Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
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Multiplying a force vector by rotated unit vector produces strange results [closed]
I'm by no means an expert in math, what I'm trying to do is to Isolate a force aligned with a vehicle in a game (specifically to do a directional friction).
the equation is simple I take a vector $v_1$...
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To find out if 3 vectors are coplanar or not [migrated]
3 vectors A,B and C are given. We have to find out if they are coplanar. I have been taught to find the cross product of any two of the 3 vector like B×C. This cross product will be perpendicular to ...
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Is there a spacetime vector projection representation for the wave function? [closed]
Is it possible to represent the wave function as a spacetime vector projection?
In QM, the inner product of the wave function is given by $\langle \Psi | \Psi \rangle$.
Is it possible to have a "...
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On which side of object should friction force be drawn on a vector diagram?
Let's say a box is moving to the right and friction is slowing it down. The friction force vector pointing to the left and the object moving to the right, should the vector be drawn on the left side ...
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Boat-river problem [closed]
A river flows from east to west at 4 km/hr. From the north bank of the river, the first boat starts traveling straight towards the other bank at a speed of 10 km/h. The second boat starts moving along ...
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Combing different SHMs which are in the same direction
Our teacher taught us this method for combining different SHMs he didn't really give a lot of formal defination etc he just said us about the algorithm to solve it as shown in the picture what seemed ...
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Why are 2D inertia tensors $2\times 2$ matrices when 2D objects can only rotate around one axis?
Why is the 2D inertia matrix defined as
$$\begin{bmatrix}I_{xx}&I_{xy}\\I_{yx}&I_{yy}\end{bmatrix}$$
and not just a vector 2 or scalar? I saw something saying that $I_{xx}$ is the moment of ...
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From where does the expression of the tangential accerelation come from?
I've seen so many times that the expression of the tangential acceleration is known to be: $$a_t=\ddot{s}$$ but from the expression of the acceleration in spherical coordinates, in the tangential ...
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Symmetry of Crystalline Lattice
In the book Solid State Physics by Kittel, it is written in Bravais Lattice's definition that "the arrangement of atoms in the crystal looks the same when viewed from the point r as when viewed ...
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Tensor to vector notation [closed]
I have the expression
$$ \partial_{k} \left( a^{-1} b^{2} \eta^{j k} \partial_{j} G \right) = a \vec{\nabla} . \left( a^{-2} b^{2} \vec{\nabla} G \right) $$
Is the transition from tensor to vector ...
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Why does force perpendicular to the velocity change only its direction; not the speed?
While analyzing the case of a force and consequently an acceleration acting perpendicular to the velocity of a given body, I do understand that force's component along the velocity will be 0 causing ...
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Teacher told us we're not allowed to write negative vectors, is this correct or not?
The question is a bit vague, so I apologize for that.
To properly explain what I mean, I'll use an example.
Let's say we've got two forces going left and right. $F_1$ is $20 \, \text{N}$, and will be ...
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Integral expression for the wave vector in Landau's collision integral
I am trying to understand a derivation presented in a lecture note on plasma physics (Landau's collision integral) regarding the wave vector $\mathbf{k}$:
$$ \int \frac{d\mathbf{k}}{(2\pi)^{3}}\frac{\...
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Why are the mechanics of different axes independent of each other?
Why are the mechanics of different axes independent of each other ?
Even though the question might seem absurd, but that is how physics works, is'nt it.
While solving projectile motion, why does the ...
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Definition of four-velocity: why define it with proper time of the object?
The four-velocity(world-velocty) is defined by : $u^μ=\frac{dx^μ}{dτ}$ ,where $τ$ is the proper time of the object.
I don't understand why it's defined with respect to the proper time but not the time ...
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How do you represent a plane wave propagating at an angle $\theta$ w.r.t. $z$-axis? [closed]
There is a plane wave $\exp(i\mathbf{k}\cdot\mathbf{r}-i\omega t)$, where $\mathbf{k}$ is the wave vector. Suppose this wave propagates at an angle $\theta$ w.r.t. $z$-axis. What will be the wave ...
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Why does $\delta \vec{r} = \delta \vec{ \theta} \times \vec{r}$?
Hello fellow physicists,
I was trying to understand some behavior on rotating objects, specifically about the formula $\vec{v} = \vec{\omega} \times \vec{r}$.
The Book (Marion, J. B. (1965). Classical ...
