# Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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### Do objects move in 2 directions at once?

If a velocity vector of an object can be divided into an x and y component relative to a second object's position, and both objects have gravity that attracts both objects to each other. We then know ...
0answers
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### Magnitude of moment in 3d space

What's the magnitude of moment about O, if the vectors F, r1 and r2 all lie in the z-y plane? I know the magnitude of the moment is the cross product of force and the perpendicular distance from the ...
0answers
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### True Airspeed from Indicated Airspeed, Temperature, and Altitude

I'm working on an aircraft problem to figure out the true heading we need to fly in order to end up where we want with the presence of wind, and I think I have the whole thing figured out except for ...
8answers
3k views

### Formal Definition of Dot Product

In most textbooks, dot product between two vectors is defined as: $$\langle x_1,x_2,x_3\rangle \cdot \langle y_1,y_2,y_3\rangle = x_1 y_1 + x_2 y_2 + x_3 y _3$$ I understand how this definition ...
7answers
98 views

### Is there centripetal acceleration with velocity of 5 m/s?

So if an object is moving at $5\ \mathrm{m\ s^{-1}}$ in a circle, is it accelerating? Me and a friend are having a conversation about this.
4answers
425 views

### Is there a scalar acceleration?

Distance is paired with Displacement and it seems to be a bigger idea than just the magnitude of Displacement. Speed is paired with Velocity. I have always thought that there is not such pairing with ...
8answers
483 views

### What actually is the vector of angular momentum?

If an object spins around a central point, it gets angular momentum which is a vector with an orientation dependent on whether its clockwise rotation or anticlockwise, i get that. But what the vector ...
2answers
55 views

### Vectors, their representation and dipole moment

I know that the length of an arrow representing a vector gives represents the magnitude of that vector, now consider a force vector. $\vec{F}$=m$\vec{a}$ , therefore in space a force vector ...
0answers
25 views

### How to solve 3-variable planar vector equilibrium problems?

While it's quite straightforward to solve problems with multiple planar vectors in equilibrium for 2 variables, I'm having issues with those where I'm asked to minimize or maximize a variable along ...
0answers
35 views

### What is meant by surface divergence of a vector function?

My book says: If there is a surface discontinuity in a vector field $\vec{E}$, we enclose it in a thin transitional layer (of width $h$) and apply divergence theorem. If $\hat{n}_1$ and $\hat{n}_2$ ...
1answer
73 views

### Vector calculus notation, maybe?

I just got a new book on turbomachinery that uses some notation I'm not familiar with. $$\nabla \lor \vec{W} = -2\vec{\Omega}$$ The del-(something)-vector format makes me think its vector calculus....
2answers
50 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{...
2answers
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### 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, ...
0answers
272 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 ...
1answer
31 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 ...
1answer
34 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 ...
0answers
41 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 ...
2answers
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### 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 ...
1answer
76 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-...
2answers
78 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 ...