Polar Definition and 1000 Threads

Homework Statement I didn't know if this was considered "advanced" physics, but it's an intermediate classical mechanics course so I'll just post my question here. Basically, if you have a cardioid ##r(\theta)=k(1+\cos(\theta))##, you can show that the ##\dot{\theta}=\frac{v}{\sqrt{2kr}}##...

Homework Statement Derive ∫(dr/dθ)^2 + R^2 )^0.5 dθ Homework Equations x = Rcosθ y = Rsinθ The Attempt at a Solution Arc length is the change in rise over run, which can be found using Pythagorean's Theorem. Rise is dy/dθ while run is dx/dθ. The arc length is [(dy/dθ)^2 + (dx/dθ)^2 ]^1/2...

I've attached the solution to this post. The question is essentially just asking to find the area in one loop for r = cos[3(theta)]. This seems like a fairly simple question (and answer). I've solved and understand the general integration, but I am just a little uncertain on why exactly...

Greetings. I have been teaching myself Calculus. To do this I ordered a used Larson's 8th Edition Calculus and a used TI-81 graphing calculator. When I got to Chapter 10, I ran into a problem: the chapter introduces equations in polar form and when I whipped out my TI-81, I had no idea how to...

How is the polar moment of inertia in a rod calculated? Thanks.

Hi ,everyone… i wanted to clear my one confusion ,that what is actual difference between polar mass moment of inertia and simply moment of inertia…??

Hello good people, I'm using http://www.ecy.wa.gov/programs/eap/models/twilight.zip by Greg Pelletier to calculate sunrise/sunset times at a desired location. However, the sheet formulae return an error message (#NUM) for latitudes above the Arctic/Antarctic Circle since the sun/moon almost...

Homework Statement r=2cos(theta) I want to find the area using polar integration. Homework Equations area=(1/2)r^2 from 0-pi The Attempt at a Solution When I plug everything in I get 2pi as the answer. I'm in multivariable calculus so this is very frustrating. What am I doing wrong, I don't...

I've been using MATLAB (ode45) to simulate the mechanics of a rocket under the forces of gravity, drag, and internal thrust.y I've recently refactored my simulation to include 2d space, orientation of the rocket, etc. (So I can try to make it orbit, finding optimal ascent profiles, etc)...

I'm aware that it orbits West to East and covers almost every part of the land on Earth. But what is the reason behind it not passing over Arctic and Antarctic regions?

Homework Statement Prove: $$\frac{d\hat{r}}{dt} = \dot{\phi} \hat{\phi }$$ and $$\frac{d\hat{\phi}}{dt} = -\dot{\phi} \hat{r }$$Homework EquationsThe Attempt at a Solution I solved this for an Analytical Mechanics assignment a month ago, and completely forgot how it goes.. $$\hat{r} ⊥...

1. Problem Consider a particle that feels an angular force only of the form: F_θ = 3mr'θ'. Show that r' = ± (Ar^4 + B)^(1/2), where A and B are constants of integration, determined by the initial conditions. Also, show that if the particle starts with θ' ≠ 0 and r' > 0, it reaches r = ∞ in a...

Homework Statement A block of mass M is on a frictionless table that has a hole a distance S from the block. The block is attached to a massless string that goes through the hole. A force F is applied to the string and the block is given an angular velocity w0 , with the hole as the origin, so...

Homework Statement r = 2\cos(\theta) Homework EquationsThe Attempt at a Solution Hello, please do not evaluate. Why do textbook state that the derivative of the polar function (symbolic) is dy/dx and not dr/d\theta? It is a function of theta, then why is the derivative dy/dx? Idea: Even...

I don't understand the concept for polar and non-polar semiconductors, generally speaking about propagation of existence of phonons (acustic or optics). Thanks. I don't find any thread about this concepts.

In a polar function, $r = 1 - 2\cos(t)$ what are the tangents at the pole, considering $t$ an angle? I am not sure what the pole is BUT! $x = \cos(t) - 2\cos^2(t)$ $y = \sin(t) - \sin(2t)$ $dx/dt = -\sin(t) + 4\cos(t)\sin(t)$ $dy/dt = \cos(t) - 2\cos(2t)$ $dy/dx = \frac{\cos(t) -...

Homework Statement The problem and its solution are attached as TheProblemAndTheSolution.jpg. If you don't want to view the attached image, the cartesian-coordinate version that the problem wants me to convert to a polar-coordinate version is the following (let "int" = "integral").: int int (1...

Homework Statement Use polar coordinates to find the volume of the solid inside the hemisphere z=sqrt(16-x^2-y^2) and inside the cylinder x^2+y^2-4x=0 Homework Equations z=sqrt(16-x2-y2) x2+y2-4x=0 x=rcos(Θ) y=rsin(Θ) z=√(16-r2) The Attempt at a Solution ∫∫ r√(16-r2) dr dΘ The problem is...

