Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
1
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2answers
37 views
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{...
4
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2answers
72 views
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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0answers
33 views
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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0answers
31 views
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
30 views
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 ...
0
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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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0answers
39 views
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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0answers
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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) Â = Ā/A
3) Ā.Ā = A^2
4) A = Ā/ Â
I think the answer includes 2 ...
0
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2answers
35 views
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 ...
2
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1answer
70 views
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-...
1
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2answers
57 views
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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2answers
67 views
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
49 views
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 ...
1
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1answer
189 views
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}...
1
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3answers
38 views
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
46 views
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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1answer
56 views
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 $T_{2x}$
$$T_{1x} ...
10
votes
4answers
722 views
0-rank tensor vs vector in 1D
What is the difference between zero-rank tensor $x$ (scalar) and vector $[x]$ in 1D?
As far as I understand tensor is anything which can be measured and different measures can be transformed into ...
1
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2answers
94 views
Why are systems in classical mechanics sets and not vector spaces?
One of my professors told me that a state in a classical system is an element of a set, while in quantum it's an element of a vector space.
From that, we combine systems in classical physics using a ...
0
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1answer
44 views
Time when two particles will meet [closed]
Particle P moves with constant speed of 13m/s always aiming at O . As P starts moving , O moves with constant velocity of 5m/s towards positive y-axis. Time taken by particle P to catch O will be?
I ...
1
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1answer
35 views
Position Vectors in Cylindrical Coordinates
So I have a query concerning position vectors and cylindrical coordinates.
In my electromagnetism text(undergrad) there's the following statements for
position vectors in cylindrical coordinates:
$$...
0
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0answers
41 views
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
92 views
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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2answers
22 views
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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3answers
88 views
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 ...
0
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1answer
86 views
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 ...
1
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1answer
28 views
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 ...
0
votes
2answers
17 views
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:$$V_x=V\cos\theta\\...
1
vote
2answers
88 views
Magnitude of the cross product of two bra-kets?
From the mathematical perspective, one can take the magnitude of a cross product:
$$
|a\times b|=|a| |b| \sin{\theta}\cdot n,
$$
where $\theta$ is the angle between a and b in the plane containing ...
0
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2answers
61 views
How does centripetal acceleration have direction/vector and magnitude while in the formula $v^2=v\cdot v$ is scalar?
$$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 ...
0
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1answer
45 views
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 ...
0
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0answers
35 views
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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2answers
48 views
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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2answers
45 views
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 ...
0
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1answer
45 views
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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2answers
64 views
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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2answers
27 views
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 ...
0
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1answer
36 views
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 $\...
1
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2answers
31 views
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
55 views
Vectors (with reference to a pendulum)
Why is the acceleration of a pendulum non-zero at its lowest point?
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1answer
48 views
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,...
0
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0answers
32 views
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 ...
0
votes
1answer
45 views
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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0answers
97 views
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
1k views
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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2answers
63 views
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$$ and why there's a negative sign?
If the gravitational force always acting in the same ...
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1answer
112 views
Transformation of $4-$velocity
Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$.
$$* * *$$
A quantity, to be ...
1
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0answers
52 views
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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2answers
48 views
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-...
