Linear mass density

Definition

Linear mass density is the measure of mass per unit length of a one-dimensional object, such as a string or rod. It is typically denoted by the symbol $\lambda$ and expressed in units of kg/m.

5 Must Know Facts For Your Next Test

1. Linear mass density ($\lambda$) is crucial for calculating the center of mass and moments of inertia for elongated objects.
2. The formula to find linear mass density is $\lambda = \frac{m}{L}$, where $m$ is the mass and $L$ is the length.
3. In problems involving waves on strings, linear mass density affects wave speed according to the equation $v = \sqrt{\frac{T}{\lambda}}$, where $T$ is tension.
4. For a non-uniform object, linear mass density may vary along its length and can be represented as a function, $\lambda(x)$.
5. To determine moments of inertia for rods or beams with varying linear mass densities, integral calculus might be necessary.

Review Questions

• What are the units commonly used for linear mass density?
• How does linear mass density affect the speed of waves on a string under tension?
• What is the relationship between an object's total mass, its length, and its linear mass density?

Related terms

Center of Mass: The point at which all of an object's mass can be considered to be concentrated for translational motion analysis.

Moment of Inertia: A measure of an object's resistance to changes in its rotation rate; depends on both the distribution of an object's mass and the axis about which it rotates.

Wave Speed: The speed at which a wave propagates through a medium; for mechanical waves on a string or rope, it depends on both tension and linear mass density.