Homework Statement The ground state wavefuntion of a system in spherical polar coordinates is given by: Ψ (r,θ, φ)= (A/r) [exp (-ar) - exp (-br)] where a, b, A are constants. i) Determine A as a function of a and b, so as to normalize the wavefuntion. ii) From Schrödinger equation find V (r)...

Hi, Say I have a variable 'x' which has the polar value 10@-75°, would '-x' be -10@+75° or 10@+75° as I am a touch confused as to which bit I have to invert

I know aqueous Ammonium Bicarbonate forms when NH4+ and HCO3- ions are present in water after they've dissolved from their gaseous states of NH3(g) and CO2(g). This occurs in the reaction: NH3(g) + H2O(l) + CO2(g) => (NH4)HCO3(aq) If Ammonia gas and CO2 are present above a polar organic...

I'm puzzled by a phenomenon that my daughter pointed out to me. If you have no plastic ware in the dishwasher, your glass and ceramic dishes will dry faster. Slow evaporation from plastic is easy to understand; the water beads up and presents a smaller surface area. What I'm not clear on is why...

How do I find the polar coordinates of the points on the polar curve r=cos(theta)+sin(theta), 0(greater than or equal to)(theta)(less than or equal to)(pi), where the tangent line is horizontal or vertical? I know that I need to convert the coordinates to x & y and then take the derivative of...

Homework Statement Convert 2cis(-pi/3)cis(pi/6) into cartesian form. Show all working to obtain full marks Homework Equations I know that the equation for it is 2((cos(theta) +isin(theta))+(cos(theta)+isin(theta))) The Attempt at a Solution Okay so cos of (-p/3) = 1/2 Sin of (-p/3) =...

Hello, for octane (C8H18), how can you tell whether or not it is polar or non-polar without drawing a lewis structure diagram? also, if you absolutely need to draw one, what is the easiest way to go about drawing a more advanced molecule like octane? I can draw simple molecules and find their...

Mod note: This post with template not used and no effort shown received a warning. Okay I am totally confused in this. This is not a homework question but rather one I saw online and was wondering for example how to solve it The question was -3-i/-8+6i to be expressed into Cartesian form...

Homework Statement Find the area inside one loop of r = 2cos(3 theta) and outside the circle r = 1 Homework EquationsThe Attempt at a Solution I need to clarify something about the limits of integration. I found the intersection of the two curves to be at an angle of pi/9. This is how I...

Given the force (derived from a potential in planar polar coordinates) F(p,w) = 2p+sin(w)e_p+cos(w)e_w Where e_p and e_w are unit vectors How do I calculate the line integral over a circumference that is defined as: p = 2 0 ≤ w ≤ 2pi Using the definition of a line integral \int_0^{2pi} \...

I have a course next semester on Classical Mechanics (mostly Lagrangian problems), for a second time. I'm ok for the theoretical preparation, but I'm trying to work ahead on problems and exercises, which was badly explained and without much of any resources. So, one of the sources to exercise on...

1.Which of the following compounds are nonpolar? 1) decene 2) decanal 3) 3-methyl-2-decene 4) 1,2-pentanediol 5) cyclohexanol Select one: a. 1,2 and 3 only b. 1 and 2 only c. 3,4 and 5 only d. 1,2,3 and 5 only e. 1 and 3 only 2. Which of the following compounds are polar? 1) 2-butyne 2)...

Homework Statement evaluate the double integral of cosh(6x^2+10y^2) dxdy by making the change of variables x=rcos(theta)/sqrt(3) and y=rsin(theta)/sqrt(5) let D be the region enclosed by the ellipse 3x^2+5y^2=1 and the line x=0 where x>0. Homework EquationsThe Attempt at a Solution first I...

In a late 1980s trade journal, I saw a full-page of polar balance diagrams for each major engine type. For each engine type (V6, V8, inline 6, inline 4, V12, etc) a circular polar chart was presented with overlaid color-coded graphs showing 1st, 2nd and 3rd order balance for 360 degrees of...

Homework Statement Find the arc length of one of the leaves of the polar curve r= 6 cos 6θ. Homework Equations L = ∫sqrt(r^2 + (dr/dθ)^2) dθ (I use twice that since the length from 0 to π/12 is only half the petal) The Attempt at a Solution I seem to get an integral that can't be...

Homework Statement Find the slope to the tangent line to the polar curve r^2 = 9 sin (3θ) at the point (3, π/6) Homework Equations dy/dx = (r cos θ + sin θ dr/dθ)/(-r sin θ + cos θ dr/dθ) The Attempt at a Solution So I have no issues with taking r^2 = 9 sin (3θ) and taking the...

Homework Statement Find the points on the given curve where the tangent is horizontal or vertical Homework Equations r = 3cos(θ) The Attempt at a Solution d/dθ = -3sin(θ) for horizontal: -3sin(θ)sin(θ) + 3cos(θ)cos(θ) I used identity and got: 3cos(2θ) = 0 I got the...

