Axis Definition and 895 Threads

This is really a nomenclature question. The radiation pattern of a typical laser diode has one axis with low divergence (the slow axis) compared to the other (the fast axis). I understand about antenna radiation patterns, spatial Fourier transforms (Fourier optics), etc. So I think I understand...

https://www.feynmanlectures.caltech.edu/I_19.html "Suppose we have an object, and we want to find its moment of inertia around some axis. That means we want the inertia needed to carry it by rotation about that axis. Now if we support the object on pivots at the center of mass, so that the...

I have had a thought experiment in my head for a while now and I am unable to find clear enough examples/info that deal with similar issues, to solve it on my own. This is why I hope that someone in this forum can at least point me towards a solution or provide hints as to where should I be...

For a 1/2 spin particle, every pure spin state may be represented as a superposition of two states of spin parallel to some arbitrary Z axis. (Upd) Particularly: $$|\uparrow_{x}>=\frac{1}{\sqrt{2}}(|\uparrow_{z}>+|\downarrow_{z}>)$$ I then wonder, if we chose the Z axis, how the X axis should...

I am trying to understand but without a succes why symmetric magnetic field around ##Z## axis make that ##\hat \phi## magnetic field is zero I can't understand why it physically happens and also how can I derive it mathematically? What does the word symmetric means when talking about magnetic...

I want to say [the bodies is under gravity field]: There cannot be torque alonge AB "since it is pivoted" There cannot be torque alonge AB "since it is pivoted" i think i am missing something.

I have not clear how to solve this problem. Here it is my attempt at a solution: Let the charge at ##-a## be the number one and the one at ##+a## the number two. the potential energy of the punctual charge ##-Q## due to each charge +Q will be then ##E_{pi}=-k \frac{Q^2}{r_i}##, whit ##r_i## the...

One part of König's theorem states that ##\vec{L} = \vec{L}_{\text{COM}} + \vec{L}^{'}##. The term ##\vec{L}^{'}## simply refers to the angular momentum wrt. the centre of mass. This is just a point, and doesn't have an axis implicitly associated with it (we have infinitely many choices!). The...

Why work done is area enclosed by graph of F v/s x on x Axis but not y axis. Suppose we apply a force on object which is proportional to displacement as ##\vec f##=## \vec x##²then area enclosed by Force and displacement on x Axis is integral of ##\vec x##²but on y-axis it should be integral of...

Hi all I was wondering if someone could help clear up some confusion about the Parallel Axis Theorem. I am trying to understand the purpose/benefit of applying the Parallel Axis Theorem with respect too the Second Moment Of Area. For example I have a beam that is under load. I have found its...

Firstly I deduced that in this situation the moment of inertia I, is not going to be parallel to w. And I calculated it as a matter of the angle, for the rod and the two point particles attached (with a mass 'm'), and the total moment of Inertia ended up being: I=((R²*sin²α)/2)*(M/6 + m) Being...

Summary:: How is the pitch axis location of an aerodynamic profile decided? Hi, I drew a wind turbine blade in a CAD software. I used information on the pitch axis location I had on the various aerodynamic profiles I used to draw the blade. I understand that it allowed me to align the various...

If a rod is on a table (horizontally) and rotating about an axis that passes through one of its ends and vertical to the table, what would be the tension on the opposite end of the rod (the end opposite to the axis) . In this post (Check this post out from Socratic QnA), the limits take while...

Earlier I read that as distance from centre of axis of rod increases it's inertia increases but why does torque increases isn't it like that if inertia increases for same force the less force should be produced?

A uniform rod AB of length ℓ is free to rotate about a horizontal axis passing through A. The rod is released from rest from the horizontal position. If the rod gets broken at midpoint C when it becomes vertical, then just after breaking of the rod. Choose multiple answeres from the below...