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Implicit assumption behind the definition of scalar, vector, and tensor fields
Let me consider a field
\begin{align}
A^\mu(x) \equiv dx^\mu,
\end{align}
which seems to be a vector field trivially.
However, to check that, we calculate as
\begin{align}
A'^\mu(x') \equiv dx'^\mu = \...
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Contradicting Basic and Force definitions of types of Equilibrium
This question is neither a check my work question and nor a homework question, it is a conceptual doubt in a question I found and I have attached a solution just for reference to show how I drew my ...
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Find the component form, magnitude, and angle of forces
Two teenagers are pulling on ropes attached to a tree. The angle between the ropes is 30.0°30.0° . David pulls with a force of 400.0 N and Stephanie pulls with a force of 300.0 N.
(a) Find the ...
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How to prove that, if $A$ and $B$ are vectors, then their cross product is still a vector? [closed]
in my course of special relativity we are introducing tensors: however, before doing that, my professor sort of re-defined vectors saying that in a 3D euclidean space, $A$ can be called a vector if, ...
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Conceptual difference between ket and bra vectors in layman's terms
From the relation $\langle a|b \rangle = \langle b|a \rangle ^*$ it can be seen that we can get same inner product by "swapping vectors" in Hilbert space and taking complex conjugate of the ...
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Is $u^{\mu} = \gamma\tfrac{dx^{\mu}}{dt}$ a 4-vector?
I understand that $c\dfrac{dx^{\mu}}{ds}$ is a 4-vector since $ds$ is a scalar. In flat space-time,
$$
ds = c\dfrac{dt}{\gamma}
$$
so $\gamma\dfrac{dx^{\mu}}{dt}$ would be a 4-vector as it is equal to ...
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Direction of a force (action-reaction forces) problem
I had an AP Physics 2 questions that says during the collision, the molecule exerts a force with magnitude F on the wall, and then asks what properly describes the force acting on the wall. The answer ...
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Proof via vector algebra that kinetic energy remains constant when a force acts perpedicularly to velocity [closed]
Given:
Initial speed $$v_{\text{initial}} = k \space \text{m/s}$$ in the positive x-direction $$\hat{i}$$
Applied force $$\mathbf{F} = n \, \text{N} $$ in the positive y-direction $$\hat{j}$$
$$ Mass ...
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Help with dispersion relations for EM waves in anisotropic dielectric materials
I am really struggling to understand the following dispersion relations which we derived in class.
For an electric field in the z-direction, we have:
$$k^2_x + k^2_y = \frac{\omega^2}{c^2}n_z^2\tag{1}$...
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Conceptual question on Force decomposition
I would like to know how to interpret the following force decomposition (Diagram (2)).
Diagram (1) is the typical force decomposition. Decomposing the force vector this way tells us about how much ...
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Four-gradient notation for Lagrangian density
In the four-gradient notation, if $\mathcal{L(\phi, \partial_\mu\phi)}$ is a Lagrangian density, what is it $\partial_\mu \mathcal{L}$? Is it a vector $(\frac{1}{c}\frac{\partial \mathcal{L}}{\partial ...
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When there are both force and gravity, what is the direction of frictional force?
The force $F$ is to the right and the gravitational force is to the left. Then what is the direction of frictional force? Should it be opposite of gravity or acting force?
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Why isn't the scalar field a covector?
A one-form (or covector) maps a vector space to its field of scalars.
A scalar field maps any position of spacetime into a scalar.
Given that the 4-position is a vector, can we say that the map of the ...
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Rotating pauli matrices along an axis
In my research, I am working with Pauli matrices along a unit-vector $\mathbf{n}$. I need to find a general form of an axis of rotation and angles for a generic vector $\mathbf{n}=(n^x, n^y, n^z)$ ...
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Proportional null vectors [closed]
the past few days I've been studying special relativity and was just now making some exercices on it. One exercice was the following:
Let $U$ and $V$ be two null vector is a $d$-dimensional Minkowski ...
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Difference in spin angular momentum
In chemistry, I learnt that the spin angular moment of a single unpaired electron in an atom can be calculated by
$\frac{\sqrt{3} h} {4\pi}$,
but while studying radioactivity, I studied that the spin ...
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How do we solve polar coordinates related questions?
A particle is subjected to a radial force: $\vec{F}=f(\vec{|r|}) \hat{e_r}$.
