Geometric object with magnitude (length) and direction.

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Vector potential

I have difficulty understanding the following vector calculus example. Text can be found here. It is the 5th Q&A -- starting with equation (31.1035).It concerns finding the vector potential of a ...
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1answer
103 views

Are fundamental forces always attractive/repulsive, i.e. parallel to the separation?

If magnetic monopoles existed it would not be the case - the forces on an electron and a magnetic monopole passing by each other would be at right angles to the vector connecting the two particles! ...
4
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1answer
87 views

Show that getting parallel transported does not change angle between them- Tensors [closed]

I must tell you that I have never seen this kind of question in Tensor Analysis. Our professor had set up this question in our exam, but I don't know whether it belongs to tensors or not. The question ...
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4answers
1k views

Can we add any two vectors?

Can we add any two vectors? If not, why is that so? I think this is not true, but I am not sure. My book says it is true, but I guess it is a misprint. For example, adding acceleration to velocity.
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92k views

Linear acceleration vs angular acceleration equation

I'm learning about angular velocity, momentum, etc. and how all the equations are parallel to linear equations such as velocity or momentum. However, I'm having trouble comparing angular acceleration ...
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251 views

Notation of vectors

It's very common to see $\text{F} = 30 \text{ N}$ when the problem is unidimensional. Yet, force is a vector. Shouldn't I write $|\overrightarrow{F}| = 30 \text{ N}$? Because if I write ...
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328 views

Relation between component and algebraic definition of covariant vectors

I studied contravariance and covariance concepts in following way: For any vector if we get its components by parallelogram way we achieve contravariant components, and if we want to get its ...
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3answers
360 views

How to distinguish 4D and 3D vectors in handwriting?

Usually vectors are denoted with bold font in printbooks and with arrows above in handwriting. In Thorn's e al. Gravitation, 4D vectors are denoted with bold and 3D vectors with bold italic. How to ...
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2answers
304 views

Importance of Kronecker product in quantum computation

To get product state of two states $|\phi \rangle$ and $|\psi \rangle$, we use Kronecker product $|\phi \rangle \otimes |\psi \rangle$. Instead of Kronecker product $\otimes$, can we use Cartesian ...
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32k views

Why work is a scalar and not a vector?

Work (in physics) is a scalar, but why? And why not a vector?
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4answers
505 views

How to determine which one would not be the resultant?

i had a physics exam yesterday, which was all in all pretty good except for this one question which i just don't get.: ...
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2answers
343 views

Lorentz algebra and its generators

I'm reading Maggiore's book A Modern Introduction to Quantum Field Theory and I'm getting a bit confused when he writes about Lorentz algebra: $$K^i = J^{i0},$$ ...
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4answers
726 views

Why do physics students find vectors so difficult to deal with? [closed]

When I teach introductory physics to undergraduates, I find that although the classes are frequently split into "algebra-based" and "calculus-based" sections, the most difficult concept for any of ...
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298 views

Position Representation in Quantum Mechanics

How does the 3d position operator look like in position representation? I know that in 1d the position operator $\hat{x}$ is just multiplication by $x$.
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2answers
205 views

“Vectors” (i.e. 1-tensors) their definition and motivation for relativity

I'm reading Einstein Gravity in a Nutshell (by Zee) and here he defines a vector as an object which is invariant under coordinate representation; concretely, if in one coordinate representation, $V$, ...
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1answer
109 views

Contradiction of a scalar product

Can anyone resolve this contradiction: ...
3
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1answer
63 views

On a horizontal plane, why does $F_N=W$?

I keep seeing this definition everywhere, but I don't understand. The forces of the weight and the normal force are going in opposite directions, so shouldn't $F_N=-W$?
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4answers
284 views

How to apply an algebraic operator expression to a ket found in Dirac's QM book?

