motion

Newton's First Law of Motion (Law of Inertia)

An object at rest stays at rest, and an object in motion continues in motion with the same speed and in the same direction unless acted upon by an unbalanced force.

Newton's Second Law of Motion (Force and Acceleration)

The acceleration of an object is directly proportional to the net force acting on the object and inversely proportional to the object's mass (F = ma).

Newton's Third Law of Motion (Action and Reaction)

For every action, there is an equal and opposite reaction.

Galilean Principle of Relativity

The laws of physics are the same in all inertial frames of reference, meaning that the mechanical laws work equally well in any frame of reference that moves at a constant speed in a straight line.

Galilean Transformation

Equations used to transform the coordinates of an event as recorded in one inertial frame to another, assuming that time is absolute and the same for all reference frames.

Inertial Reference Frames

Reference frames in which an object either is at rest or moves at a constant velocity, implying that no net force is acting on the object.

Relative Motion

The calculation of the motion of an object with regard to some other moving object.

Centripetal Force and Acceleration

The force and acceleration that causes an object to move in a circular path, directed towards the center around which the object is moving.

Law of Universal Gravitation

Every mass attracts every other mass with a force directly proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

Conservation of Momentum in Inelastic and Elastic Collisions

In all collisions between isolated systems, the total momentum before the collision equals the total momentum after the collision.

Coriolis Effect (in the context of rotating reference frames)

An apparent force that acts on a mass moving in a rotating system, such as the Earth, resulting from the mass's inertia.

Mach's Principle

The hypothesis that the inertia of any system is the result of its interaction with the mass of the universe, indicating a form of relativity of inertia to distant celestial bodies.

Non-inertial (Accelerating) Reference Frames

Reference frames where objects appear to be subjected to fictitious forces because the frame itself is accelerating. This includes phenomena such as the centrifugal force and the Coriolis effect.

Equivalence Principle (General Relativity)

The principle stating that the effects of gravity are indistinguishable from the effects of acceleration, which underpins Einstein's theory of general relativity.

Frame-dragging Effect

Predicted by general relativity, this effect occurs when massive rotating objects (like Earth) drag spacetime around with them, affecting the motion of objects and light in the vicinity.

Time Dilation (Special Relativity)

The phenomenon that a clock moving relative to an observer will be measured to tick slower than a clock that is at rest in the observer's own frame of reference.

Length Contraction (Special Relativity)

The phenomenon that objects moving at a significant fraction of the speed of light will be measured to be shorter in the direction of motion, from the perspective of the observer.

Lorentz Transformation

The mathematical framework for transforming between the coordinates of two systems moving at constant velocity relative to each other, taking into account the finite and constant speed of light for all observers.

Energy-Momentum Relation

A fundamental principle in both special relativity and classical mechanics, expressing the relationship between an object's energy, its momentum, and its mass. In special relativity, it's given by E2=(mc2)2+(pc)2.

Principle of Least Action (Hamilton's Principle)

The path taken by a system between two states is the one for which the action integral is minimized. This principle is foundational in classical mechanics, quantum mechanics, and even general relativity.

Newton's Bucket Argument

An argument devised by Newton to demonstrate the existence of absolute space through the behavior of water in a spinning bucket.

The Twin Paradox (Special Relativity)

A thought experiment that illustrates the effects of time dilation, where one twin travels at relativistic speeds into space, and upon return, is younger than the twin who stayed on Earth.

The Michelson-Morley Experiment

An important historical experiment that demonstrated the constancy of the speed of light and helped refute the existence of the "luminiferous ether," leading to the development of special relativity.

The Problem of Motion in Newtonian Mechanics and General Relativity

Contrasting Newton's absolute space and time with Einstein's spacetime continuum, exploring how these frameworks conceptualize motion differently.

Rotational Inertia and Angular Momentum Conservation

The resistance of an object to changes in its rotational motion and the principle that the total angular momentum of a system remains constant if it is not acted upon by external torques.

Reference Frame Definition

A coordinate system or a set of axes within which to measure the position, orientation, and other properties of objects in it. It can be stationary or moving.

Principle of Galilean Relativity

The laws of motion are the same in all inertial frames. No experiments conducted within an inertial frame can detect any motion of the frame itself, provided the frame moves at constant velocity.

Leibniz's Principle of the Equipollence of Hypotheses (Equivalence of Hypotheses)

No two hypotheses should be considered more physically real than the other if they adequately describe a phenomenon purely by relating the observable quantities, despite differing in unobservable aspects

corollary V

The motions of bodies included in a given space are the same among themselves, whether that space is at rest, or moves uniformly forwards in a right line without any circular motion.

corollary VI

If bodies move in any manner whatsoever with respect to each other and are urged on in parallel directions by equal accelerative forces, they will all proceed to move in the same manner with respect to each other, as if they had not been acted upon by those forces