The American Anthropological Association (AAA) is an organization of scholars and practitioners in the field of anthropology. With 10,000 members, the association, based in Arlington, Virginia, includes archaeologists, cultural anthropologists, biological (or physical) anthropologists, linguistic anthropologists, linguists, medical anthropologists and applied anthropologists in universities and colleges, research institutions, government agencies, museums, corporations and non-profits throughout the world. The AAA publishes more than 20 peer-reviewed scholarly journals, available in print and online through AnthroSource. The AAA was founded in 1902.
Hi all any help on this would be great I cant seem to progress with the theorem,
z= -2 + j > R sqrt (-2)'2 + (-1)'2
r = 2.24
0= Arctan(-1) = 26.57 Polar form = 2.24(cos(26.58)+jsin(26.58)
-2
Demoivre - (cos0+jsin0)'n = cosn0 +jsinno
Could some one...
In the following%3A%20https://pubs.rsc.org/en/content/articlehtml/2013/sm/c3sm00140g?casa_token=3O_jwMdswQQAAAAA%3AaSRtvg3XUHSnUwFKEDo01etmudxmMm8lcU4dIUSkJ52Hzitv2c_RSQJYsoHE1Bm2ubZ3sdt6mq5S-w'] paper, the surface velocity for a moving, spherical particle is given as (eq 1)...
So I want to subtract the two surfaces, right? I really don't know where to start... I am guessing this would be some sort of triple integral, however I am very confused with the bounds.
Any help would be greatly appreciated!
Thanks!!
Consider for example Carbon Dioxide. Oxygen is more electronegative than carbon so should obtain the "lion's share" of the paired electrons in the double bonds. But (as I see it anyway) the oxygen atoms on either side of the central carbon "assist" the carbon atom to maintain an even share of...
The 2D Fourier transform is given by: \hat{f}(k,l)=\int_{\mathbb{R}^{2}}f(x,y)e^{-ikx-ily}dxdy
In terms of polar co-ordinates: \hat{f}(\rho,\phi)=\int_{0}^{\infty}\int_{-\pi}^{\pi}rf(r,\theta)e^{-ir\rho\cos(\theta-\phi)}drd\theta
For Fourier transforms in cartesian co-ordinates, relating the...
I made this exercise up to acquire more skill with polar coordinates. The idea is you're given the acceleration vector and have to find the position vector corresponding to it, working in reverse of the image.
My attempts are the following, I proceed using 3 "independent" methods just as you...
Hello, I am trying to solve the following problem:
If ##z=f(x,y)##, where ##x=rcos\theta## and ##y=rsin\theta##, find ##\frac {\partial z} {\partial r}## and ##\frac {\partial z} {\partial \theta}## and show that ##\left( \frac {\partial z} {\partial x}\right){^2}+\left( \frac {\partial z}...
The wavefunction of ##|\psi\rangle## is given by the bra ket
##\psi (x,y,z)=
\langle r| \psi\rangle##
I can convert the wavefunction from Cartesian to polar and have the wavefunction as ## \psi (r,\theta,\phi)##
What bra should act on the ket ##|\psi\rangle## to give me the wavefunction as ##...
$$L = \frac {mv^2}{2} - mgy$$
It is clear that ##\dot{x}=\dot{\theta}L## and ##y=-Lcos \theta##. After substituting these two equations to Lagrange equation, we will get the answer by simply using this equation: $$\frac {d} {dt} \frac {∂L}{∂\dot{\theta}} - \frac {∂L}{∂\theta }= 0$$
But, What if...
I'm having trouble trying to calculate how the answer below was achieved from an example i have seen, see below:
208L0 - 2.5L90 x 27.42L36.9 which is then calculated to 255.12L-12.4.
I have tried converting everything to rectangular form, subtract where required and the convert back to polar...
Hello everybody,
Currently I am doing my master's thesis and I've encountered a physics problem which is very difficult for me to solve. The problem I have is finding equations for the magnetic scalar potential inside and outside a ferromagnetic wire for specific boundary conditions...
In my job, I was given the task of calculating a force that operates an ultrasound transmitter on a receiver. The calculation is made by assuming that each point on the transmitter is a small transmitter and integration should be made on the surface of the transmitter.
Since the transmitter is...
I have a function in polar coordinates:
t (rho, phi) = H^2 / (H^2 + rho^2) (1)
I have moved the center to the right and want to get the new formulae.