Homework Statement The projectile A is being tracked by the radar at O. At a given instant, the radar readings are θ = 30degrees, R = 2000m, dR/dt = 200 m/s, and d^2R/dt^2 = 20 m/s^2. Determine the speed of the projectile at that instant. THE ANSWER AT THE BACK IS 299.7m/s [PLEASE SEE...

Homework Statement "Put each of the following into the form Acos(ωt+θ)..." (a.) 4ejt+4e-jt Homework Equations Euler's Identity: ejθ = cos(θ)+jsin(θ) Phasor Analysis(?): Mcos(ωt+θ) ←→ Mejθ j = ej π/2 Trignometric Identities The Attempt at a Solution I attempted to use phasor analysis to...

Homework Statement As a part of my self study I am trying to find the covariant basis vectors in the spherical polar coordinates. Since I have never done anything like this before I would appreciate if someone could tell me whether I am on the rigth track. Homework Equations...

The torque contribution due to the uniaxial anisotropy is given by the equation below \frac{\Gamma}{l_m K} = (2 \sin\theta \cos\theta)[\sin\phi e_x - \cos\phi e_y] (3) This contribution can be taken in the LLG equation to derive the LLG equation in polar coordinates \frac{\partial...

Homework Statement My answer seems to differ from the books answer, so I'm wondering where something has gone wrong. Find the volume inside the prism bounded by the planes ##y = x##, ##y = 0##, ##x = \frac{a}{\sqrt{2}}##, ##z = 0## and the cone ##az = h\sqrt{x^2 + y^2}##. Homework...

I'm reading Leonard Susskind's The Theoretical Minimum Vol. 1. 1. The problem: I'm on the section in which he asks the readers to derive the Lagrangian for a particle on a rotating carousel in polar coordinates. 2. Relevant ideas: The same Lagrangian in Cartesian coordinates is given as...

Let me say from the beginning I'm not talking about the non-coordinate unit vectors for polar coordinates. I'm talking about basis vectors. Let me just ask it as boldly as possible: how does one use these basis vectors in order to describe a vector? I know they are different at every point, so...

Alright, so I was reading up on tensors and such with non-Cartesian coordinate systems all day but now I'm a bit tired an confused so you'll have to forgive me if it's a stupid question. So to express the dot product in some coordinate system, it's: g(\vec{A}\,,\vec{B})=A^aB^bg_{ab} And, if...

Find the points of intersection of $\rho=\cos\left({2\theta}\right)$ and $\rho=\cos\left({\theta}\right)$ By setting $\cos\left({2\theta}\right)=\cos\left({\theta}\right)$, we get the solutions $\theta=0,\frac{2\pi}{3},\frac{4\pi}{3}$. My question is how come that doesn't give us all the...

Homework Statement Find the Volume of the solid that the cylinder ##r = acos\theta## cuts out of the sphere of radius a centered at the origin.Homework Equations The Attempt at a Solution I have defined the polar region as follows, $$D = \{ (r,\theta) | -\pi/2 ≤ \theta ≤ \pi/2 , 0 ≤ r...

Hello, I'm working with a problem in linear elasticity, and I have to calculate the strain energy function as follows: 2W = σijεij Where σ and ε are symmetric rank 2 tensors. For cartesian coordinates it is really easy because the metric is just the identity matrix, hence: 2W = σxxεxx +...

Hey Everyone! I have three questions that I do not know how to approach/solve. I've been checking online, the textbook, etc, and nothing. This is Calculus 2.1. Find the points with the given slope. x=9cos(theta), y=9sin(theta), slope = 1/2. Answer: (-9rt5/5, 18rt5/5), (9rt5/5, -18rt5/5)...

$r=5$ and $\theta=\pi/6$$\frac{dy}{dx}=\frac{\frac{dy}{d \theta}}{\frac{dx}{d \theta}}=\frac{\frac{dr}{d \theta}sin(\theta)+rcos(\theta)}{\frac{dr}{d \theta}cos(\theta)-rsin(\theta)}$ $\frac{0*sin(\pi/3)+5cos(\pi/3)}{0*cos(\pi/3)-5sin(\pi/3)}=-\frac{\sqrt{3}}{3}$is that right?

Suppose T=T(r,θ)=G(x,y) How do you prove ∇T(r,θ)=∇G(x,y)? I can think of some arguments in favor of this equality, but I want an actual proof or a very good intuitive argument. My arguments in favor go something like this: -Gradient vectors should be the same because if my directional...

So I'm wondering, should I use Cartesian or Polar Coordinates to store intergalactic objects in DB? I'm currently prototyping a game idea that can be oversimplified as a spaceship simulator in infinite space. I'm considering grouping objects together so that they have a "parent super-space"...