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Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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Covariant surface vector

On pg 74 of Dalarsson's Tensors, Relativity and Cosmology (The Integral theorems for tensor field chapter), the covariant surface vector was defined as: $$dS_k=\frac{1}{2}\epsilon_{kmn}dx^mdx^n=\frac{...
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There are two velocities on the sphere. How to sum them on the sphere?

As shown in the figure, there are two velocities on the sphere, one is the velocity along the meridian direction, the arc length is its size, the other is the velocity along the equatorial direction, ...
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Rain Car problem [on hold]

Rain falls with a speed of $10√2$ m/s. It makes 45° with vertical and 45° with a line drawn towards the north. Find the velocity with which car has to travel in the east direction so that for a person ...
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What is an axial and polar vector?

Can someone please explain this type of vector to me, I can not understand it. Axial vectors have an inner orientation, i.e. the direction of the vector indicates the positive orientation. For ...
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1answer
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Why the lens is pushed to the right after light goes through?

I am asking myself why the lens must be pushed to the right in the following scenario: (image coming from Atoms and Sporks' nice video https://www.youtube.com/watch?v=UAmdoOX3870&t=327s) This can ...
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1answer
31 views

Centripetal Force Static Friction

I understand that when a car is turning, it is using static friction to do so. The wheel is turned where the perpendicular component of the wheel is opposing the direction of motion, creating a force ...
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Transformation of Vectors

let $\Psi \in V$ be a vector and we have the action of a lorentz transformation on the object $\sigma_2 \Psi $. And $\sigma_2 \Psi $ is then in V as well. V is "Weyl or Dirac space". And the lorentz ...
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The vector A has magnitude [closed]

A vector Ā has magnitude A and  is a unit vector in the direction of Ā , then which of the following are correct: 1) Ā. = A 2)  = Ā/A 3) Ā.Ā = A^2 4) A = Ā/  I think the answer includes 2 ...
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When calculating centripetal force, do we ignore non-radial or tangential forces

Suppose an object moving in circular motion in the vertical plane (ie such that gravity points directly downwards) around a central point attached by a string; the object is constantly accelerating as ...
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1answer
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Can two physical vectors form a physical cross product if they are physically separated?

I would say that they can't create a cross product. If they can create a cross product, which seems to be the case from the comments below and answer, then is that cross product consider local or non-...
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Why the electric field of an infinity line is dependent on distance? [duplicate]

A very common question about Gauss law is being asked in schools or Internet: Why the electric field of an infinite plane is independent on distance? Actually I was one of who asked this ...
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1answer
50 views

Definition of Vector

In a book on General Relativity that I am reading, it defines a vector as an object or array of numbers that transforms like a vector (under rotations). I understand that under rotation $\theta$, a ...
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What qualifies a set of operators as a “vector operator” in QM?

In quantum mechanics, there are many vector operators like position, momentum, all the types of angular momentum, etc. In Binney's QM book, he often references vector operators and scalar operators. ...
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4answers
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Why is the centripetal net force always to the center?

I recently came across this diagram in my physics textbook I got a bit confused by this diagram. I thought that the reason why the object accelerates towards the center is because of a net force, not ...
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1answer
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Physical significance of one-form in a velocity field

Still tentatively feeling my way through this stuff, so please go easy. The velocity of a fluid at a point P are the components $V^{a}$ of a contravariant vector:$$v^{x},v^{y},v^{z}\equiv\frac{dx}{dt}...
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Magnetic flux (and flux in general)

The general interpretation of flux as I understand it (and please correct me if I'm wrong) is that it represents how much something is going through another (surface or volume (and perhaps lines?)), I'...
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1answer
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Minimum separation between two bodies [closed]

Let Bodies A and B be kept at two points in the x-y plane. They are allowed to move in the x-y plane. Suppose the velocity of B is constant, and the speed of body A is fixed, how must the body A ...
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5.61b University physics with modern physics [closed]

$$ \sum F_{y} = 0 $$ $$ \sum F_{y} = T_{1y} + T_{2y} - mg $$ $$ mg = (4400N)\sin{60} + (4400N)\sin{40} $$ $$ mg = 6640N $$ Why is this wrong? solution $T_{1x}$ has to be equal to $T_{2x}$ $$T_{1x} ...
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0-rank tensor vs vector in 1D

What is the difference between zero-rank tensor $x$ (scalar) and vector $[x]$ in 1D? As far as I understand tensor is anything which can be measured and different measures can be transformed into ...
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2answers
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Why are systems in classical mechanics sets and not vector spaces?

One of my professors told me that a state in a classical system is an element of a set, while in quantum it's an element of a vector space. From that, we combine systems in classical physics using a ...
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1answer
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Time when two particles will meet [closed]

Particle P moves with constant speed of 13m/s always aiming at O . As P starts moving , O moves with constant velocity of 5m/s towards positive y-axis. Time taken by particle P to catch O will be? I ...
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Position Vectors in Cylindrical Coordinates

So I have a query concerning position vectors and cylindrical coordinates. In my electromagnetism text(undergrad) there's the following statements for position vectors in cylindrical coordinates: $$...
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Name of real-valued representation of density matrix?

This is a specialization of my question https://math.stackexchange.com/q/3157300/ on math.SE. There are many ways to write the density matrix $\hat \rho$ as vector $\vec \rho$. In the Liouville space,...
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4answers
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How to resolve velocity components?

In the arrangement shown in the figure, the ends P and Q of an inextensible string move downwards with uniform speed $u$, pulleys A and B are fixed. With what speed does the mass M move upwards? My ...
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element of surface area versus vector element of surface area

In the context of calculating electric flux, is there a difference between element of surface area versus vector element of surface area? Thanks
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What makes displacement a vector?

