Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
2,604
questions
0
votes
1
answer
183
views
Isomorphism of the tangent space and the space of directional derivatives [closed]
I have already constructed the tangent space to a manifold, denoted $T_pM$, and I have a good basis for it $\{\hat e_{(\mu)}\}$. (I followed the method of equivalence classes of curves tangent at $p$....
- 713
1
vote
1
answer
81
views
Electromagnetic duality and vector/pseudovector transformation properties
One consequence of electromagnetic duality (see e.g., https://doi.org/10.1038/s41467-023-36420-4) is that if we have a system described by permittivity and permeability profile $(\varepsilon, \mu)(\...
- 136
1
vote
3
answers
250
views
A confusion about the inner product keeps disturbing me [duplicate]
I get very confused about the concept of inner product. When an inner product is defined in a vector space, $\mathbb{V}$, don't we define it as an operation between two vectors from $\mathbb{V}$ ...
- 11.8k
0
votes
0
answers
44
views
Finding angular velocity of a frame given an angular velocity in another frame
I was trying to understand the Earth's frame of reference. You stick a coordinate system on the surface of the Earth and due to the Earth's rotation the coordinate rotates with respect to the axis of ...
- 122
0
votes
0
answers
8
views
Tensions in the chains [duplicate]
What is the physics behind this mechanism? What would be the free body diagram be like regarding all the magnitudes of the tension forces present in the chains?
- 23
2
votes
2
answers
111
views
Tensions in the chains
What is the physics behind this mechanism? What would be the free body diagram be like regarding all the magnitudes of the tension forces present in the chains?
- 23
7
votes
2
answers
330
views
Is the electromagnetic 4-potential a Lorentz 4-vector in the Coulomb gauge?
In the course of Classical Electrodynamics I learned that in the Lorenz gauge it is easy to prove that the 4-potential $A$ is a 4-vector, that is its components $A^\mu=(\phi/c,\vec{A})$ transform as ...
4
votes
3
answers
147
views
When we apply these concepts to physics, where do we put the UNITS in vector spaces and manifolds? Do units have a clear mathematical meaning?
We know that the space of all displacements is a vector space.
The vector space is defined as a mathematical object $(V,k,+,\cdot)$ such that it satisfies the 8 properties, where $k$ is a field.
We ...
- 151
0
votes
1
answer
51
views
Avg. velocity in plane polar coordinates
It's fairly easy to describe velocity, acceleration and displacement in plane polar coordinate system is the time interval is approaching to 0, but how can we calculate velocity, acceleration and ...
- 51
0
votes
1
answer
62
views
Pseudo forces in accelerating reference frames
I was going through HC Verma's lecture on this and he mathematically derived the pseudo force in reference frames that are going under translational acceleration with respect to an inertial reference ...
- 122
0
votes
1
answer
28
views
Signs terms including acceleration
Am I right in saying that accelerations can only be given a sign if a coordinate system is defined in relation to which they are described?
Is this idea applied to any vector quantity?
Is there a ...
- 123
1
vote
1
answer
134
views
Lorentz boost that result in $\vec{E}$ parallel to $\vec{B}$
This is a question related to the an answer for this question regarding boosts which make $\vec{E}$ parallel to $\vec{B}$ in the boosted frame.
I do understand the approach and the cases 1a and 1b. ...
- 13
0
votes
1
answer
74
views
Newton's Law of Gravitation Explanation?
Based on Fundamental Astronomy by Hannu Karttunen page 318. It is mentioned that the planet experiences a gravity pull toward the Sun that is proportional to the mass and inversely proportional with ...
0
votes
2
answers
144
views
Calculating the magnitude of the average acceleration of a clock hand
I've been stuck on the following question from Isaac Physics for quite some time now and I'm not really sure where to even begin:
The time shown on a clock changes from 4:00 to 4:30. The minute hand, ...
4
votes
1
answer
174
views
Schmidt decomposition of density matrix
For a bipartite system:
$\mathcal{H}=\mathcal{H}_{a}\otimes\mathcal{H}_{b}$ described by a density operator $\hat{\rho}_{ab}$, I can promote it to a vector in the Liouville space, $|\hat{\rho}_{ab}\...
