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**Newton’s laws of motion**, relations between the forces acting on a body and the motion of the body, first formulated by English physicist and mathematician Sir Isaac Newton.

Newton’s first law states that, if a body is at rest or moving at a constant speed in a straight line, it will remain at rest or keep moving in a straight line at constant speed unless it is acted upon by a force. This postulate is known as the law of inertia. The law of inertia was first formulated by Galileo Galilei for horizontal motion on Earth and was later generalized by René Descartes. Before Galileo it had been thought that all horizontal motion required a direct cause, but Galileo deduced from his experiments that a body in motion would remain in motion unless a force (such as friction) caused it to come to rest.

Newton’s second law is a quantitative description of the changes that a force can produce on the motion of a body. It states that the time rate of change of the momentum of a body is equal in both magnitude and direction to the force imposed on it. The momentum of a body is equal to the product of its mass and its velocity. Momentum, like velocity, is a vector quantity, having both magnitude and direction. A force applied to a body can change the magnitude of the momentum, or its direction, or both. Newton’s second law is one of the most important in all of physics. For a body whose mass *m* is constant, it can be written in the form *F* = *m**a*, where *F* (force) and *a* (acceleration) are both vector quantities. If a body has a net force acting on it, it is accelerated in accordance with the equation. Conversely, if a body is not accelerated, there is no net force acting on it.

Newton’s third law states that when two bodies interact, they apply forces to one another that are equal in magnitude and opposite in direction. The third law is also known as the law of action and reaction. This law is important in analyzing problems of static equilibrium, where all forces are balanced, but it also applies to bodies in uniform or accelerated motion. The forces it describes are real ones, not mere bookkeeping devices. For example, a book resting on a table applies a downward force equal to its weight on the table. According to the third law, the table applies an equal and opposite force to the book. This force occurs because the weight of the book causes the table to deform slightly so that it pushes back on the book like a coiled spring.

Newton’s laws first appeared in his masterpiece, Philosophiae Naturalis Principia Mathematica (1687), commonly known as the Principia. In 1543 Nicolaus Copernicus suggested that the Sun, rather than Earth, might be at the centre of the universe. In the intervening years Galileo, Johannes Kepler, and Descartes laid the foundations of a new science that would both replace the Aristotelian worldview, inherited from the ancient Greeks, and explain the workings of a heliocentric universe. In the Principia Newton created that new science. He developed his three laws in order to explain why the orbits of the planets are ellipses rather than circles, at which he succeeded, but it turned out that he explained much more. The series of events from Copernicus to Newton is known collectively as the scientific revolution.

In the 20th century Newton’s laws were replaced by quantum mechanics and relativity as the most fundamental laws of physics. Nevertheless, Newton’s laws continue to give an accurate account of nature, except for very small bodies such as electrons or for bodies moving close to the speed of light. Quantum mechanics and relativity reduce to Newton’s laws for larger bodies or for bodies moving more slowly.

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