I've been trying to learn quantum mechanics from a formal point of view, so I picked up Dirac's book. In the fourth edition, 33rd page, starting from this:$$\xi|\xi'\rangle=\xi'|\xi'\rangle$$ (Where ...
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2answers
178 views

The force of gravity is $F_g=+mg$ or $F_g=-mg$?

I have noticed that in my classical mechanics course and in the textbook I read for it, seem to ignore the gravitational force's position. For example, if we were dealing with a system with a ball of ...
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3answers
369 views

Is it possible to have a non conservative vector field, such that the closed loop integral is $0$ for only some specific path(s)?

I was wondering whether there exists some non conservative field in which the closed loop integral over some specific path(s) is $0$, even if it's not $0$ for all the closed loop integrals. Or to put ...
3
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3answers
150 views

4-velocities in different frames

We have an observer in an inertial frame $S$ who measures a particle's 4-velocity as $U$. We then have another inertial frame $S'$ with $X'=\Lambda{X}$, where $\Lambda$ is a matrix representing a ...
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5answers
462 views

Forces as vectors in Newtonian mechanics

I seem to be confused about the nature of forces as vectors, in the basic Newtonian mechanics framework. I know what a vector is as a mathematical object, an element of $R^3$. I understand that if a ...
3
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1answer
409 views

Equivalent definitions of vectors

Equivalent definitions of vectors. In maths a vector is an object that obeys some axioms of a vector space. But in physics a vector can be thought as an object which is invariant under rotations of ...
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1answer
52k views

How does force relate to velocity

I had originally asked this question on math overflow and it was suggested that I ask it here. So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
3
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1answer
460 views

How is weight distributed when legs are astride?

Is there a simple and quick formula to find the weight (the force acting) on each leg, especially when legs are astride and they are not equally stretched? (or, better) not equally distant from the ...
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3answers
279 views

What is the relative velocity of this plane relative to the helicopter? [closed]

There is a plane moving 100 m/s due east relative to the ground without vertical motion. There is a helicopter facing north moving straight up at 20 m/s. From the perspective of the helicopter, is the ...
3
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2answers
102 views

Scattering geometry question

While reading up on light scattering I came across this slide: My vector maths is a bit rusty and I am having trouble understanding the last term (scattering geometry). What is the significance of ...
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2answers
2k views

Meaning of angular velocity in a rotating system

When you study the motion of a rigid body you have $\vec\omega$, the vector associated to angular velocity. In the case you are using Euler angles and want a quick formula for the rotational kinetic ...
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1answer
77 views

What is the difference between scalar and vector mesons?

My understanding is that vectors and pseudooscalars change sign under parity operation and pseudovectors and scalars do not. However, I don't understand what the difference between a vector and ...
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2answers
63 views

Heuristic explanation of the difference between vectors and scalars in physics

I'm trying to give a student a (physically) intuitive, heuristic explanation as to why certain quantities are vectors and others are scalars. Here is what I have come up with: Scalars are quantities ...
3
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1answer
137 views

How does the Lorentz group act on a 4-vector in the spinor-helicity formalism $p_{\alpha\dot{\alpha}}$?

Given a 4-vector $p^\mu$ the Lorentz group acts on it in the vector representation: $$ \tag{1} p^\mu \longrightarrow (J_V[\Lambda])^\mu_{\,\,\nu} p^\nu\equiv \Lambda^\mu_{\,\,\nu} p^\nu. $$ However, I ...
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110 views

Why scalar function of vector can only depend on norm of vector?

In Field Quantization by Greiner and Reinhardt as well as The Qunatum Theory of Fields by Weinberg, concerning the spectral function, the authors say a scalar function of the four-vector $p^\mu$ can ...
3
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4answers
565 views

More about the right hand rule?

