Area density Definition - Calculus I Key Term

Definition

Area density is a measure of mass per unit area. It is commonly used in physical applications to quantify how mass is distributed over a surface.

The formula for area density ($\sigma$) is $\sigma = \frac{m}{A}$ where $m$ is mass and $A$ is area.
It has units of kilograms per square meter (kg/m²) or grams per square centimeter (g/cm²).
Area density can be integrated over a surface to find the total mass.
In problems involving thin plates or surfaces, area density helps convert between mass and surface area.
Applications often involve calculating moments of inertia, center of mass, and pressure distributions using area density.

Mass Density: Mass per unit volume, typically measured in kilograms per cubic meter (kg/m³).

Linear Density: Mass per unit length, usually expressed in kilograms per meter (kg/m).

Moment of Inertia: A quantity expressing an object's tendency to resist angular acceleration, which can be calculated using distribution of mass.