# What is Radial: Definition and 480 Discussions

The radial engine is a reciprocating type internal combustion engine configuration in which the cylinders "radiate" outward from a central crankcase like the spokes of a wheel. It resembles a stylized star when viewed from the front, and is called a "star engine" in some languages (German Sternmotor, French moteur en étoile, Japanese 星型エンジン (hoshigata enjin), Italian motore stellare). The radial configuration was commonly used for aircraft engines before gas turbine engines became predominant.

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Y11 I can´t find Rl(r) written out on the internet.
2. ### A Solving the Radial Equation for the Dirac Hydrogen Atom Solution

I'm going to be a bit sketchy here, at least to start with. If you want me to show you exactly where I am I might post a pdf, if that's okay. (Only because it will simplify coding several pages of LaTeX.) Briefly, what I'm trying to do is take this system of equations: ##F^{ \prime } +...
3. ### Find the electric field of a long line charge at a radial distance

TL;DR Summary: Find the electric field of a long line charge at a radial distance where the potential is 24V higher than at a radial distance r_1=3m where E=4V/m. Answer: 29.5V/m. Never mind: I retract this question. The integral apparently is supposed to diverge! I apologize for not reading...
4. ### The FBD Mystery: Why Isn't Normal Force Along Radial Line?

so this is what the FBD is.... but to be fair, to me this one looks as if the normal force in the direction of the radial line, yet it isn't???? here in the solution, it's not along the radial line, whys that???
5. ### Angle between normal force and radial line for cylindrical coordinates

so I was wondering. there is this normal force on the can from the path. And there's this formula to find the angle between the radial line and the tangent or also between the normal force and either the radial or theta axis. the formula is ##\psi = r/dr/d\theta##. The thing is that here they...
6. ### Derive an expression for the radial charge distribution of an E field

I know we're supposed to attempt a solution but I'm honestly super confused here. I think the second an third terms of the del equation can be cancelled out because there is only an E field in the r hat direction, so no e field in the theta and phi directions. That leaves us with ##\nabla \cdot...
7. ### Engineering How do radial tooth clutches function?

Greetings I have a hard time understanding how the radial tooth clutch function when it stops transferring power . Basically I understand that clutches: 1) transfer power from input shaft to output shaft 3) disengage when the torque transmitted has reached a certain limit ( normally when the...
8. ### Why is magnetic field B along a straight wire circular not radial?

Statement: The magnetic field around a straight wire carrying a current can be explained Relativistically by changing the inertial frame of reference to the frame of the moving electrons - i.e., a Lorentz contraction of the positive charges in the wire will give a denser concentration of the...
9. ### I Radial position operator

While trying to find the expectation value of the radial distance ##r## of an electron in hydrogen atom in ground state the expression is : ##\begin{aligned}\langle r\rangle &=\langle n \ell m|r| n \ell m\rangle=\langle 100|r| 100\rangle \\ &=\int r\left|\psi_{n \ell m}(r, \theta...
10. ### Automotive Calculating radial and axial loads for a tapered roller bearing

Hi I'm analyzing a tapered roller bearing as part of a differential. I know the shaft is providing input torque of 333.5 N-m @ 4000RPM, and I know the bore size of the bearing, 30mm. I need to find the radial and axial forces given that torque, so I can move on to finding C10, L10, rated load...
11. ### I Electric field vector takes into account the field's radial direction?

Does the electric field vector takes into account the field's radial direction? Usually when we calculate the electric field, we use ##\vec E = \frac{kq}{r^2}\vec j##, which is a straight line vector of a positive charge q's electric field. This electric field points from a positive charge q to...
12. ### Radial oscillations of a star

So far I have not made much meaningful progress beyond two equations; \begin{align*} \rho \frac{D\mathbf{u}}{Dt} = - \nabla p \implies \rho \left( \frac{\partial}{\partial t} + u \frac{\partial}{\partial r} \right)u = - \frac{\partial p}{\partial r} \end{align*}and thermal energy:\begin{align*}...
13. ### Engineering Why are the radial and the axial stress in a rotating thin ring null?

