# Differential Length (Cylindrical Coordinates)

• salman213
In summary, the conversation is about finding the differential length or distance between two points using cylindrical coordinates. The individual is confused about the notation and integration process, specifically when the variable "p" is not constant. They have provided a diagram from their textbook for reference. The expert suggests that the order of integration matters and that variables can be treated as constants within the integral.
salman213

Find the differential length or distance between the two points.

P(2,pi/2,-1) and Q(5,3pi/2,5)I know this

for cylindrical

dL = dp (ap) + p dphi (aphi) + dz (az)

So i would integrate

I have a few questions does it matter if for example for dp

i integrate from 2 to 5 or from 5 to 2?

also in the aphi part, there is a "p" which is not constant in my problem so how can i do the integral with respect to dphi when p is not constant!

can I even use this?

helpEDITED: MY TEXT USES A DIFFERENT NOTATION I POSTED ANOTHER QUESTION AND THE INDIVIDUAL ALSO HAD PROBLEMS WITH MY NOTATION I HOPE THIS DIAGRAM HELPS IT'S FROM MY TEXTBOOK:

http://img261.imageshack.us/img261/7998/53164335jl9.jpg

Last edited by a moderator:
I am a bit confused as to your notation but;

It does matter which order you integrate from. By convention length must be a positive quantity and so our integral must output positive values. Choosing the integral with upper limit of integration as 5, and lower limit as 2, we achieve that, but if we were to do it the other way around, the value we would get is negative.

Also, I'm a bit confused as to what specifically you are talking about, but if the integral is with respect to the variable phi, and that variable is not a function of p, even if p is not a constant within the whole problem we can regard it as a constant within the integral.

But if I were to have any integral say

Integral of (ydx)

I have understand from my courses I cannot do this integral since y is not a function of x. But you are saying just treat it like a constant?

Pi and phi are constants yes.

## 1. What is differential length in cylindrical coordinates?

Differential length in cylindrical coordinates refers to the change in length of a curve or surface in three-dimensional space, measured along the cylindrical coordinate system.

## 2. How is differential length calculated in cylindrical coordinates?

In cylindrical coordinates, differential length is calculated using the formula dl = √(dr² + r²dθ² + dz²), where dr is the change in the radial direction, is the change in the circumferential direction, and dz is the change in the vertical direction.

## 3. What is the significance of differential length in cylindrical coordinates?

Differential length in cylindrical coordinates is important in calculus and physics, as it allows for the calculation of surface area and volume of curved objects. It is also used in mathematical models of physical systems.

## 4. How is differential length related to other coordinate systems?

Differential length in cylindrical coordinates is related to differential length in other coordinate systems, such as Cartesian and spherical coordinates. It can be converted to and from these coordinate systems using specific formulas.

## 5. What are some real-world applications of differential length in cylindrical coordinates?

Differential length in cylindrical coordinates has various applications in fields such as engineering, physics, and mathematics. It is used in the design and analysis of cylindrical objects, such as pipes and cylinders, in fluid dynamics, and in the study of electric and magnetic fields.

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