Mass

*Mass* is an intrinsic property of matter.
From Newton's second law,
, we have that the amount of
force required to accelerate an object, by a given amount, is
proportional to its mass. Thus, the mass of an object quantifies its
*inertia*--its resistance to a change in velocity.

We can measure the mass of an object by measuring the
*gravitational force* between it and another known mass,
as described in the next section. This is a special case of measuring
its acceleration in response to a known force. Whatever the force
,
the mass
is given by
divided by the resulting acceleration
, again by Newton's second law
.

The usual mathematical model for an ideal mass is a dimensionless
*point* at some location in space. While no real objects are
dimensionless, they can often be treated mathematically as
dimensionless points located at their *center of mass*, or
*centroid* (§B.4.1).

The *physical state* of a mass
at time
consists of its
*position*
and *velocity*
in 3D space.
The amount of mass itself,
, is regarded as a fixed parameter that
does not change. In other words, the *state*
of a
physical system typically changes over time, while any
*parameters* of the system, such as mass
, remain fixed over
time (unless otherwise specified).

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University