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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.
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 ().
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.
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.
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]
In classical mechanics, impulse (symbolized by J or Imp) is the change in momentum of an object. If the initial momentum of an object is p 1, and a subsequent momentum is p 2, the object has received an impulse J: =. Momentum is a vector quantity, so impulse is also a vector quantity.
The definition of angular momentum for a single point particle is: = where p is the particle's linear momentum and r is the position vector from the origin. The time-derivative of this is: The time-derivative of this is:
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 =.