Greetings, while studying the stress in the rotating thing ring and find out the last equation that says I would like to understand why? Thank you!
14. ### Fourier transform radial component of magnetic field

Hello everybody! I have a question concerning the Fourier transformation: So far I have experimentially measured the magnetic field of a quadrupole but as the hall effect sensor had a fixed orientation I did two series, one for the x, one for y component of the magnetic field, I have 50 values...
15. ### Mass conservation in a sphere to find radial velocity of a flame

I am not sure what form of mass conservation to use to solve the above problem from An Introduction to Combustion by Stephen Turns. Can anyone explain what form of mass conservation applies to a sphere in this context?
16. ### I Image for increase in gravitational potential energy in radial field

A question to physicists: What sort of real world scenario / image would *best* depict the increase in gravitational potential energy in a radial field? Would a rocket traveling through the Earth's atmosphere suffice or are there better alternatives? This image would have to be relevant to the...
17. ### A Radial Excess Calc: GR, 4πGρ & R00

Which is the mathematical procedure to obtain ##\delta r = \frac{GM}{3c^2}## from ##\nabla^2 V = R_{00} = 4\pi G\rho## where ##\nabla^2 V## is volume contraction of a spherical mass of density ##\rho## and ##R_{00}## is the 00 component of Ricci tensor ##R_{ij}##?
18. ### Finding Radial Force from Free Body Diagram

I have a question regarding a homework exercise. My professor asked me to find the radial force in the free body diagram in the image included. There is a weight Fz from above and it is assumed that it is countered by the vertical component of both the Ff (friction force) and the Fn (normal...
19. ### How to picture a radial field around a 3d object?

Hello! First off, for a), I am not too sure how to picture a radial field around a 3d object. I know that this spherical metal dome is basically a enlarged version of an atom, but since with problems on radial field around an atom, I don't have to consider its diameter, I'm not sure how the...
20. ### Drawing Radial Field Equipotentials and Field Lines

I have just attached a standard depiction of a radial field as one may similarly choose to draw it. So I understand that the gravitational field strength in a field is defined as the force per unit mass at that point. The field lines in a radial field move further apart further away from the...
21. ### A Radial acceleration for spherically symmetric systems in GR

Hello, I was reading few papers discussing modified gravity theories and their use in understanding galaxies with no dark matter by checking for anomalous velocity dispersion. Now, the author was using 4 gravity theories MOND, Weyl, MOG and Emergent gravity. The thing is he had provided the...
22. ### Radial solutions to the Laplace equation

Part 1 $$\Delta u(x)=\Delta v(|x|)$$ Substitute $$|x|=r=\sqrt{\sum_{i=1}^n{x^2_i}}$$ $$u'(x)= v'(r)\frac{\sum_{i=1}^nx_i}{\sqrt{\sum_{i=1}^n{x^2_i}}}$$ $$u''(x)=v''(r)\frac{\sum_{i=1}^nx_i}{\sqrt{\sum_{i=1}^n{x^2_i}}}+v'(r)f(x)=v''(r)+v'(r)f(x)$$...
23. ### I Orbital maneuver by applying a thrust in the radial direction

The author of my textbook writes that a spacecraft 's "thrust in the radial direction at perigee changes the energy but not the angular momentum". Such a thrust increases the eccentricity of the elliptical orbit of the spacecraft because ##\epsilon \equiv \sqrt{1+2EL^2/\mu C^2}##, where...
24. ### Separating a wave function into radial and azimuthal parts

I know how to work through this problem but I have a question on the initial separation of the wave function. Assuming ##\psi(\rho, \phi) = R(\rho)\Phi(\phi)## then for the azimuthal part of the wavefunction we have ##\Phi(\phi)=B\left(\frac \rho\Delta cos\phi+sin\phi\right)##, but this function...
25. ### Radial Geodesic in Kerr's metric

The Kerr metric is given by \begin{align*} (ds)^2 &= -\left(1-\frac{2GMr}{\rho^2} \right)(dt)^2 - \frac{2GMar \sin^2 \theta}{\rho^2}(dt d\phi + d\phi dt) \\ &+ \frac{\rho^2}{\Delta}(dr)^2 + \rho^2 (d \theta)^2 + \frac{\sin^2 \theta}{\rho^2} \left[ \underbrace{(r^2+a^2)^2-a^2 \Delta \sin^2...
26. ### A Feynman solution for the radial wave function of the hydrogen atom