We started learning about electromagnetism in physics class, and the Right Hand Rule comes in handy as seems easy to use, but I'm curious as to how it actually works. I guess it's more of a math ...
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2answers
6k views

Resultant of two forces acting in the same line

I'm quoting the definition of Resultant of two forces acting in the same line from the book "A FIRST COURSE IN PHYSICS" one of whose authors is Robert Andrews Millikan: The resultant of two forces ...
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2answers
2k views

Finding force vectors

A tugboat tows a ship at a constant velocity. The tow harness consists of a single tow cable attached to the tugboat at point $A$ that splits at point $B$ and attaches to the ship at points $C$ and ...
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3answers
722 views

How do I meaningfully divide by a vector?

How long does it take a baseball with velocity $(30, 20, 25) m/s$ to travel from location $r_1 = (3, 7,−9) m$ to location $r_2 = (18, 17, 3.5)m$? I am thinking that it should be the ...
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1answer
2k views

Electric field a distance $z$ above the center of a circular loop. The Hard way [closed]

Problem 2.5: Find the electric field a distance $z$ above the center of a circular loop of radius $r$ which carries a uniform line charge $\lambda$. This problem is in refereced here (with ...
3
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1answer
451 views

Why can we use just one angular velocity vector to describe the rotation of a whole non-inertial reference frame?

The other day in class the professor was explaining non-inertial reference frames. We were working out how to find the acceleration of a point as measured from the non-inertial reference frame, and ...
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2answers
128 views

Why is the “complete metric space” property of Hilbert spaces needed in quantum mechanics?

I have been learning more about Hilbert spaces in an effort to better understand quantum mechanics. Most of the properties of Hilbert spaces seem useful (e.g. vector space, inner product, complex ...
3
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1answer
500 views

Rolling a ball into a cone; what should the forces overall be?

This is my solution to finding angular displacement/velocity/acceleration on cone so far. Consider a cone, with an apex of half-angle $\psi$ pointing down, and a height of $h$. If I roll a ball into ...
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3answers
543 views

Why does the moment of force (aka. torque) depend on the perpendicular distance?

Couyld anyone explain how the lecturer concluded that $$(\underline{r_2} - \underline{r_1}) \times \underline{H} = \underline{p} \times \underline{H}$$
3
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0answers
109 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
2
votes
3answers
27k views

Uses of vectors in real life [closed]

I always wonder how vectors are used in real life.Vectors and decomposition of vectors,dot and cross products are taught in the early stage in every undergraduate physics course and in every ...
2
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3answers
310 views

Deriving cross product from angular momentum algebra

Is it possible to derive: \begin{equation} \hat{L}=\hat{r}\times \hat{p} \end{equation} from the angular momentum algebra: \begin{equation} [\hat{L}_i,\hat{L}_j]=i\ \hbar\ \epsilon_{ijk}\hat{L}_k\ ? ...
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2answers
118 views

Differentiating a vector product

$$m_i\mathbf{r}_i\times\frac{\mathrm{d}^2\mathbf{r}_i}{\mathrm{d}t^2} = \frac{\mathrm{d}}{\mathrm{d}t}\biggl(m_i\mathbf{r}_i\times\frac{\mathrm{d}\mathbf{r}_i}{\mathrm{d}t}\biggr)$$ I do not ...
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3answers
1k views

The velocity formula $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ for 1D, 2D, 3D . What is the difference?

Could I use $\mathbf{v} = \mathbf{u} + \mathbf{a}t$ for calculating velocity in these 3 different dimensions? If not, what's the difference between these 3 dimensions? How would you calculate ...
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4answers
1k views

Gradient is covariant or contravariant?

I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of ...
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3answers
240 views

Dimension of vector resulting from tensorial product

I'm quoting what I found in a book about quantum computation: Individual state spaces of $n$ particles combine quantum mechanically through the tensor product. If $X$ and $Y$ are vectors, then ...
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2answers
9k views

Derive vector gradient in spherical coordinates from first principles

Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient. I've derived the spherical unit vectors but now I don't understand how to transform ...
2
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2answers
219 views

A whole lot of doubts on Lorentz representation

Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on ...