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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 ().
5.1 Moment arm formula. 5.2 Static equilibrium. 5.3 Net force versus torque. ... The equation for the magnitude of a torque, arising from a perpendicular force:
The kinetic energy equations are exceptions to the above replacement rule. The equations are still one-dimensional, but each scalar represents the magnitude of the vector, for example, = + +. Each vector equation represents three scalar equations.
Angular momentum (sometimes called moment of momentum or rotational momentum) is the rotational analog of linear momentum. It is an important physical quantity because it is a conserved quantity – the total angular momentum of a closed system remains constant. Angular momentum has both a direction and a magnitude, and both are conserved.
A stronger mathematical definition is to use vector algebra, since a quantity with magnitude and direction, like the dipole moment of two point charges, can be expressed in vector form = where d is the displacement vector pointing from the negative charge to the positive charge.
The inverse cube nature of this equation is more readily seen by expressing the location vector as the product of its magnitude times the unit vector in its direction (= | | ^) so that: = ^ (^) | |. The equivalent equations for the magnetic B {\displaystyle \mathbf {B} } -field are the same except for a multiplicative factor of μ 0 = 4 π × ...
If the two forces are F and −F, then the magnitude of the torque is given by the following formula: = where is the moment of couple; F is the magnitude of the force; d is the perpendicular distance (moment) between the two parallel forces
This equation holds for a body or system, such as one or more particles, with total energy E, invariant mass m 0, and momentum of magnitude p; the constant c is the speed of light. It assumes the special relativity case of flat spacetime [1] [2] [3] and that the particles are free.