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This type of impulse is often idealized so that the change in momentum produced by the force happens with no change in time. This sort of change is a step change , and is not physically possible. However, this is a useful model for computing the effects of ideal collisions (such as in videogame physics engines ).
The previous equations for planar motion can be used here: corollaries of momentum, angular momentum etc. can immediately follow by applying the above definitions. For any object moving in any path in a plane, = = ^ the following general results apply to the particle.
These are known as the Navier–Stokes equations. [35] The momentum balance equations can be extended to more general materials, including solids. For each surface with normal in direction i and force in direction j, there is a stress component σ ij. The nine components make up the Cauchy stress tensor σ, which includes both pressure and shear.
In quantum physics, position and momentum are represented by mathematical entities known as Hermitian operators, and the Born rule is used to calculate the expectation values of a position measurement or a momentum measurement. These expectation values will generally change over time; that is, depending on the time at which (for example) a ...
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 energy and momentum of an object measured in two inertial frames in energy–momentum space – the yellow frame measures E and p while the blue frame measures E ′ and p ′. The green arrow is the four-momentum P of an object with length proportional to its rest mass m 0.
The momentum operator can be described as a symmetric (i.e. Hermitian), unbounded operator acting on a dense subspace of the quantum state space. If the operator acts on a (normalizable) quantum state then the operator is self-adjoint. In physics the term Hermitian often refers to both symmetric and self-adjoint operators. [7] [8]
The newton-second (also newton second; symbol: N⋅s or N s) [1] is the unit of impulse in the International System of Units (SI). It is dimensionally equivalent to the momentum unit kilogram-metre per second (kg⋅m/s). One newton-second corresponds to a one-newton force applied for one second.