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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

In discrete form, a system of point masses m_i located at positions r_i yields a first moment

Example: A 5 kg mass located 2 m from the origin contributes 10 kg·m to the first

Relation to other units: 1 kg·m is equivalent to 1 N·s^2 since N = kg·m/s^2. Kilogrammeter is not

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

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.
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.
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.
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.