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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 momentum does not change. Momentum is also conserved in special relativity (with a modified formula) and, in a modified form, in electrodynamics, quantum mechanics ...
Internal forces between the particles that make up a body do not contribute to changing the momentum of the body as there is an equal and opposite force resulting in no net effect. [3] The linear momentum of a rigid body is the product of the mass of the body and the velocity of its center of mass v cm. [1] [4] [5]
Therefore, = = = =, where Δp is the change in linear momentum from time t 1 to t 2. This is often called the impulse-momentum theorem [ 3 ] (analogous to the work-energy theorem ). As a result, an impulse may also be regarded as the change in momentum of an object to which a resultant force is applied.
In modern notation, the momentum of a body is the product of its mass and its velocity: =, where all three quantities can change over time. Newton's second law, in modern form, states that the time derivative of the momentum is the force: F = d p d t . {\displaystyle \mathbf {F} ={\frac {d\mathbf {p} }{dt}}\,.}
There are two main descriptions of motion: dynamics and kinematics.Dynamics is general, since the momenta, forces and energy of the particles are taken into account. In this instance, sometimes the term dynamics refers to the differential equations that the system satisfies (e.g., Newton's second law or Euler–Lagrange equations), and sometimes to the solutions to those equations.
Left: intrinsic "spin" angular momentum S is really orbital angular momentum of the object at every point, right: extrinsic orbital angular momentum L about an axis, top: the moment of inertia tensor I and angular velocity ω (L is not always parallel to ω) [6] bottom: momentum p and its radial position r from the axis.
Since m 0 does not change from frame to frame, the energy–momentum relation is used in relativistic mechanics and particle physics calculations, as energy and momentum are given in a particle's rest frame (that is, E ′ and p ′ as an observer moving with the particle would conclude to be) and measured in the lab frame (i.e. E and p as ...
Since the partial derivative is a linear operator, the momentum operator is also linear, and because any wave function can be expressed as a superposition of other states, when this momentum operator acts on the entire superimposed wave, it yields the momentum eigenvalues for each plane wave component. These new components then superimpose to ...