The sketch above shows the situation of the problem. Clearly, as the rotation is taking place in the ##y-z## plane, the x-components of the two vectors remain unchanged : ##A_x = B_x##. Let the projection of the vector ##\vec B## on to the y-z plane be vector ##(\vec B)_{yz} = B_y \hat y + B_z...

Veritasium posted a video, featuring a visualization of an "intuitive" explanation of the Intermediate Axis Theorem by Terry Tao, based on centrifugal forces in a rotating frame of reference: Unfortunately, the animation is just as incomplete, as Tao's original explanation from 2011, and...

Hi! I need help with this problem. I tried to solve it like this: First I calculated the electric field of each ring: Thus the electric field at a point that is at a distance z from the ring is ##E=\frac{Qz}{4\pi\epsilon_0(z^2+r^2)^{3/2}}##, Thuss for the upper ring, the electric field would be...

Well, I drew the polar and standard axis centered in the particle and wrote which angles were equal to 60° so I could decompose the velocity. The problem says "moves towards it (the radar) with velocity v=5 m/s, so that's one of the components. But I realized that the velocity "cuts" the angle...

Let's say I have a massless bar of length ##l## with two different masses, ##m_1## and ##m_2##. Suppose an identical spring is attached to each individual mass, with the other end being attached to the ceiling. How would I go about determining the rotational kinetic energy of the system. Do I...

Hi, I have a question regarding a pendulum and it's motion/momentum given the axis it moves around. In the below picture, there are two version of a pendulum with a weight at the bottom. It moves in and out of the screen, around an axis resting on two nails (red). My question is, how does the...

So I figured out the potential is: dV = (1/(4*Pi*Epsilon_0))*[λ dl/sqrt(z^2+a^2)] . From that expression: We can figure out that since its half a ring we have to integrate from 0 to pi*a, so we would get: V = (1/(4*Pi*Epsilon_0))*[λ {pi*a]/sqrt(z^2+a^2)] In that expression: a = sqrt(x^2+y^2)...

Why is there a preferred z axis even though the potential energy function is perfectly spherical? Shouldn't the electron be around the nucleus in a spherically symmetrical way?

Now, Uranus seems to have had an eventful early life. According to theory, it got hit by a large planetary body, which knocked it's axis to nearly 90°. Also according to another theory, it apparently had a close encounter with Neptune which took Neptune further away, when initially it was closer...

Aristotle's absolute space and time can be represented as ordered pairs (s, t) but not as fibers π(s) = t of time as is the case of Galileo and Newton's space time. That is to say that the space of Galileo and Newton is the projection π(s) = t on the time axis. The time space of Galileo and...

The contribution coming from a little segment of the ring is ##d\vec{E}=\frac{dQ}{r^2}cos\theta \hat{z}##, assuming that the horizontal components cancel out. But how can we show that?

I thought about solving it using components of IAB but since it is a scalar quantity it doesn't seems to be correct . I don't think Perpendicular Axis theorem will work as required Inertia is in the same plane.

I first took out the variation of conductivity along the radius of cylinder.Also we know that J=sigmaE.Therefore i have to find variation of E also.But how will i find that as potential is also not given.Help.

##I_{AB} = I_{GXX} + A.(y^{2})## Same applies to CD; ##I_{CD} = I_{GYY} + A.(x^{2})## In the above statement, "any axis in its plane" where does the plane exist in this sketch?

How does " an axis normal to the plane containing the structure" look like?

Options are at the top of page as a) b) c) d) Answer may more than one. Now since 'a' is distance from the smaller surface of cone so as we move along the axis area will increase,So current charge density will decrease and as we know J=sigma E,E will decrease,but V will remain constant since...

My attempt-:I extended the axis and made a triangle by joining other adjacent vertex to the line such that its angles are 15°,75° and 90°.I found the distance between the centre of square and upper vertex of triangle by using law of sines.And then i found out inertia along upper vertex of...

There is a disaster movie about a global cataclysm that results in Kilimantzaro becoming the north pole or something. Maybe this is plausible in terms of plate tectonics. Or maybe not. But I've got another question, a purely mathematical one: if the Earth were a solid sphere, no plates and such...

