}$

Here m, v, a, and p are the mass, velocity, acceleration, and momentum respectively of the body upon which the force is exerted. When a body experiences a nonzero net force for any period of time, its velocity and momentum change over that time. Calculus is required to model the functional relations between these physical quantities, although models for forces are typically introduced to students through average quantities to simplify the analysis.

Laws of Motion

The physical laws that Newton presented in his Principia are sufficient to introduce the most universal features of force and its effect on bodies.

According to Newton's first law of motion, the velocity of a body is constant when the net force exerted upon that body is zero. Whether the velocity is zero or nonzero has no bearing on its constancy in the absence of a net force. Historically, this constancy had been attributed to a vis insita or internal force that maintains the body's state of rest or motion but today it is understood that motion is only relatively distinguishable from rest and this constancy is a well-established law without deeper explanation. Despite its simplicity, this constancy correlates with the resistance of a body to change in its motion - known more technically as inertia - and has a significant place in the general theory of relativity.

As already stated, Newton's second law expresses how the force on a body is proportional to its resulting acceleration.

Newton's third law of motion captures the fact that a force is an interaction between two objects. It states that, if one object exerts a force on a second object, then the second object exerts a force of equal magnitude, and in the opposite direction, on the first object. This is often phrased as, "For every action, there is an equal and opposite reaction," and the forces that any two objects exert on each other are referred to as an action-reaction force pair.