Mass

Mass is an intrinsic property of matter. From Newton's second law, $f(t)=m\,a(t)$ , 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 $f$ , the mass $m$ is given by $f$ divided by the resulting acceleration $a$ , again by Newton's second law $f=ma$ .

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