Hey Guys/Gals i understand the general premise of this question and can calculate the solution but i am a bit confused. I am supposed to represent a generic state as a linear combination of the |-,x> , |+,x> basis vectors. However i don't know why, is the question actually asking for the...

I am trying to link the upper axis with the lower axis in gnu plot, that is print out values on the upper axis given a relationship between the upper axis, x2, quantities and the lower axis, x, ones. The relationship between them is x2 = 2*c**2/(2*x**2-c**2) with c=3.1 The following should be...

I assumed to find it I would need to find the area under the graph. I also assumed that the part under x would cancel out so I would be left with 2b*10=1 if it was, in fact, true that it had to equal to one. So my final answer was (1/10)/2 nm^-1 but the actual answer was 0.0845 nm^-1/2 and I'm...

Hello I think this image's calculation is wrong. I cannot convert units(What is arcsec??How convert to pc??) How do you think ??I would like to see your calculation process. I'm so grad if you show.

Since the metric is euclidean in coordinates ##(ict,x)## it can be drawn in a plane, but if the metric is ##diag(1,-1)##, can both axis still be drawn in a plane ?

So I first wrote the moment of inertia of the cylinder, since it says that it is thin-walled, I think that its moment of inertia is ##I=\eta mR^2##. After that I wrote the sum of torques, I think that there are three forces that cause torque, the two forces of friction, the one caused by the...

Homework Statement I have a conceptual question regarding why the x and y-axis must be perpendicular. Chapter 2 in section 2-1 of Giancoli's Physics states that " The x and y axes are always perpendicular". This chapter is one-dimensional motion and the section is Reference frames and...

in the case of a disc rotating about the centroidal axis and having an unbalanced mass we used the formula F(force)=m x r x w^2, where r is the distance from the center to the center, m mass of the unbalanced, w rotational speed in the case of a disc rotating about axis parallel to the...

Santa Fe is approximately 33.88 degrees north of the equator. Given that the Earth's radius at the equator is 3960 mi and the Earth spins around its axis completely in 24 hours, what is the linear speed of Santa Fe around the Earth's axis in mi/hr? I don't know where to start! Thank you so much!

Homework Statement [/B] Hello, I would like to request some help in solving this mechanics problem. Consider the attached drawing of a solid structure which is pinned to the ground on points A and B. Distances AC=Xa, CB=Xb, CD=H1 and DE=H2 A torque with magnitude M is applied on point E. How do...

When we solve Euler's differential equations for rigid bodies we find the angular acceleration ##\dot{\boldsymbol\omega}## and then the angular velocity ##\boldsymbol\omega##. Integrating ##\boldsymbol\omega## is less straightforward, so we start from a representation of the attitude, take its...

Hi, How is the inertial force Fi (acceleration) when the system is vertical. I noted Fi_horizontal=m.a, Ff=mg.μ.cos(Θ) et Fg=mg.sin(Θ) .

Please see the attached page to see what I'm talking about. In the top right paragraph, it states to use "the positive direction of the x-axis". It is given that ##θ_2=30°## and it shown visually at the bottom of the page. In the problem it's using -60° and I'm not sure how they're getting that.

I have been struggling to visualize how three rotating reaction wheels on bearings and affixed to each other at 90 degree angles, one at each axis (picture the kind of 3-axis reaction devices used in satalites), would behave when torque is applied to the whole assembly. If all three reaction...

1.Data: We have an truncated cone with a volumentric charge density ρ, and it's uniform. The image show the truncated cone and show some info of the radios. 2. Question. We need to calculate the potential on the vertical axis. note: adding an image of the problem but it's in spanish, hope...

Homework Statement A ball A is rotating on a table with an angular velocity ω about its vertical axis. An identical ball B collides with the ball A elastically. After collision the ball A starts sliding over the table. The coefficient of friction is µ. Find: 1) the angle α between the angular...