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One may compare linear motion to general motion. In general motion, a particle's position and velocity are described by vectors, which have a magnitude and direction. In linear motion, the directions of all the vectors describing the system are equal and constant which means the objects move along the same axis and do not change direction.
Euler's second law states that the rate of change of angular momentum L about a point that is fixed in an inertial reference frame (often the center of mass of the body), is equal to the sum of the external moments of force acting on that body M about that point: [1] [4] [5]
of a point-like particle are combined into a four-dimensional bivector in terms of the 4-position X and the 4-momentum P of the particle: [8] [9] = where ∧ denotes the exterior product. This tensor is additive: the total angular momentum of a system is the sum of the angular momentum tensors for each constituent of the system.
Depending on the action principle, the two points connected by paths in a diagram may represent two particle positions at different times, or the two points may represent values in a configuration space or in a phase space. The mathematical technology and terminology of action principles can be learned by thinking in terms of physical space ...
This condition implies that the speed of the particle is close to the speed of light. According to the Lorentz factor formula, this requires the particle to move at roughly 85% of the speed of light. Such relativistic particles are generated in particle accelerators, [a] as well as naturally occurring in cosmic radiation.
Newton showed that the force acting on the second particle equals the force F 1 (r) acting on the first particle, plus an inverse-cube central force [30] = + where L 1 is the magnitude of the first particle's angular momentum. If k 2 is greater than one, F 2 −F 1 is a negative number; thus, the added inverse-cube force is attractive.
Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.)
The flash of light is shown as the 45° red lines. The points at which the two light flashes hit the ends of the train are at the same level in the diagram. This means that the events are simultaneous. In the second diagram, the two ends of the train moving to the right, are shown by parallel lines.