Polar coordinates Definition and 569 Threads

Do you think you could do vector operations in polar coordinates?

Hi! Can someone please help? I'm trying to solve the heat equation in polar coordinates. Forgive my way of typing it in, I'm battling to make it look right. The d for derivative should be partial, alpha is the Greek alpha symbol and theta is the Greek theta symbol. du/dt =...

Please I need help about polar coordinates. I have this expression: \int_0^{\infty}\int_0^{\infty}e^\frac{-(t^2 + u^2)}{2}dtdu.. Now they say: "Let's convert to polar coordinates. Define t = r cos \theta, u = r sin \theta. Then t^2 + u^2 = r^2 (this is OK) and dtdu = rd \theta dr...

Question answered! Thanks!

A particle P describes the curve with polar equation r = a e^{\theta \sqrt{3}} \cosh 2\theta in such a manner that the radius vector from the origin rotates with uniform angular speed \omega. Show that the resultant acceleration of the particle at any instant makes an angle of 30 degrees in the...

Hi, I'm having problems with converting to polar coordinates when evaluating integrals. Here is an example, it comes down to writing the following equality. After that the evaluation of the intergral is straight forward. \int\limits_0^2 {\int_{ - \sqrt {4 - y^2 } }^{\sqrt {4 - y^2 } } {x^2...

As I understand it, the polar coordinates of a point is defined by the rectangular coordinates of that point according to the transformation T from R² to R² defined by T:(x,y)\mapsto (\sqrt{x^2+y^2},tan\left(\frac{y}{x}\right)) But this definition fails for y=pi and x=2 because tan(pi/2)...

When using cartesian coordinates, I use the following expressions to calculate the cross product of the basis vectors: i \times j = k j \times k = i k \times i = j j \times i = -k k \times j = -i i \times k = -j Can I do the same in polar coordinates? How could I write the cross...

What is the difference in the "uniqueness" of the representations of Cartesian coordinates and in polar coordinates? :confused: Also, what is the non-uniqueness?

Another problem that I cannot figure out. Convert the follorwing into polar coordinates: \int_{-1}^{1} \int_{-\sqrt{1 - y^2}}^{\sqrt{1 - y^2}} ln\left(x^2 + y^2 + 1\right) dx\;dy I did this so far: ln\left(x^2 + y^2 + 1\right) = ln\left(r^2 + 1\right) \sqrt{1 - y^2} = \sqrt{1 - r^2...

Is it possible to do vector operations in polar coordinates?

Is it possible to do vector operations in polar coordinates?

You know this should be simple but it's just not. A friend asked me this earlier and I was unable to disprove him. We're all aware of how one derives the area of a polar equation.. it's \pi r^2 \frac {\theta}{2 \pi} and make theta infinitely small and integrate. Why can't a similar process...

Do you think you could do vector operations in polar coordinates?

Are Cartesian coordinates two or three dimensional?

What are the differences in the "uniqueness" of the representations in Cartesian coordinates and in polar coordinates?

Just got back into physics after 4 years in social science and I have forgotten how to convert cartesian coordinates to polar coordinates. The textbook I have makes no metion of it. probably bc I am expected to know this, but I can't remember. I remember how to calculate the distace between two...

How do you add or subtract in polar coordinates if not given the rectangular coordinates? Thanks.

The problem is: Write the vector V=i+j+k=(1,1,1) at the point (x,y,z)=(1,1,1) in cylindrical polar coordinates. What is the gradient of the function phi=x(x^2+y^2)z at this point? Answer: I don't know how to write the vector in cylindrical polar coordinates. I know that the coordinates...