Reading the classical Feynman lectures, I encounter the formula(19.53) that gives the radial component of the wave function: $$F_{n,l}(\rho)=\frac{e^{-\alpha\rho}}{\rho}\sum_{k=l+1}^n a_k \rho^k$$ that, for ##n=l+1## becomes $$F_{n,l}=\frac{e^{-\rho/n}}{\rho}a_n\rho^n$$ To find ##a_n## I...
27. ### Divergence of a radial field ##F=\hat{r}/r^{2+\varepsilon}##

Following (1), \begin{align*} \text{div} F = \vec{\nabla} \cdot \vec{F} &= \frac{1}{r^2} \frac{\partial}{\partial r} \left( r^2 F_{r}\right) \\ &= \frac{1}{r^2} \frac{\partial }{\partial r} \left( r^2 \frac{1}{r^{2+\varepsilon}}\right) \\ &= \frac{1}{r^2} \frac{\partial}{\partial r}...
28. ### A Normalization of the radial part of the spherical harmonics

Im trying to solve the equation 62.7 of this numerical on mathematica. Whenever i try to normalized the function it shows function diverges. As the Bessel function contains trigonometry term so it diverges. I don't know how to solve the integral. Can i use the hydrogen atom wavefunction in exp...
29. E

### "Total" radial force on a hoop

I was just reading through these lecture notes regarding the stresses in solenoids, and came across the following regarding a current-carrying ring orthogonal to a uniform magnetic field, I wondered if this is a piece of terminology that I haven't come across? To me the total radial force is...
30. ### A particle moving with zero radial acceleration in polar coordinates

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.
31. ### Relationship between radial distance and charge density of a capacitor

So this is a question from my lab report on capacitance. The aim of the experiment is to find out the relationship between surface charge density and radial distance from the centre of the plate capacitor. And in this experiment I have recorded 5 sets of data, namely r=0, V=4, r=1, V=3.5, r=2...
32. ### I The proper Schwarzschild radial distance between two spherical shells

For the purpose of this thread the metric is ds2 = - (1-rs/r) c2 dt2 + dr2 / (1-rs/r) where rs = 2GM/c2. (I modified the above from https://jila.colorado.edu/~ajsh/bh/schwp.html .) I assume that the two spherical shells are stationary. Therefore dt = 0. The r coordinate for the radii of the...
33. ### Parameterize Radial Vector of Electric Field due to Spherical Shell

Homework statement: Find the electric field a distance z from the center of a spherical shell of radius R that carries a uniform charge density σ. Relevant Equations: Gauss' Law $$\vec{E}=k\int\frac{\sigma}{r^2}\hat{r}da$$ My Attempt: By using the spherical symmetry, it is fairly obvious...
34. ### I Lithium Atom Ground State Radial Wavefunction

I would like to see what the shape of the ground state radial wavefunction for the Lithium atom is. An approximate function that shows the shape would be fine. Thanks.
35. ### Plotting the radial wave function of Deuteron in a finite well

To plot ##u(r)## we need to find the solutions for each region. Which is in the relevant equations part. Now, I have to do this numerically. Using python 3.7 I made an ##u## which is filled with zeros and a for loop with if/elseif statement, basically telling it to plot values for whenever...
36. ### Radial acceleration derivation with minimal knowledge

Just started learning about uniform circular motion. I really don't understand how we get aΔt2/2 on the side. I also searched on the internet for a similar derivation, but there are none so simple. Thanks for your help! P.S There is a mistake in calculation in second line (textbook error).
37. ### I Radial Vector in Cartesian form

If I wanted to write ##\hat{r}##in terms of ##\hat{x}##and ##\hat{y}##, is it ##\frac{\hat{x} + \hat{y}}{\sqrt{2}}## ?
38. ### A Derive Radial Momentum Eq. in Kerr Geometry

