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Momentum depends on the frame of reference, but in any inertial frame of reference, 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 ...
Therefore, = = = =, where Δp is the change in linear momentum from time t 1 to t 2. This is often called the impulse-momentum theorem (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.
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.
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}}\,.}
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]
The moment of force, or torque, is a first moment: =, or, more generally, .; Similarly, angular momentum is the 1st moment of momentum: =.Momentum itself is not a moment.; The electric dipole moment is also a 1st moment: = for two opposite point charges or () for a distributed charge with charge density ().
Symbol Description SI derived unit Dimension Comments Absorbed dose rate: D: Absorbed dose received per unit of time Gy/s L 2 T −3: Action: S: Momentum of particle multiplied by distance travelled J/Hz L 2 M T −1: scalar Angular acceleration: ω a: Change in angular velocity per unit time rad/s 2: T −2: Area: A: Extent of a surface m 2: L ...
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.