# Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

117 questions with no upvoted or accepted answers
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### 3-force in General Relativity

Lets consider definition of 3-force in different theories: Newtonian mechnics In Newtonian mechnics we can define the force as a cause of changing momentum $p=m\vec{v}$ with time. According to the ...
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### Variables in calculation of drag coefficient

Okay, so I looked up drag force equation, and I found that the equation involved the drag coefficient. Then I looked up the drag coefficient, and the equation for it involved the drag force. ...
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### Connection between contra-/covariant vectors in SR and complex numbers?

If we take a spacetime with one spatial dimension, we can write a vector as $A^\mu=(t, x)$. This is a contravariant vector, and we can calculate the covariant vector by multiplying it with the ...
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### New way to compensate for gyroscopic drift

Let us assume two points in 3D space and we only care about their orientation, no velocity, position or acceleration. Now connect those two points with a rigid body of certain length, so that the ...
138 views

### Acceleration vector of tipping object (robot)

I am about to develop a simulation application of a robot. For that reason, I would need to calculate the acceleration of the robot (centre of mass) when its centre of mass exceeds its feet (ie it ...
659 views

### “Hypersurface orthogonal” component of covariant derivative of normal vector

I believe that answer to my question is rather trivial but I can't seem to get my head around it. In the context of the ADM formulation of gravity (or any other differential geometry context, I guess) ...
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If a car is moving on a banked frictionless road one of the component of normal reaction force acts as the centripetal force required for the turn. But normal reaction force is a reaction force. ...
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### Definition of velocity in classical mechanics

Let $(r_1,r_2,r_3)$ be the coordinates of a particle $r$ in the coordinate system $\phi$. Let $\{\hat{e_1},\hat{e_2},\hat{e_3}\}$ be the coordinate basis of $\phi$. Why do we define the velocity $v$ ...
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### Cross product of vectors

I am unable to comprehend the following lines given in page 657 of Shankar's Principles of Quantum mechanics: One tricky point: The cross product is defined to be orthogonal to the vectors in the ...
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### How Newton's laws replicate themselves on a larger scale?

Now I was reading The Feynman Lectures on Physics and found this which I found somewhat peculiar and deep and thus want your assistance here. So here it goes: The theorem concerning the motion of ...
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### Constraints on the factorization of a unit quaternion rotation operator

In Jack B. Kuipers' Quaternions and Rotation Sequences page 194-195, section 8.7.1 explains how to decompose a tracking sequence quaternion $q = q_0 + \vec{i}q_1+\vec{j}q_2+\vec{k}q_3$ into two other ...
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### What are the freedom of breaking vectors into it's components?

I came across some problems in which the way I broke vectors into it's components didn't gave me answer. Here are few of them: Above mass $m$ is hanging with spring as shown, they broke $T$ in ...
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### How to calculate acceleration vector of a moving object to intercept a stationary object

The short version: I'm moving on a certain straight-line trajectory (two dimensions only, thank goodness), and I want to intercept a stationary object, with constraints on maximum acceleration and ...
534 views

### Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
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### Difference between vacuum and pseudovacuum vector?

What exactly is the difference between the vacuum and pseudovacuum vector? In my case the ground state of a system is the vacuum vector and by letting operators act on that vacuum vector magnons are ...
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### Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
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### Surface normal on the earth to the sun at a given point in time

How complicated is it to calculate a surface normal on the spherical approximation of the earths surface pointing towards the sun at a given point in time? What I try do is to highlight a small area ...
25 views

### How to solve 3-variable planar vector equilibrium problems?

While it's quite straightforward to solve problems with multiple planar vectors in equilibrium for 2 variables, I'm having issues with those where I'm asked to minimize or maximize a variable along ...
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### Physical meaning of Vector Calculus Corollaries

The divergence theorem and the Stokes theorem have well known physical interpretations. For example, the divergence theorem merely states that the amount that a vector flows out through a closed ...
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### superposition at pi/4 phase-offset of elliptically polarised light

in an earlier question, i asked if elliptically-polarised light could be superimposed in a way that allowed the vector(s) E (the jones vectors) to make sense: superposition of elliptically polarised ...
490 views

### How to calculate angular velocity about a second axis?

A point in space at $(a,b)$ revolves around the origin with an angular velocity omega. I wish to compute its angular velocity about a second axis, running parallel to the $z$ axis at point $(x,y)$. ...
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### validity of “law of vector addition of current elements”

In several articles and books, I have read that "the magnetic force on or due to a small element of a circuit is equivalent to two or more of its component elements, provided that the current remains ...
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### Electromagnetism Current Equation

In my book(Field and Wave Electromagnetics), it says that $\Delta I= \Delta Q / \Delta t = \vec J \cdot \Delta \vec s$. My understanding is that $\Delta$ can be replaced by $d$ which represents the ...
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### Vector Derivative: General Case

From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector". In this section, towards the end, ...
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### Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
132 views

### Calculus/Vector Calculus and so on in special relativity book recommandation

I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...
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### What does 'vector-like' mean?

What are properties of vector-like field/particle? What's the counterpart of it? Chiral like?
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### Why is the angular average of the direction of the momentum squared a third instead of one?

In the article http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf (in going from eq. (6.13) to eq. (6.14)) it is stated that \langle\hat{p}\cdot\hat{p}\rangle_{\hat{p}}=\dfrac{1}{3}...
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### A way to determine if a body accelerates or loses speed at a certain time

With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval? Can this be determined, for instance, by simply observing ...
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### What is a diffusionless fluid?

I'm taking a course in astrophysical fluid dynamics and have come across a problem involving "small diffusionless disturbances" of a fluid. Based on the nature of the course I expect the examiner to ...
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### How do I show $e_r$ and its first- and second time derivative?

What does a charge q moving in a circular orbit with a constant velocity (a "rotating charge") and a stationary observer that measures the E field look like? And how do I show $e_r$ and its first- and ...
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### Laboratory fixed-vector components

What are laboratory fixed-vector components? I have an effective Hamiltonian derived from a 40-something year-old Chemical Physics paper. The article mentions the term laboratory fixed-vector ...
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### Speed with wind resistance

This is probably a basic question, but it has been a while since I did anything like this. If a boat is sailing forward at speed $x$ and the direction of the wind, with magnitude $y$, is either equal, ...
Trying to understand how the unit vector ${\mathcal{\hat{r}}}$ defined as $\frac{r' - r}{|r' - r|}$ (where $r'$ is the source point) works in this problem: Work out the electric field, $E$, at point ...
Basically I have a set of vectors of unit length, $\{\nu_i\}$, describing the movement of phonons (all orthogonal to each other), $\{\omega_i\}$. Lets say I only have two atoms, $m_1$ and $m_2$. In ...