Displacements are vectors because they add like vectors is the answer. It is also an experimental fact. Though rotations are displacements but not vectors. Is there any more fundamental or intuitive ...
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1answer
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Can you apply product rule to arg of a bra-ket?

I found the following expression in a paper: $$ \frac{d}{dt}\arg\langle\phi_+|\dot{\phi_-}\rangle $$ where the $\arg$ term is the argument of the complex number given by inner product between two ...
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1answer
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Signs in relative vector addition

So I know the formula for relative vector addition is $$w = \frac{v-u}{1-\frac{uv}{c^2}}.$$ How do I chose when to use this formula or its inverse transformation for solving vector addition problems ...
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2answers
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Aerodynamic Force Decomposition

We know that aerodynamic drag is proportional to the square of the velocity of the incoming flow: $$D=kV^2.$$ If I decompose velocity into arbitrary orthogonal $x$-$y$ directions:$$V_x=V\cos\theta\\...
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2answers
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Magnitude of the cross product of two bra-kets?

From the mathematical perspective, one can take the magnitude of a cross product: $$ |a\times b|=|a| |b| \sin{\theta}\cdot n, $$ where $\theta$ is the angle between a and b in the plane containing ...
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2answers
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How does centripetal acceleration have direction/vector and magnitude while in the formula $v^2=v\cdot v$ is scalar?

$$a_c=v^2/r$$ 1. How does centripetal acceleration have direction or vector while in the formula dot product between velocity vector is scalar (as in kinetic energy)? Radius is scalar quantity. What ...
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1answer
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How do I know whether members are in tension or compression when using Method of Sections?

So we started doing structural analysis in my engineering class lately, and are doing trusses. However, I'm not quite sure how method of sections works conceptually. I'm getting the right numbers, but ...
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Why is current-density a vector? [duplicate]

I was told that current has a direction but does not follow vector-laws, so it is a scalar quantity. That's okay. I thought it through Kirchoff's junction law: assume two currents joining at 90 deg, ...
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What is the difference between velocity and speed? [duplicate]

What is the difference between velocity and speed? could anyone describe it more specific? does velocity have direction?
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Different results when using generalized coordinates?

I'm solving an imaginary double pendulum (that is, two pendulums whose motion doesn't affect each other). The two pendulums have a "normal" motion, but they are attached. Taking the point to wich the ...
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1answer
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Four momentum squared and collisions

So, I am not asking is the square of four-momentum of a particle an invariant to Lorentz trasnformations, but rather,is it invariant in dynamic situations? It seems to me that this also has to hold. ...
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Why don't the electric field vectors cancel each other out in a non-conducting infinite plane sheet?

Why do these vectors not cancel each other out in spite of their being in the opposite directions?
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What is meant by 'The components of a force along a given axis'

I'm new to mechanics, and I'm having trouble interpreting what this means. So there's a force, okay. Then it has its components on the xyz axis, okay. But what does it mean by along a given axis, I ...
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1answer
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What does the notation of the subscript behind the brackets in the differential mean?

From "Theoretical Mechanics of Particles and Continua" by A. Fetter and J. Walecka. As emphasized in the preceding section, the general expression $(7.11)$ can be applied to the coordinate vector $\...
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2answers
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How do I determine the components of a cinematic jump, for vertical and horizontal velocity?

I have been tasked with determining the feasibility of The Rock's jump in the movie 'Skyscraper' I am using projectile motion equations to determine it, but have gotten stuck whilst calculating my ...
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1answer
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Vectors (with reference to a pendulum)

Why is the acceleration of a pendulum non-zero at its lowest point?
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What does the “$T$” superscript mean on vector?

My relativity book defines the "worldline" of a system as: \begin{equation} x(\tau)=(x^0(\tau),x^1(\tau),x^2(\tau),x^3(\tau))^T \end{equation} I often see velocities written in the same form: $U=(0,...
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Torque/Cross Product [duplicate]

Ok! My question is, what is the physical meaning of the vector produced by a cross product? For instance, in torque, what does the cross product’s resultant vector mean? What does it tell me about ...
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1answer
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Downward force applied on a wedge

If a vertical (downward) force is applied on a wedge (on the sloping surface) then what would be its component in horizontal direction? It should be zero as the angle between them is 90 degrees. But ...
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Angular velocity of rigidly rotating orbit in 3D

Consider a circle in 3-dimensional space. On this circular orbit, a rigid bead moves, thus changing its angle $\phi$ with a reference radius on the circle. The intrinsic angular velocity is given by ...
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3answers
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When does a vector component keep being a vector, exactly?

English is not my native language, so please forgive my errors. Consider this example: This is a classic: an exercise requiring you to calculate the electric field produced by a charged ring on its ...
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A few questions on Gravity [closed]

What role does the unit vector $ \mathbf{e}_r $ play in $$ \mathbf{F} = - G \dfrac{Mm}{r^2} \mathbf{e}_r$$ and why there's a negative sign? If the gravitational force always acting in the same ...
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1answer
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Transformation of $4-$velocity

Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$. $$* * *$$ A quantity, to be ...
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Does the proper four-acceleration $A^{\mu} = (0,0)?$

Let the proper four-position vector $x^{\mu}(\tau) = (0, \tau)$. Differentiating this successively wrt $\tau$ I get the four-velocity $u^{\mu}(\tau) = (0, 1)$ and then the four-acceleration $A^{\mu}(\...
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Can the world line of a particle be successively differentiated to any order to always give a four-vector?

Starting with the world line of a particle given by $x^{\mu}$, this can be successively differentiated with the particle's proper time $\tau$ to give the four-velocity from the four-position, four-...