# Polar Coordinates Homework: Converting to Cartesian and Strain Rate Tensor

• JSBeckton
In summary, the conversation discusses how to convert a velocity field for a line source in polar coordinates to cartesian coordinates and calculate the strain rate tensor. The equations used include R=sqrt(x^2+y^2) and theta=arctan(y/x). The person asking for help is unsure about what value to use for theta and is looking for clarification.
JSBeckton

## Homework Statement

The velocity field for a line source in polar coordinates (r,theta) is given by:

V=m/(2(pi)r) (in the "e" little r vector direction)

convert to cartesian and calculate the strain rate tensor.

## Homework Equations

R=Sqrt(x2+y2);
Theta=ArcTan(Y/X);

Cartesian form:
X= R*cos(Theta)
Y= R*sin(Theta)

## The Attempt at a Solution

I just need to convert this, i understand how to get the strain rate tensor. I know how to compute between polar and cartesian but need theta. Or am I suppposed to assume theta=0?

if theta=0 then y=0 andf x=r*sin(theta) but what do i use for r? If i solve for r i th efirst equation I get r=m/(2pi)

x=rcos(0)
x=m/(2pi)

This doesn't seem right becasue I need a velocity field in terms of V(u,v) where u and v are in terms of x and y.

Any help is greatly appreciated, Thanks

I do not know what exactly you are asking, but if you are just asknig how to get from cartesian coordinates to polar ones than

theta=arctan(y/x) while R=sqrt(x^2+y^2)

I understand that as stated in my post under "Relevant Equations", thanks anyways

## 1. What are polar coordinates and how are they different from Cartesian coordinates?

Polar coordinates are a system of representing points in a two-dimensional plane using a distance from the origin and an angle. This is different from Cartesian coordinates, which use perpendicular axes (x and y) to represent points in a plane.

## 2. Why do we need to convert from polar to Cartesian coordinates?

Converting from polar to Cartesian coordinates allows us to represent points in different coordinate systems, making it easier to solve certain problems and visualize data. It also allows us to use different mathematical techniques and equations when working with polar coordinates.

## 3. How do you convert from polar to Cartesian coordinates?

To convert from polar to Cartesian coordinates, we use the equations x = r*cos(theta) and y = r*sin(theta), where r is the distance from the origin and theta is the angle. These equations allow us to find the x and y coordinates of a point in Cartesian form.

## 4. What is a strain rate tensor and how is it related to polar coordinates?

A strain rate tensor is a mathematical tool used to describe the deformation of a material. It is related to polar coordinates because it allows us to calculate the rate of deformation at a particular point, taking into account both the distance from the origin and the angle.

## 5. Can you provide an example of converting from polar to Cartesian coordinates and using a strain rate tensor?

Sure, let's say we have a point located at r = 3 and theta = 30 degrees in polar coordinates. We can convert this to Cartesian coordinates using the equations x = 3*cos(30) = 2.6 and y = 3*sin(30) = 1.5. Then, using the strain rate tensor, we can calculate the rate of deformation at this point by taking the derivative of the displacement in the x and y directions with respect to time. This allows us to analyze the deformation of a material at this specific point in polar coordinates.

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