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When Newton's laws are applied to rotating extended bodies, they lead to new quantities that are analogous to those invoked in the original laws. The analogue of mass is the moment of inertia, the counterpart of momentum is angular momentum, and the counterpart of force is torque. Angular momentum is calculated with respect to a reference point ...
With respect to a coordinate frame whose origin coincides with the body's center of mass for τ() and an inertial frame of reference for F(), they can be expressed in matrix form as:
where τ zx is the flux of x-directed momentum in the z-direction, ν is μ/ρ, the momentum diffusivity, z is the distance of transport or diffusion, ρ is the density, and μ is the dynamic viscosity. Newton's law of viscosity is the simplest relationship between the flux of momentum and the velocity gradient.
The relationship, described by Schwedler's theorem, between distributed load and shear force magnitude is: [3] d Q d x = − q {\displaystyle {\frac {dQ}{dx}}=-q} Some direct results of this is that a shear diagram will have a point change in magnitude if a point load is applied to a member, and a linearly varying shear magnitude as a result of ...
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 ().
In Newtonian mechanics, momentum (pl.: momenta or momentums; more specifically linear momentum or translational momentum) is the product of the mass and velocity of an object. It is a vector quantity, possessing a magnitude and a direction.
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where F ext is the net external force on the body, v rel is the relative velocity of the escaping or incoming mass with respect to the center of mass of the body, and v is the velocity of the body. [3] In astrodynamics, which deals with the mechanics of rockets, the term v rel is often called the effective exhaust velocity and denoted v e. [4]