Moment

In physics, the moment M of a vector B is

M_A = r × B,

where r is the position where the quantity B is applied. If r is a vector relative to a point A, then the moment is the "moment M with respect to axis that goes through the point A" or simply "moment M around A". If A is the origin, one often omits A and says simply moment.

Since the moment is dependent on the given axis, the moment expression possess a common property when the observation axis is changed. If M_A is the moment around A, then the moment around the axis that goes through a point B is

M_B = M_A + R×B,

where R is the vector from point B to point A. This expression is usually refered to as the parallell axis theorem. For cases when the moment is the sum of individual "submoments", such as in rigid body dynamics where each particle of the body contribute to a moment, the axis change is the sum of a macroscopic and microscopic quantity,

M_B = R×B + ∑_ir_i×b_(i),

where B = ∑_ib_i , or in the form

M_B = R×B + M_A.

There are certain three kinds of important momentums in physics.

• B = mv: Angular momentum, which is typically the cause of both rotation and translation movements of a body.
• B = m ω×r: Moment of inertia, which, when describing rotational motions, plays the same role as the mass does for translation motion. But this "mass" is often dependent on time and also on the reference axis.
• B = F: Torque, which is a force applied on a position of the body, but not on the center of mass. When no torque is applied, the angular momentum is conserved.