How do we show that $\vec{F}×\vec{L}=-mf(r)[-\vec{r}\dot r+r \dot {\vec{r}}]$
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What is the tension on a string with unbalanced forces on each side?
If a string is pulling on an object of mass $M_1$ with force $F_1$, and the other side is pulling an object of mass $M_2$ with force $F_2$, what is the tension in the rope?
Intuitively, it makes sense ...
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Relativistic Velocity-addition formula adds a scalar to a vector?
Sorry if this is a stupid question.
The formula for relativistic Velocity-addition is
$u = (v + u') / (1 + (vu'/c^2))$
It seems that v, v', u, and u' are vectors, while c is a scalar.
But 1 seems to ...
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Problematic conversion of phasor form of field in electromagnetic wave equation
Edit (answer)
Although I do not have enough reputation to post a formal answer to the question, thanks to Mike Stone and Triatticus (see comments below), it became apparent that the issue was with ...
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Why does $\vec{r}\cdot\dot{\vec{r}}=r\dot{r}$?
Why is $$\vec{r}\cdot\dot{\vec{r}}=r\dot {r}$$ true? Before saying anything, I have seen the proofs using spherical coordinates for $$\dot{\vec {r}}= \dot{r}\vec{u_r}+r\dot{\theta}\vec{u_\theta}+r\sin\...
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Question about velocities in different reference frames
Suppose $\hat{x^{'}}, \hat{y^{'}}, \hat{z^{'}} $ are the unit vectors of an inertial frame and $\hat{x}, \hat{y}, \hat{z} $ are the unit vectors of a frame which maybe accelerating, rotating, whatever....
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Doubt in fictitious forces chapter in Morin
The question is this -
I know 2 is what the non-inertial frame measures, but isn't $\frac{d\mathbf{A}}{dt}$ the real thing, the physical thing? And you can write that too in terms of the unit vectors ...
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Transformations that preserve the metric [duplicate]
I know that transformations that preserve the metric (like the Lorentz transformation, or rotations) have the property:
$$S^T \eta S = \eta$$
However, I'm getting: $S^TS = I$ and I'm not sure why:
$$\...
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Is $Fx = Fcosθ$ or $Fx = Fsinθ$? [closed]
Sorry for the stupid question, but I've learned that Fx = Fsinθ. But then I've seen in the internet some websites saying that it was actually Fx = Fsinθ, and others saying it was Fx = Fcosθ. What ...
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Doubt about product of four-vectors and Minkowski metric [closed]
Given the Minkowski metric $\eta_{\mu\nu}$
And $\eta^{\mu\nu}\eta_{\mu\nu}$=4
I can write $\eta^{\mu\nu}\eta_{\mu\nu}k^{\mu}k^{\nu}$=$4k^{\mu}k^{\nu}$
But $\eta^{\mu\nu}\eta_{\mu\nu}k^{\mu}k^{\nu}$=$\...
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How is the angular velocity tensor defined?
Assume we have a position vector $\mathbf r$ dictating the position of a particle in a rotating frame. Then, for a time dependent rotation matrix $\mathbf R(t)\in SO(3)$ that describes the motion of ...
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The direction of net force in circular motion
The small ball attached by a thin string is in uniform circular motion as shown in the picture (vertical plane). There are two forces acting on the ball, Gravitational force $F_g$ and Tension force ...
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Constant vector in changing basis
If the unit vectors in the cylindrical coordinate system are functions of position, then how can I get a constant vector?
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Derivation of equations of motion using vectors
I was trying to draw the motion of a point mass given an initial position, velocity and constant acceleration. I figured that the change in position $\Delta \vec{r}$ over an interval $\Delta t$ would ...
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How can you determine direction of spin-1/2 states?
How do you determine the direction of the state of a spin-1/2 particle? For instance, given the quantum state $|\psi\rangle=(1,0)$, where does this vector point in space? I would say that it points in ...
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On the isomorphism between directed line segments and "abstract vectors" (Gregory Classical Mechanics)
I have just begun reading Gregory's Classical Mechanics and, amazingly, he has blown my mind in the first chapter discussing nothing more than measly old vector algebra. Fascinating that Gregory was ...
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In general relativity, how to get geometric velocity from 4-vector velocity field?
Currently, I‘m listening to the lecture of Prof. Hughes (https://ocw.mit.edu/courses/8-962-general-relativity-spring-2020/video_galleries/video-lectures/).
In General, I‘m able to follow the lecture, ...
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