# Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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### What is a Tensor, intuitively?

Before reporting this a duplicate, this post explains the computations of tensors nicely, but I still have questions regarding why they are needed. Also, what makes a tensor actually tensor? The way ...
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### Necessary and sufficient conditions for periodic motion

Let us fix a reference frame $S$ with origin in $O$ in the euclidean space $\Bbb R^3$, then let us also define a periodic motion in the following manner: A motion is periodic if and only if the time-...
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### Three perpendicular vectors, one has unknown directional cosines [closed]

I need help figuring out this textbook excersise. I know the relations: $$\hat{a} \cdot \hat{c} = 0$$ $$\hat{b} \cdot \hat{c} = 0$$ and $$\alpha{}^2 + \beta{}^2 + \gamma{}^2= 1$$ but am still a bit ...
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### What direction should i exactly put for negative displacements?

If I have A....p....B....d....C points If I am initially on B and walk towards c, it's a positive displacement. Example: BC=10m east and then all of sudden I change my vector and walk to d. Is ...
1 vote
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### Change in kinetic energy when force is perpendicular to velocity

I am a high school student and a have a fundamental doubt. It is said that when force is applied perpendicular to velocity, there is no change in kinetic energy since there is no change in speed. For ...
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### How to remember which way the magnetic field goes?

For the case of a current in a wire, we learn the direction of the associated magnetic field by learning the right hand rule. But what about a bar magnet and the names 'north' and 'south' for the ends ...
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### Doubt regarding simplification of Lense-Thirring precession frequency formula

The standard result for Lense-Thirring precession frequency in the weak-field approximation is given by $$\vec{\Omega}_{LT}=\frac{1}{r^3}[3(\vec{J}\cdot\hat{r})\hat{r}-\vec{J}].$$ I am trying to ...
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### In an $n$ particle system, why is the Hamiltonian summed over $n$?

Suppose I am working in a system consisting of $n$ particles. Thus the phase space will be $\mathbb{R}^{6n}$, and both the momentum and position space will be $\mathbb{R}^{3n}$ each. Then, for some ...
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### Velocity of points in a rigid body

I'm trying to derive the following statement: Let $\mathcal{B}$ be a rigid body. Then there is an unique vector $\vec{\omega}$ such that for every pair of points $P,Q\in \mathcal{B}$ the following ...
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### Clarifications on proving lightlike vectors must be orthogonal with themselves

I'm trying to prove that lightlike vectors in Minkowski space must be orthogonal to themselves, and I have two questions about this. I tried two different approaches: If lightlike, $ds^2=0$ By ...
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### Abstract definition of four-vector

It is a long time that I am looking for an abstract definition of four-vectors. This is the definition that I have reach to so far: A four-vector is an element of the representation space of the ...
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### How can I see the Calculation process of the skyrmion number?

I'm having a problem calculating a skyrmion number. below equations are from Wikipedia - Magnetic skyrmion I know that I should use the chain rule with the polar, spherical coordinate system. But I ...
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### Why do coordinates have to be inverted to form a dual basis?

I am reading Guidry's Modern General Relativity, and there is a definition for dual basis vectors that are as follows: If we have three coordinates $x(u,v,w)$, $y(u,v,w)$, and $z(u,v,w)$ where we ...
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### How time-like unit four-vector is tangent to the observer's world-line?

I just have started studying special relativity and moving to general relativity Special relativity only deals with inertial frame (non accelerated frame) but there are no inertial frame in the curved ...
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### Do we have to use the metric constructed from the tangent basis to form a line element?

I'm working through Guidry's Modern General Relativity, and there is a problem where it asks to construct the metric using the tangent and dual basis vectors provided. I have done this, and my metrics ...
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### Simple difference between module of velocity and time derivative of module of position [duplicate]

What is the conceptually difference between the two: $$\frac{d|\vec{r}|}{dt}=\frac{\vec{r}\cdot\frac{d\vec{r}}{dt}}{|\vec{r}|}\neq|\dot{\vec{r}}|\equiv \bigg|\frac{d\vec{r}}{dt}\bigg|$$ ...
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### Which force should I break into components?

One really common problem in almost all physics textbooks is that of the wedge. So let us say that a block is resting on a wedge that is inclined at angle x from the horizontal. The block has mass mg. ...
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### Which of these is the beta factor in special relativity? [closed]

Obviously, $\beta=v/c$. But in this case, I'm not too sure what $v$ represents. I've mostly done 1-D special relativity and therefore it is pretty clear in those cases. However say there are two ...
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### Vector form of centrepetal force

We know the centripetal force $F_c$ had magnitude $m\omega^2r$. But let's try to write it in vector form. First of all,since it is directed along the radius,the unit vector in radial direction in this ...
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### Why does four-momentum have the same transformation matrix as spacetime coordinates?

I will outline my question in 1+1D for brevity. We can passively transform our coordinate system using a Lorentz boost; $\Lambda^{\bar{\nu}}_{\mu}x^{\mu}=x^{\bar{\nu}}$. I've seen that, by stipulating ...
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### Normal to the hypersurface

I have a given metric and I want to choose a spacelike hypersurface and find the normal to that hypersurface. I know that if the hypersurface is spacelike, then the normal is timelike. The given ...
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### How to calculate velocity vector from scalar angular velocity and position vector in 2D?

I would like to know, if I have an angular velocity as scalar, how can I calculate the velocity vector. I know that the product of angular velocity and the length of the distance gives the speed, but ...