Mass
The basic SI unit of mass is the kilogram (kg). In physics, mass is not the same as weight, even though mass is often determined by measuring the object's weight using a spring scale, rather than balance scale comparing it directly with known masses. An object on the Moon would weigh less than it does on Earth because of the lower gravity, but it would still have the same mass. This is because weight is a force, while mass is the property that (along with gravity) determines the strength of this force.
Linear density
Consider a long, thin rod of mass formula_1 and length formula_2. To calculate the average linear mass density, formula_3, of this one dimensional object, we can simply divide the total mass, formula_1, by the total length, formula_2:
If we describe the rod as having a varying mass (one that varies as a function of position along the length of the rod, formula_7), we can write:
Each infinitesimal unit of mass, formula_9, is equal to the product of its linear mass density, formula_10, and the infinitesimal unit of length, formula_11:
The linear mass density can then be understood as the derivative of the mass function with respect to the one dimension of the rod (the position along its length formula_13)