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In physics, a conservation law states that a particular measurable property of an isolated physical system does not change as the system evolves over time. Exact conservation laws include conservation of mass-energy, conservation of linear momentum, conservation of angular momentum, and conservation of electric charge.
Conservation of momentum is a mathematical consequence of the homogeneity (shift symmetry) of space (position in space is the canonical conjugate quantity to momentum). That is, conservation of momentum is a consequence of the fact that the laws of physics do not depend on position; this is a special case of Noether's theorem. [25] For systems ...
A form of Newton's second law, that force is the rate of change of momentum, also holds, as does the conservation of momentum. However, the definition of momentum is modified. Among the consequences of this is the fact that the more quickly a body moves, the harder it is to accelerate, and so, no matter how much force is applied, a body cannot ...
The global versions can be united into a single global conservation law: the conservation of the energy-momentum 4-vector. The local versions of energy and momentum conservation (at any point in space-time) can also be united, into the conservation of a quantity defined locally at the space-time point: the stress–energy tensor [ 11 ] : 592 ...
Examples of integrals of motion are the angular momentum vector, =, or a Hamiltonian without time dependence, such as (,) = + (). An example of a function that is a constant of motion but not an integral of motion would be the function C ( x , v , t ) = x − v t {\displaystyle C(x,v,t)=x-vt} for an object moving at a constant speed in one ...
In Definition III, he defined the force that resists a change in motion as the vis inertia of Descartes. Newton’s Third Law of Motion (for every action there is an equal and opposite reaction) is also equivalent to the principle of conservation of momentum.
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The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.