Momentum | Wikipedia audio article
Channel: wikipedia tts
Date: 24/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Momentum


00:02:02 1 Newtonian
00:02:33 1.1 Single particle
00:03:42 1.2 Many particles
00:06:02 1.3 Relation to force
00:07:07 1.4 Conservation
00:07:37 1.5 Dependence on reference frame
00:08:53 1.6 Application to collisions
00:08:56 1.6.1 Elastic collisions
00:09:05 1.6.2 Inelastic collisions
00:11:58 1.7 Multiple dimensions
00:14:40 1.8 Objects of variable mass
00:15:09 2 Relativistic
00:20:30 2.1 Lorentz invariance
00:23:17 2.2 Four-vector formulation
00:25:58 3 Generalized
00:26:27 3.1 Lagrangian mechanics
00:29:39 3.2 Hamiltonian mechanics
00:29:48 3.3 Symmetry and conservation
00:32:44 4 Electromagnetic
00:34:35 4.1 Particle in a field
00:39:39 4.2 Conservation
00:39:51 4.2.1 Vacuum
00:40:00 4.2.2 Media
00:40:53 5 Quantum mechanical
00:43:37 6 In deformable bodies and fluids
00:45:33 6.1 Conservation in a continuum
00:46:02 6.2 Acoustic waves
00:46:11 7 History of the concept
00:47:48 8 See also
00:48:21 9 References
00:53:23 10 Bibliography
00:54:50 11 External links
00:57:11 In deformable bodies and fluids
00:57:21 Conservation in a continuum
01:02:32 Acoustic waves
01:03:48 History of the concept



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SUMMARY
=======
In Newtonian mechanics, linear momentum, translational momentum, or simply momentum (pl. momenta) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction in three-dimensional space. If m is an object's mass and v is the velocity (also a vector), then the momentum is

  
    
      
        
          p
        
        =
        m
        
          v
        
        ,
      
    
    {\displaystyle \mathbf {p} =m\mathbf {v} ,}
  In SI units, it is measured in kilogram meters per second (kg⋅m/s). Newton's second law of motion states that a body's rate of change in momentum is equal to the net force acting on it.
Momentum depends on the frame of reference, but in any inertial frame it is a conserved quantity, meaning that if a closed system is not affected by external forces, its total linear momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form,  in electrodynamics, quantum mechanics, quantum field theory, and general relativity. It is an expression of one of the fundamental symmetries of space and time: translational symmetry.
Advanced formulations of classical mechanics, Lagrangian and Hamiltonian mechanics, allow one to choose coordinate systems that incorporate symmetries and constraints. In these systems the conserved quantity is  generalized momentum, and in general this is different from the kinetic momentum defined above. The concept of generalized momentum is carried over into quantum mechanics, where it becomes an operator on a wave function. The momentum and position operators are related by the Heisenberg uncertainty principle.
In continuous systems such as electromagnetic fields, fluids and deformable bodies, a momentum density can be defined, and a continuum version of the conservation of momentum leads to equations such as the Navier–Stokes equations for fluids or the Cauchy momentum equation for deformable solids or fluids.