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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 ().
Momentum is conservative: any change in momentum of an object requires an equal and opposite change of some other objects. Hence the recoil: imparting momentum to the projectile requires imparting opposite momentum to the gun. A change in momentum of a mass requires applying a force (this is Newton's laws of motion).
Momentum: the drag experienced by a rain drop as it falls in the atmosphere is an example of momentum diffusion (the rain drop loses momentum to the surrounding air through viscous stresses and decelerates). The molecular transfer equations of Newton's law for fluid momentum, Fourier's law for heat, and Fick's law for mass are
The quantity mv is called the momentum. The net force on a particle is thus equal to the rate of change of the momentum of the particle with time. Since the definition of acceleration is a = dv/dt, the second law can be written in the simplified and more familiar form: =.
The conservation laws may be applied to a region of the flow called a control volume. A control volume is a discrete volume in space through which fluid is assumed to flow. The integral formulations of the conservation laws are used to describe the change of mass, momentum, or energy within the control volume.
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:
Power in mechanical systems is the combination of forces and movement. In particular, power is the product of a force on an object and the object's velocity, or the product of a torque on a shaft and the shaft's angular velocity. Mechanical power is also described as the time derivative of work.