### 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).

**Next Section:**

Gravitational Force

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Newton's Three Laws of Motion