Components Definition and 949 Threads

We know that a = vdv/dx But is it applicable in only one dimensional components or is this actually a vector equation? If so then how do we exactly differentiate with respect to position 'vector'?

I had made a silly inattention mistake. Once corrected everything worked out. I have updated the pictures to show the correct answer.

TL;DR Summary: In Morin 3.7 sliding sideways on a plane I used a completely different method than he did and got the correct answer is my method right The problem statement is as follows I split up the friction force into x and y components derived a diff eq for v_y in terms of v_x then took...

It's a 4th-dimensional 4th-rank tensor so at first we have ##4^4=256## components. According to the book, Given that ##R_{iklm}=-R_{ikml}## 256 components reduces to 96. But I cannot see how. For one pair of i,k 16 components are dependent. We have 12 pairs of i,k(for ##i≠k## becsuse for i=k...

Hi all, playing with fancy e textiles and I wish to run a current through it. I don’t want to use mains, or d cell batteries. Can you point me in the right direction what components I could use and also how to get away with any grounding as it’s just a small area to put a current through...

I don't get what is the difference when I am asked to re-solve components and find projections to axes other than the Y and X I know that the parallelogram works for the first one and the dot product for the second but what's the diffrence!

I've already got the answer and the way to solve it (parallelogram), but I'm just wondering why I cannot use the technique I've learned in the lesson torque. Let's focus on the line AB, if I use what I've learned in torque, the components would be like this: To find the force component in...

Question: Solution: I need help with the last part. I think my numerical factors are incorrect, even if I add the last term it will get worse. What have I done wrong, or is there a better way to deal with this?

Determine the amount and type (tensile or compressive) of the spring force so that the resulting force is a vertical force. Also get the resultant force. i find 60N (compressive) and resultant forces is 10800 is that correct?

I have a terminological question: should system parts defined by functional interactions or by being inside (and including) the system’s physical boundary? System components are often defined as part of a system based upon their interactions that lead to the system’s success in achieving its...

I first tried to use a method based on Gram Schmidt orthogonalization method: $$ v_{\parallel}=\left(v\ldotp\frac{u}{\left\Vert u\right\Vert }\right)\frac{u}{\left\Vert u\right\Vert }+\left(v\ldotp\frac{w}{\left\Vert w\right\Vert }\right)\frac{w}{\left\Vert w\right\Vert }, $$ and $$...

I have typed up the main problem in latex (see photo below) It seems all such integrals evaluates to 0, but that is apparantly unreasonable for in classical mechanics such a free particle is with nonzero angular momentum with respect to y axis.

Hello everyone, I am working on a very low cost, small and basic vending machine ($300) with wooden cabinet for small neighborhood stores. As you may know, it is necessary to properly protect the components to prevent users from trying to steal money or damage the components. The PCB has a TFT...

I know what x and y components are but this is really confusing me. And the angle I think is the inverse of tan something. part 3 is so confusing smh

I am reading Tensor Calculus for Physics by Dwight E. Neuenschwander and am having difficulties in following his logic regarding proceeding to derive the components of Angular Momentum and from there the components of the Inertia Tensor ... On page 36 we read the following: In the above text...

Hi guys/gals, I am looking for ways to securely fasten components together for aerospace applications and in ways that can be quickly unfastened if replacement is required. I have two main components, (1) a cylindrical (non-circular cross-section) lip in front of (2) a cylindrical barrel...

The image i provided is a section of microcontroller circuit that i used to interface code in C with the I/O port of the microcontroller, in Proteus. I have realized i was only ever told to learn how to measure the voltage and current across the components, Kirchhoff's rules and all, and...

I often watch instructional YouTube videos on my tablet with Bluetooth headphones. The delay/latency in the audio often isn't so noticeable, but when I see someone using a hammer, or sandpaper, the delay between the visual of the hammer hit or sandpaper swipe and the audible "bam" or "swoosh" is...

I'm studying orbital angular momentum in the quantum domain, and I've come up with the Robertson uncertainty relation for the components of orbital angular momentum. Therefore, I read that it is necessary to pay attention to the triviality problem, because in the case where the commutator is...

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I'm working on a problem involving some hypothetical spacetimes (i.e. no tables/data-sheets available) and need to calculate a bunch of ##R_{\mu \nu \rho \sigma}## and ##R_{\mu \nu}## values, as well as ##R##. The metrics contain some arbitrary functions ##f(x^i)## of the spatial co-ordinates...

Divergence formula $$\vec{\nabla} \cdot \vec{A}= \frac{1}{\sqrt{G}} \frac{\partial}{\partial q^{j}} (A^{j} \sqrt{G})$$ If we express it in terms of the components of ##\vec{A}## in unit basis using $$A^{*j} = \sqrt{g^{jj}} A^{j}$$ , we get $$\vec{\nabla} \cdot \vec{A}= \frac{1}{\sqrt{G}}...

There is an ambiguity for me about vector components and basis vectors. I think this is how to interpret it and clear it all up but I could be wrong. I understand a vector component is not a vector itself but a scalar. Yet, we break a vector into its "components" and then add them vectorially...

(This is my first time posting here, sorry in advance for any difficulties. ) All componenets of same type has same magnitude, so e.g. the two resistors both have $R$ resistance. Given the difficulty of the previous exercises, I believe I'm over complicating the problem. However, here is what...