I use cartesian coordinates to simplify the transformation (L =...
Hi,
I am trying to find open-form solutions to the integrals attached below. Lambda and Eta are positive, known constants, smaller than 10 (if it helps). I would appreciate any help! Thank you!
Probability distribution - uniform on unit circle. In polar coordinates ##dg(r,a)=\frac{1}{2\pi}\delta(r-1)rdrda##. This transforms in ##df(x,y)=\frac{1}{2\pi}\delta(\sqrt{x^2+y^2}-1)dxdy##. The problem I ran into was the second integral was 1/2 instead of 1.
Greetings!
I have the following integral
and here is the solution of the book (which I understand perfectly)
I have an altenative method I want to apply that does not seems to gives me the final resultMy method
which doesn't give me the final results!
where is my mistake?
thank you!
I am trying to do exercise 8.5 from Misner Thorne and Wheeler and am a bit stuck on part (d).
There seem to be some typos and I would rewrite the first part of question (d) as follows
Verify that the noncoordinate basis ##{e}_{\hat{r}}\equiv{e}_r=\frac{\partial\mathcal{P}}{\partial r},\...
If my understanding is correct, the polar covalent bond in HCl creates a polar molecule because the molecule is unsymmetrical.
1. Does this mean that the partially positive H of one HCl molecule will be attracted to the partially negative Cl of another HCl molecule and vice versa, to create a...
Summary:: I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student:
I wish this video (and YouTube in general) was around when I took intermediate level mechanics as an undergraduate physics student:
Hi
I was always under the impression that i could write
a2 = a.a = a2 Equation 1
where a⋅ is a vector and a is its modulus but when it comes to the kinetic energy term for a particle in plane polar coordinates I'm confused ( i apologise here as i don't know how to write time derivative with...
Question:
Diagram:
So the common approach to this problem is using polar coordinates.
The definition of infinitesimal rotational inertia at O is ##dI_O=r^2\sigma\, dA##. Therefore the r. inertia of the triangle is
$$I_O=\int_{0}^{\pi/3}\int_{0}^{\sec\theta}r^2r\,drd\theta$$
whose value is...
I have a question that might be considered vague or even downright idiotic but just wanted to know that once we find out the velocity & acceleration of a body in angular motion in plane polar coordinates, and are asked to integrate the expressions in order to find position at some specified time...
I am trying to derive the tangential acceleration of a particle. We have tangential velocity, radius and angular velocity. $$v_{tangential}= \omega r$$ then by multiplication rule, $$\dot v_{tangential} = a_{tangential} = \dot \omega r + \omega \dot r$$ and $$a_{tangential} = \ddot \theta r +...
The text says that the following conic, r = 15/[3-2cos(theta)], can be rearranged to 5/[1-(2/3)cos(theta)]. The graph of the conic is an ellipse with e=2/3.
Then it says that the vertices lie at (15,0) and (3,pi). How did they find the vertices? Thanks.
The equation I'm trying to graph on desmos is this with A & B as numbers, but I'm unsure how as it is a vector.
r = (A cosθ sinθ cscθ - B sinθ cscθ) i + (A cosθ sinθ cscθ + B sinθ cscθ) j
Hello,
Today I started to think about why graphs, of the same equation, look different on the Cartesian plane vs. the polar grid. I have this visualization where every point on the cartesian plane gets mapped to a point on the polar grid through a transformation of the grids themselves...
Hello,
In the plane, using Cartesian coordinates ##x## and ##y##, an equation (or a function) is a relationship between the ##x## and ##y## variables expressed as ##y=f(x)##. The variable ##y## is usually the dependent variable while ##x## is the independent variable.
The polar coordinates...
Doing a review for my SAT Physics test and I'm practicing vectors. However, I am lost on this problem I know I need to use trigonometry to get the lengths then use c^2=a^2+b^2. But I need help going about this.
I got a polar function.
$$ \psi = P(\theta )R(r) $$
When I calculate the Laplacian:
$$ \ \vec \nabla^2 \psi = P(\theta)R^{\prime\prime}(r) + \frac{P(\theta)R^{\prime}(r)}{r} + \frac{R(r)P^{\prime\prime}(\theta)}{r^{2}}
$$
Now I need to convert this one into cartesian coordinates and then...
there is a problem in a book that asks to find the orthogonal trajectories to the curves described by the equation :
$$r^{2} = a^{2}\cos(\theta)$$
the attempt of a solution is as following :
1- i defferntiate with respect to ##\theta## :
$$2r \frac{dr}{d\theta} = -a^{2}\;\sin(\theta)$$
2- i...
