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Newton's second law, in modern form, states that the time derivative of the momentum is the force: =. If the mass m {\displaystyle m} does not change with time, then the derivative acts only upon the velocity, and so the force equals the product of the mass and the time derivative of the velocity, which is the acceleration: [ 22 ] F = m d v d t ...
So for a free particle, Newton's second law coincides with the geodesic equation and states that free particles follow geodesics, the extremal trajectories it can move along. If the particle is subject to forces F ≠ 0 , the particle accelerates due to forces acting on it and deviates away from the geodesics it would follow if free.
Using Newton's second law, the force exerted by a body (particle 2) on another body (particle 1) is: =. The force exerted by particle 1 on particle 2 is: = According to Newton's third law, the force that particle 2 exerts on particle 1 is equal and opposite to the force that particle 1 exerts on particle 2: =
So long as the force acting on a particle is known, Newton's second law is sufficient to describe the motion of a particle. Once independent relations for each force acting on a particle are available, they can be substituted into Newton's second law to obtain an ordinary differential equation, which is called the equation of motion.
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Some definitions and concepts from classical mechanics do carry over to SR, such as force as the time derivative of momentum (Newton's second law), the work done by a particle as the line integral of force exerted on the particle along a path, and power as the time derivative of work done. However, there are a number of significant ...
i.e. they take the form of Newton's second law applied to a single particle with the unit mass =.. Definition.The equations are called the equations of a Newtonian dynamical system in a flat multidimensional Euclidean space, which is called the configuration space of this system.
From a cross-project redirect: This is a redirect from a title linked to an item on Wikidata.The Wikidata item linked to this page is Newton's second law of motion for constant mass (Q2397319).