I am trying to derive the radial momentum equation in the equatorial Kerr geometry obtained from the equation $$(P+\rho)u^\nu u^r_{;\nu}+(g^{r\nu}+u^ru^\nu)P_{,r}=0 \qquad$$. Expressing the first term in the equation as $$(P+\rho)u^\nu u^r_{;\nu}=(P+\rho)u^r u^r_{;r}$$ I obtained the...
39. ### Exploring Radial Acceleration and Displacement

From what I understand, ##a_{r} = v_{tan}^2 /r## ##a_{r} = (r\omega)^2 /r## ##a_{r} = r\omega^2## ##\omega^2 = \frac{a_{r}}{r}## ##\omega^2 = \frac{2+2t}{0.12}## ##\omega = \sqrt{\frac{2+2t}{0.12}}## ##s =\int_{0}^{2} \sqrt{\frac{2+2t}{0.12}}## After integrating, I still can't seem to get the...
40. ### Light intensity profile along all radial distances

Hello, I have an ordinary light (not laser) collimated to produce a parallel beam. After traveling a distance in air, the beam has diverged significantly. The intensity decreases as the radial distance increases. Now I need to estimate the intensity profile along all radial distances inside the...
41. ### I Is there a radial gradient of redshifts within individual galaxies?

The summary says it all. Such small gradients, if they exist, would be visible in the Milky Way and local galaxies in our cluster. I'm not familiar enough with the raw data--and haven't tried to search the astronomical literature--to know whether any such small effect has been reported. (If...

Imagine the following scenario. A pipe is strapped to a larger "host" pipe using a steel strap and a spacer block as shown in the image below. If anyone could have a look at my calculations to confirm they are correct that would be brilliant! Variables Assuming the following general values I...
43. ### I Proving radial properties of particular dimensionless surface plots?

We have a surface function z = f(x,y) ; f(x,y) only contains dimensionless constants, and is itself dimensionless. If we convert it to cylindrical co-ordinates, z = f(r,θ) , does z only depend on θ? Meaning we can remove r from the equation, literally.
44. ### Radial and tangential components of acceleration

Hello, In 2D kinematics, the acceleration vector ##a(t)## can be expressed either in Cartesian coordinates ##a_x## and ##a_y## or in polar coordinates ##r## an ##\theta##. It depends on the problem. But it is also possible to express the acceleration ##a(t)## in the so called "intrinsic...
45. ### I What is the gravitational component in the radial direction?

Hey guys, I reading over Taylor's Classical Mechanics book. Chapter 9, Centrifugal Acceleration Section. In p.346 he mentions that for a free fall acceleration: g = g_0 + Ω^2 * Rsinθ ρ Where its radial component would be...
46. ### Why does radial acceleration act toward the center?

Acceleration of a rotating link has two components,Tangential (change in the direction) Radial (change in the magnitude). Why the direction of Radial acceleration is considered towards center (Centripetal)? what about centrifugal?
47. ### Calculate the radial force acting on bearings in a carousel

Dear Physicians, I am in the process of developing a playground carousel (see example attached) and need to calculate some forces acting on the construction in order to design the bearing mechanism and select the correct bearings for the job. I've made an outline which you'll find attached...
48. ### Radial Acceleration in Polar/Cylindrical Coordinates

My question is why isn't the radial component e→r of acceleration in cylindrical coords simply r'' ? If r'' is the rate at which the rate of change of position is changing in the radial direction, wouldn't that make it the radial acceleration? I.e, the acceleration of the radius is the...
49. ### A Normalization of Radial Distribution Function

Hello all, I have a Radial Distribution Function in which the y-axis ie., g(r) value goes up to 40. But the other atoms values for g(r) are, say within 5. So when i plot these two it is difficult to see the smaller graph. So how do i normalize these value..?? I have attached an image. Any...
50. ### Spherical Capacitor Discharging Through Radial Resistor

Homework Statement A spherical capacitor has internal radius ##a## and external radius ##b##. At time ##t = 0##, the charge of the capacitor is ##Q_0## Then the two shells are connected by a resistor in the radial direction of resistance ##R##. Find the Poynting vector and the energy...