Summary:: Hello, my question asks if the complex exponential equation 4e^(-j) is equal to 4 ∠-180°. I tried to use polar/rectangular conversions: a+bj=c∠θ with c=(√a^2 +b^2) and θ=tan^(-1)[b/a]
4e^(-j)=4 ∠-180°
c=4, 4=(√a^2 +b^2)
solving for a : a=(√16-b^2)
θ=tan^(-1)[b/a]= -1
b/(√16-b^2)=...
Hi,
I was just working on a homework problem where the first part is about proving some formula related to Stokes' Theorem. If we have a vector \vec a = U \vec b , where \vec b is a constant vector, then we can get from Stokes' theorem to the following:
\iint_S U \vec{dS} = \iiint_V \nabla...
where the region of integration is the cube [0,1]x[0,1]x[0,1]
my question is where can we use the polar coordinate? is it only usable if the region of integration looks like a circle regardless of the function inside the integral? (if yes it means that using this kind of transformation is wrong...
I encountered a question which asked me to describe the rose petal sketched below in polar coordinates. The complete answer is
R = {(r, θ): 0 ≤ r ≤ 6 cos(3θ), 0 ≤ θ ≤ π}. That makes sense to me for the right petal. What about the other two on the left?
The equations of motion are:
\ddot{r}-r{\dot{\theta}} ^{2} = -\frac{1}{r^{2}}
for the radial acceleration and
r\ddot{\theta} + 2\dot{r}\dot{\theta}= 0
for the transverse acceleration
When I integrate these equations I get only circles. The energy of the system is constant and the angular...
Hello! Brand new to the forums, hopefully someone here can help me out.
Paths start out at the edge of a circle and "flow" along a polar equation that determines phi based off the initial phi (phi0) and a variable radius (ie. as your radius grows, your phi is changing). Hopefully this image...
If I use cartesian co-ordinates, I get:
##\bar{x}=\frac{1}{A}\iint x\, dA=\frac{1}{A} \iint r^2\cos\theta\, dr\, d\theta= \frac{2a\sin\theta}{3\theta}##
##\bar{y}=\frac{1}{A}\iint y\, dA=\frac{1}{A}\iint r^2\sin\theta\, dr\, d\theta= \frac{2a(1-\cos\theta)}{3\theta}##
But if I use polar...
In the example above, the authors claim that when ##r=r_0e^{\beta t}##, the radial acceleration of the particle is 0. I don't quite understand it because they did not assume ##\beta=\pm \omega##.
Can anyone please explain it to me? Many thanks.
I am learning to use polar coordinates to describe the motions of particles. Now I know how to use polar coordinates to solve problems and the derivations of many equations. However, the big picture of polar coordinates remains unclear to me. Would you mind sharing your insight with me so that I...
##\vec r=r \hat r##
##\vec v=\dot r \hat r + r \dot \theta \hat \theta##
##\vec a = (\ddot r - r \dot \theta^2)\hat r + (2 \dot r \dot \theta + r \ddot \theta)\hat \theta##
Given that,
##2 \dot r \dot \theta + r \ddot \theta =0##
Also,
##r \theta=constant##
##\Rightarrow \dot r \theta + r \dot...
My textbook says ##\vec r (\theta) = r \hat r (\theta)##, where ##\hat r (\theta)## is the terminal arm (a position vector in some sense). It can be seen that both ##\vec r (\theta)## and ##\hat r (\theta) ## are function of ##\theta##; whereas, the length of the vector ##r## is not. I...
I attempted to solve this problem by finding the angles of an intersection point by equalling both ##r=sin(\theta)## and ##r=\sqrt 3*cos(\theta)##. The angle of the first intersection point is pi/3. The second intersection point is, obviously, at the pole point (if theta=0 for the sine curve and...
The velocity of a particle below is expressed in polar coordinates, with bases e r and e theta. I know that the length of a vector expressed in i,j,k is the square of its components. But here er and e theta are not i,j,k. Plus they are changing as well. Can someone help convince me that the...