- 95
1
vote
2
answers
81
views
$\vec{ds}$ vector of work formula
I know $W= \int_{x_1}^{x_2}\vec{F}\,.\vec{ds}\ $
I am working with frictional force. Here $x_2>x_1$, $\vec{F}$= - $\mu mgcos\theta \hat{i}$
As $x_2>x_1$, $\vec{ds}= \hat{i}dx $
So the ...
- 43
0
votes
0
answers
45
views
Force due to ring of charge [duplicate]
I am currently taking Physics II and have recently been focused on this problem: Suppose there is a ring of uniform linear charge density $\:\lambda\:$ and radius R and a point P at a height $\: z_{_\...
0
votes
1
answer
72
views
When doing Ice Skating, is it more painful to fall in motion or without motion?
Let's imagine I'm ice skating on a perfectly flat surface.
In the first scenario, I am falling motionless. I expect my forces to looks like this:
In the second scenario, I am falling with some speed, ...
- 101
3
votes
1
answer
360
views
Can anyone explain what the second corollary in Newton's Principia is about?
I was reading but it is unclear to me what Newton is trying to say in his second corollary, it is in the page 91 of the pdf and 84 of the book here is a photo of the proposition
- 39
2
votes
2
answers
161
views
Is $W = \vec{F}\cdot\vec{D}$ actually a dot product or just calculated that way?
I know that work = force times displacement with vectors ($W = \vec{F}\cdot\vec{D}$) can be calculated in the same way as a dot product, but it seems to me that it isn't really a dot product. The ...
- 151
0
votes
2
answers
121
views
Current density $J$ when θ = 90°
I've searched a lot on the internet, but so far, nothing has been able to resolve my doubt completely. So here it goes,
We know that,
$ I = \vec J • \vec A $
So, $ J = \frac {I}{Acosθ} $
Now, ...
- 41
0
votes
1
answer
61
views
Resolving a vector into components [closed]
Scenario 1:
There is a block on a horizontal table on which I'm applying a force of 10N.
Scenario 2:
Block B has mass m and block A has mass 3m. Tension in cord CD while B is sliding down A is $\frac{...
user386835
5
votes
2
answers
200
views
Lorentz covariant but Lorentz inconsistent $4$-forces?
We often say that the benefit of relativistic index notation is that we can write down equations of motion that are automatically Lorentz covariant. However, I'm starting to feel that there are many ...
- 2,292
1
vote
2
answers
231
views
Tangent vectors as equivalence classes of curves
Given a smooth (differentiable) manifold $M$ and intervals $I_1,I_2\subset\mathbb{R}$, two curves
\begin{equation}
\gamma_1:I_1\to M\quad\text{and}\quad\gamma_2:I_2\to M~~,
\end{equation}
are ...
- 713
0
votes
2
answers
86
views
Basic vector confusion [closed]
The context is that there is a charge $q$ moving with velocity $\vec{V}$ in magnetic field $\vec{B}$. The angle between $\vec{V}$ and $\vec{B}$ is given as $30^{\circ}$
The formula to calculate the ...
1
vote
0
answers
86
views
An object which was initially at rest explodes in three pieces. Is it necessary that all the pieces will be in same plane and not in 3 dimensions? [closed]
I found this question in a test paper and the answer was all the three pieces must be in same plane because three vectors must be in same plane to cancel each other but if we consider a case like this-...
- 11
0
votes
0
answers
71
views
Calculate wind speed on aircraft given measurements of speed and heading
I have X amount of speed measurements of an aircraft, each measurement includes a heading and a forward ground speed.
What I want to do is to calculate the wind speed affecting the craft.
For example:
...
- 1
0
votes
0
answers
11
views
Wave vector components from 2 column data
if I have 10 data in each column for speed (2D), how to connect those data as wave form?
I need to find the components of wave vector ($k_x, K_y$).
I request any suggestions regarding this.
- 31
0
votes
1
answer
72
views
Gradient vector of a function under transformation
The following question from Griffiths Electromagnetism states :
Suppose that f is a function of two variables (y and z) only.
Show that the gradient ∇ f = (∂f/∂y)y + (∂f/∂z)z transforms as a vector ...
- 143
4
votes
2
answers
211
views
Why do we consider the shortest length (displacement) for doing the calculations?
Whenever we calculate any lengths in Physics, we tend to express using displacements. For example, while calculating energy, which is given by the formula-
E = Fswhere E represents the energy, F ...
- 41