# What is the density of a constant? (spring constant)

• zazi77
In summary, the author is discussing the use of Young's modulus as a spring constant and how it can be used to determine the center of rotation for teeth.
zazi77
Hi, I could you explain me what is the density of a constant (particurarly the spring constant, or should I say "stiffness" constant)? I guess it's a probabilty function but would like more details. I would like an answer that at first describe the concept and later refine the mathematical explanation . Thank you

Welcome to the PF.

Can you post a couple links to where you have seen this?

I'm reading this paper written by an engineer(I'm a dentist passionate with biomechanics). From theorem of reciprocal synatrosis a theory of tooth movement has been derived (a constant of center of rotation based on stress distribution function of periodontal ligament). I can understand the calcultions more or less, but I'm curious about this density because I could
find no explanation about it.

I guess the concept is more or less this one. In the first part of the paper an intervertbral disk is considered. It can be assumed to be a spring and each infinite element is a small spring . These little springs can be distributed in some ways, so that is it possible to define a "density". Moreover it also depends on the kind on model of disk (continuity, discontinuity). If you can explain me these concepts and link me something to study (for someone approaching the subject) it would be great.

Hi @zazi77
Here is a brief consideration on using Young's modulus as a spring constant, which is what the article is doing.
https://ccrma.stanford.edu/~jos/pasp/Young_s_Modulus_Spring_Constant.html
Note that F/S is pressure, where S is an area.
If you move S to the right hand side you have ΔL [ the dy ] times Y ( Young's Modulus ) / L( length) times S(area)

If you consider upon the Y/L as a density, that is related to the number of little springs that are in the total length L, and acting upon the area.

Maybe someone can explain that better.

JBA and berkeman
thank you for your reply, I already saw that link. What I don't get is why Y/L is a density

Please give us a reference to the source of the .png in post #3.

Do you also have a download link ?

## 1. What is the definition of density?

Density is the measure of how much matter is packed into a given space. It is usually expressed in units of mass per unit volume, such as grams per cubic centimeter or kilograms per cubic meter.

## 2. What is a constant?

A constant is a value that does not change in a given situation or under certain conditions. In scientific terms, it is a fixed and unchanging quantity.

## 3. What is a spring constant?

A spring constant is a measure of the stiffness of a spring. It is the amount of force required to stretch or compress a spring by a certain distance.

## 4. How is density related to a constant (spring constant)?

Density is not directly related to a constant, but it can be used in calculations involving a spring constant. For example, the density of an object can affect the amount of force needed to compress a spring attached to it.

## 5. Can the density of a constant (spring constant) change?

No, the density of a constant cannot change because it is a fixed value. However, the density of an object or material that is being measured using a spring constant may change depending on factors such as temperature or pressure.

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