Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
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How do vectors accurately predict the outcomes?
In the beginning of every physics class in school, we learn vectors.
And, then learn their algebra.
Then start using them, as we do with a lot other math branches, in physics.
We say that the force is ...
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Time derivative of a "general" vector $\vec A$ in an accelerating frame: what about e.g. velocity $\vec v$?
According to Morin "Classical Mechanics" (Section 10.1, page 459), the derivative of a general vector $\vec A$ in an accelerating frame may be given as
$$\frac{d\vec A}{dt}=\frac{\delta \vec ...
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Magnetohydrodynamic Walens Equation [closed]
How to derive Walens Equation from Continuity Equation and Induction Equation.
Continuity Equation:
$\frac{d \rho}{dt} + \rho \nabla.v + v.\nabla\rho=0$
Induction Equation:
$\frac{dB}{dt}= -B(\nabla.v)...
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Understanding velocity as a vector quantity [closed]
Why is velocity classified as a vector quantity. Can it be explained by the same way as force referring to the Phys.SE post Where am I confused about force addition?
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Polar coordinates: Orthonormal basis
In polar coordinates we have $r= c(\hat{r})$, where $c$ is the distance of a point from origin, and $r$ is the position vector.
So, what is the use of $\hat{\theta}$ especially given that it is always ...
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Relation between vector of force and energy [duplicate]
According to the diagram, we know that if we apply a respectively force of 3N and 4N in the relative direction, then the resultant force will be 5N on its direction. But it's that means some of the ...
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Linearization of momentum equation of MHD equations
The momentum equation of the MHD equations is as follows
$$\rho \left(\frac{\partial \mathbf{v}}{\partial t} + (\mathbf{v} \cdot \nabla) \mathbf{v}\right) = -\nabla p + \frac{1}{\mu_0} (\nabla \times \...
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Applications of time derivative of unit vector
A math methods textbook I'm currently reading went into great detail deriving the following expression for the time derivative of a generic unit vector $\hat{r}$.
$$
\frac{d\hat{r}}{dt} = \frac{1}{r^2}...
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Stationary Obversers in Brinkmann Coordinates
The four-velocity of a stationary observer is defined as $U^{u}$ = $\left (\dot{t},0,0,0 \right )$, where t is the time coordinate in some four-dimensional coordinate system, and overdot represents ...
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Normal Contact Force
I've been introduced to the normal contact force and have been told that it acts in a direction which is perpendicular to the contact surface.
What I'm confused about is how do we define a normal to a ...
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Book Recommendation: One that has a lot of problems and theory associated with polar coordinates and spherical polar coordinates [closed]
I would like to "master" polar coordinates and spherical polar coordinates. In the sense, I would like to become as well versed with them as I am with cartesian coordinates.
I have gone ...
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Why is it wrong to find centripetal acceleration using change of velocity over change of time?
This question asks to find the centripetal acceleration by giving the initial and final velocity over the change of time.
As shown, my book combined two rules to find the acceleration. I utterly ...
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Convention or reality?
In case of a disc rotating about an axis perpendicular to its plane passing through its centre of mass, the torque vector points up or down depending upon direction of rotation. Is it just convention, ...
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How to get the coordinates for rotated axes?
I'm quoting from the Feynman Lectures:
"Assume that Moe’s axes have rotated relative to Joe’s by an angle θ. The two coordinate systems are shown in Fig. 11-2, which is restricted to two ...
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classically is there any application of vector that can not be solved by geometric or algebraic concepts
I am trying to find the classical application of vector where the problem can be solved only by vector multiplication concept and not by any other geometric or algebraic method.
for example: volume of ...
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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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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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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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