Mass

Mass measures inertia and acts as the source of Newtonian gravity.

A historical unit of mass, equal to approximately 64.8 milligrams. The unit must not be confused with a minim, which measures volume.

The dimensionless ratio of two specified masses.

Passive gravitational mass is the coefficient in $\mathbf{F}=m_{\mathrm{g}}\mathbf{g}$ for an imposed Newtonian gravitational field. Active gravitational mass instead measures a body's contribution to the source of that field in Newton's law of universal gravitation. Universality of the ratio of passive gravitational mass to inertial mass is the Newtonian content of the weak equivalence principle. In general relativity, the source is the full stress-energy tensor, rather than a single scalar gravitational mass.

In Newtonian mechanics, inertial mass is the coefficient in $\mathbf{F}=m_{\mathrm{i}}\mathbf{a}$, measuring a body's response to a net force. The weak equivalence principle makes its ratio to passive gravitational mass universal; choosing compatible units then sets the two equal.

A description of how mass is assigned to positions, expressed for example by point masses, a mass density, or a measure. Writing $dm$ allows centre of mass and moment of inertia formulas to cover both discrete and continuous cases.

A planar lamina is an ideal mass distribution confined to a plane, with surface mass density $\sigma$ and infinitesimal mass $dm=\sigma dA$. Its moment of inertia about an axis is the integral of squared perpendicular distance against this mass element. Three mutually perpendicular axes through one point, with two in the lamina's plane, obey the perpendicular axis theorem even when the density is nonuniform.

A point mass idealizes a localized body's mass density as $\rho (\mathbf{x},t)=m{\delta }^{(3)}(\mathbf{x}-\mathbf{z}(t))$, using the Dirac delta function. Its second mass moment tensor is $I_{ij}=m{z}_i{z}_j$. The approximation ignores its internal size and structure.