In this video I go over a useful physics application for derivatives and show that the linear density of an object such as a metal rod is simply the derivative of the mass in terms of the length of the rod.

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Derivatives Application Example: Linear Density

Linear Density

The linear density is defined as the mass per unit length and is usually in units of kg/m.

A rod or a piece of wire illustrates the concept of linear density:

If the Linear Density is not uniform:

Example

Find the average density for a rod between 1 ≤ x ≤ 1.2 meters and find the linear density at x = 1 meters if the mass is given by:

Solution