kilogrammeter

Kilogrammeter (kg·m) is the product of mass in kilograms and length in meters. It is not an official SI base or widely adopted derived unit, but it is used in some contexts to denote the first moment of mass about a chosen origin.

The first moment of mass is defined as M = ∫ r dm, where r is the position vector and dm is an elemental mass. The result has units of kilograms times meters (kg·m). This quantity by itself does not correspond to momentum or torque, but it appears in center-of-mass calculations and related analyses.

In discrete form, a system of point masses m_i located at positions r_i yields a first moment S = sum over i of m_i r_i. The center of mass is then r_cm = S / M, where M is the total mass. Thus the vector ∫ r dm has units of kg·m, and dividing by total mass yields a length.

Example: A 5 kg mass located 2 m from the origin contributes 10 kg·m to the first moment. If a system has total mass 20 kg and a first moment of 40 kg·m, its center of mass lies at 2 m from the origin in the direction of the moment.

Relation to other units: 1 kg·m is equivalent to 1 N·s^2 since N = kg·m/s^2. Kilogrammeter is not used as a standalone unit of energy or momentum in modern practice; equations typically use kg and m separately. Historically it has appeared in discussions of mass moments but remains largely of mathematical interest.

See also: center of mass, first moment of mass, moment of inertia, momentum, torque.