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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.
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]
A body remains at rest, or in motion at a constant speed in a straight line, except insofar as it is acted upon by a force. At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time.
In physics and engineering, a free body diagram (FBD; also called a force diagram) [1] is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies).
The trivial case of the angular momentum of a body in an orbit is given by = where is the mass of the orbiting object, is the orbit's frequency and is the orbit's radius.. The angular momentum of a uniform rigid sphere rotating around its axis, instead, is given by = where is the sphere's mass, is the frequency of rotation and is the sphere's radius.
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 ().
The scalar moment of inertia, , of a body about a specified axis whose direction is specified by the unit vector ^ and passes through the body at a point is as follows: [7] = ^ (= []) ^ = ^ ^ = ^ ^, where is the moment of inertia matrix of the system relative to the reference point , and [] is the skew symmetric matrix obtained from the vector =.
If the body is at rest (v = 0), i.e. in its center-of-momentum frame (p = 0), we have E = E 0 and m = m 0; thus the energy–momentum relation and both forms of the mass–energy relation (mentioned above) all become the same. A more general form of relation holds for general relativity.