It is given that the charge density of a particle of charge ##q_0##, world line ##z^{\mu}(\tau)## (and 4-velocity ##u^{\mu}##) in a spin-##s## force field is a ##s##-tensor\begin{align*} T^{\mu \nu \dots \rho}(x^{\sigma}) = q_0 \int u^{\mu} u^{\nu} \dots u^{\rho} \delta^4[x^{\sigma} -...

x component of ##F_3## ##F_{3x}= m a_x- F_{1x}-F_{2x}## = ##ma\cos 50-F_1\cos(-150)-F_2\cos90## y component of ##F_3## ##F_{3y}= m a_y-F_{1y}-F_{2y}## =##ma\sin50-F_1\sin(-150)-F_2\sin90## And so on… My question how we can represent it in diagram ##F_1\sin(-150)##. I suppose...

Forgive me if you've heard this song before, but I don't understand how to interpret the \psi_3 and \psi_4 components of the Dirac equation. For instance, at 8:27 of this video we see that while an electron at rest can be in a state like [1,0,0,0], the same electron as viewed from a...

Another user suggested adding the forces in the x and y direction then dividing by 1.4. Doing this for A) gave me 4.285 which was wrong any suggestions?

The picture may be blurry. I couldn't take more less blurry picture hence, giving it. The question is : Find value of ##\theta## when ##V_x## component and ##V_y## component same. I was using a simple equation of vector. $$C=\sqrt{A^2+B^2+2AB\cos\theta}$$...

Hi. I'm really stuck with this problem and would appreciate some help. For example, if i take the total intensity from the ##^2\text{P}_{3/2}## level, i get ##a+b##. Since ##b## is 9 times larger than ##a##, i get that the total intensity is ##10a##. This should then be proportional to the...

Does the position of the origin for the body’s rotating coordinate frame 1) stay fixed to the moving body or 2) does it stay fixed to the inertial frame, yet still able to rotate as the body rotates with the only restriction that it cannot translate with the body i.e. only affixed at the...

Hello to all members! I'm looking for specific names of 3 mechanical components from the video: Component name 1: min 0:52 from the video Component name 2: min 1:01 from the video Component name 3 (the brake): min 3:53 from the video Perhaps anyone also has a link to the 3 components? I...

I am in the middle of a problem for the Kerr geometry, I need to do the integral ##\int_{\mathcal{N}} \star J## over a null hypersurface ##\mathcal{N}## which is a subset of ##\mathcal{H}^+##, where ##J_a = -T_{ab} k^b## and the orientation on ##\mathcal{N}## is ##dv \wedge d\theta \wedge...

I have to perform a calculation on my data. Here is an example of data from just one time step (data from other time steps would appear as additional rows). X Y Z Total 2 2 1 3 Total = SQRT(X2 + Y2 + Z2). The calculation I have to do is: (N • N), where "N" is an average. I tried...

The operator is the ##T_{xyz}## component of the rank 3 tensor ##T=\vec{r}\otimes\vec{r}\otimes\vec{r}## whose Cartesian components are ##T_{ijk}=r_ir_jr_k##. This tensor ##T## also has spherical components ##T_{q}^{(k)}## where ##k=0,1,2,3##, which in principle can be related to their Cartesian...

When we overclock CPU or GPU or RAM we also have to increase the voltage to achieve stable operation (provided we have adequate cooling). Why is that?

The answer is D (60 degrees) and I understand how to get that answer. But this assumes that the new velocity's component of v/4 can form right angles with another component of the new velocity. So I'm confused whether vector components always form right angles to each other. When I searched...

I have no idea how to solve this problem. The solution says that the component parallel to the plane of separation is conserved, i am not sure why. Seems to me that in the problem was assumed a special field, but not a generic field.

It seems most people say that a vector is either contravariant or covariant. To me it seems like contra/covariance is a property of the components of a vector (with respect to some basis) and not of the vector itself. Any basis {bi} has a reciprocal basis {bi} and any vector can be expressed...

I am not completely sure what the formulas ##v_j = v^a\frac {\partial x^j} {\partial \chi^a}## and ##v^b = v^a\frac {\partial \chi^b} {\partial x^j}## mean. Is ##v_j## the j:th cartesian component of the vector ##\vec v## or could it hold for other bases as well? What does the second equation...

In which coordinate system the components of angular momentum are quantized? Better to say, if we can select the coordinate system arbitrarily, how the components of angular momentum, say z-component, are always ##L_z=m\hbar##?

The components of a vector ##v## are related in two coordinate systems via ##v'^\mu = \frac{\partial x'^\mu}{\partial x^\sigma}v^\sigma##. When evaluating this at a specific ##x'(x_0) \equiv x'_0##, how should we proceed? ##v'^\mu(x'_0) = \frac{\partial x'^\mu}{\partial...

That is, the triad forms a basis.

I'm studying 'A Most Incomprehensible Thing - Notes towards a very gentle introduction to the mathematics of relativity' by Collier, specifically the section 'More detail - contravariant vectors'. To give some background, I'm aware that basis vectors in tangent space are given by...

Good day, I have a question about breaking an atom down in it's components. For an example we have a neutral 4-helium atom. The helium atom have a nucleus which contains 2 protons and 2 neutrons. Around the nucleus of the helium atom 2 electron orbits in the k-shell (according to Bohr's...

Through my 2 analog classes and 2 electronics classes I have learned about resistors, inductors, capacitors, BJTs, Mosfets, and FETS. What are some other fundamental components that I should be taking a look at? To add to this, I don't consider gates as fundamental because they are built up from...

This is not a homework question, it is for my understanding so please do not answer this question with a question. I have found this great animated gif but it appears to be for a fixed end (notice wave inversions at the end). Has anyone seen a similar one for a free end? Many Thanks