Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
1,381
questions
0
votes
2answers
29 views
What is the three dimensional generalisation of a conservative force?
I was studying about conservative forces from a physics book (NCERT, a standard Indian textbook) and came to a para which is as follows:
A force is conservative if it can be derived from a scalar ...
3
votes
1answer
45 views
What's the meaning of the coordinates if we use a polar coordinate system?
In general, the coordinates of a vector are defined as the projections of it onto the coordinate axis. Moreover, in a polar coordinate system, the basis vectors $\hat e_\phi$, $\hat e_r$ depend on the ...
0
votes
0answers
16 views
Two equal masses are glued to a massless hoop of radius R. Find position vector and velocity? [closed]
Two equal masses are glued to a massless hoop of radius R that is free to rotate about its center in a vertical plane. The angle between the masses is 2*theta. Find position vector and velocity?
For ...
-3
votes
0answers
52 views
Please help me with this physics question, I am stuck with it. Thank you [closed]
This question is about mechanical engineering, pin frame problem. I am not getting the answer not even close to it.
-1
votes
0answers
52 views
Traveler moving at half the speed of light in both $x$ and $y$ directions [closed]
This is under the purview of Lorentz transformations.
An inertial frame $F'$ moves in the $x$-direction with speed $v=0.9c$ relative to another frame $F$. A traveler is moving with velocity $\...
0
votes
1answer
60 views
Divergence of a vector multiplied by dot product [closed]
If I am correct, then
$\operatorname{div} [(\vec A\cdot \vec B)\vec C] = (\vec A \cdot \vec B) \operatorname{div} \vec C + \vec C \cdot \nabla (\vec A\cdot\vec B)= (\vec A \cdot \vec B) \operatorname{...
1
vote
1answer
36 views
How does the Lorenz Gauge condition lead to four wave equations?
The 1972 book by L. Eyges's, The Classical Electromagnetic Field, on p. 184, in $\S$11.7, Integral Forms of The Potential, the statement
"We now turn to the problem of finding $\mathbf{A}$ and $\...
0
votes
0answers
68 views
Converting velocity vector formula from Cartesian coordinate system to polar coordinate system
I have a little question about converting Velocity formula that is derived as,
$$\vec{V}=\frac{d\vec{r}}{dt}=\frac{dx}{dt}\hat{x}+\frac{dy}{dt}\hat{y}+\frac{dz}{dt}\hat{z}$$
in Cartesian Coordinate ...
0
votes
0answers
28 views
Given no strain and uniform angle of rotation, can the displacement field be expressed as a uniform rotation?
Consider displacement vector $\xi$ where $\mathbf{\xi}=\mathbf{\phi} \times \mathbf{x}$. $\phi$ is an angle vector along the axis of rotation and $\mathbf{x}$ is the position vector. Let $W_{ij}=\frac{...
1
vote
1answer
36 views
Meaning of normal acceleration?
acceleration means the rate of change in velocity (vector quantity) and the differentiation means to divide a certain quantity into small elements (i.e $dx$) as we do to find the acceleration at any ...
0
votes
3answers
64 views
Cross product and handeness
I'm having some difficulties understanding the cross product in a left-handed coordinate system. I want to compute $\hat{i} \times \hat{j}$ for both systems in the picture (the first one is right-...
0
votes
0answers
14 views
Invariant quantities? [duplicate]
Every phisical quantity is tensor quantity (special cases of tensors are vectors and scalars). There are transformation rules for tensors. For example for scalar quantity F transformation rule is F'(x'...
0
votes
1answer
37 views
How do I derive the formula for radial acceleration when there is no uniform circular motion? [duplicate]
My lecturer states that $a_r=\dfrac{v_t^2}{r}=\omega^2r$ where $v_t$ is tangential velocity, he also wrote that this is derived the same way that radial acceleration is derived in uniform circular ...
1
vote
4answers
100 views
3 Dimensional Law of Cosines? Magnetic Vector Potential Problem
I am working on a problem similar to one in my textbook - however, I am having an issue understanding the example. Can someone explain the formulas from this picture? I am confused about using the law ...
1
vote
3answers
84 views
What causes the block to move horizontally on a FIXED wedge
Questions:
For a block kept on a FRICTIONLESS FIXED INCLINE the acceleration down the plane is g*sin(A) (A is the angle of inclination) this acceleration can be further said to have components in the ...
0
votes
1answer
49 views
Why do we neglect $\Delta t^2(\frac{d\vec{r}}{dt}\frac{d\vec{\hat{r}}}{dt})$ at Taylor Expansion?
I'm just started to Ankara University Physics Department two weeks ago. I have missed my 2 hours of PHY105 course that is the last week Wednesdey. The subject that i missed was Derivatives of Vectors. ...
0
votes
1answer
18 views
Vector in an inverted frame of reference using Euler's Angles
Having some issues regarding the Euler's angles. Following is the short description of them problem.
In the first step, I determined the Euler's angles to invert my frame of reference that is X, Y ...
0
votes
3answers
74 views
A textbook problem on vectors [closed]
I am stuck on a textbook problem on vectors (a new topic for me). The problem given in my book says:
A man can swim with a speed of 4 km/h in still water. How long does he take to cross a river 1 ...
0
votes
2answers
79 views
Velocity in circular motion, $v = r × \omega$ or $v = \omega × r$?
I know it might sound silly to ask, but is the relation between linear velocity and angular velocity of an object undergoing circular motion $ v = r × \omega$ or $v = \omega × r$? I didn't notice it ...
0
votes
0answers
43 views
Commutators of dot and cross products
I apologize if this question is too basic, but I am wondering if identities for commutators such as $[AB,C]=A[B,C]+[A,C]B$ also hold for dot and cross products within the commutator (i.e., $[A\times ...
-1
votes
3answers
67 views
The components of the vector in a simple pendulum
Okay so this has been bugging me. Every book I've read so far just breaks down the vectors in a position where the pendulum is pulled to the right like the picture above.
But it doesn't say HOW it did ...
-1
votes
0answers
37 views
What is open expression of a vector's magnitude? [migrated]
I'm 1st grade Physics student and my school started this week at 16.09.2019. I have seen 4.5 hours of lesson about vectors this week. We have seen such thing called Products of Vectors. My teacher ...
0
votes
1answer
46 views
Feynman Lectures on Physics: Vol 1, 11-6: acceleration vector
I’m trying to get through 11-6 section of Feynman’s Lectures on Physics, Vol 1, particularly explanation of acceleration vector calculation in his example:
It’s clear that acceleration ...
1
vote
0answers
26 views
Angle of friction force of a weighted ball on a surface
If a block had constant density and laid on a slope with angle $\theta$ then the angle of friction and the horizontal would be $\theta$. If there was a ball with constant density then the friction ...
2
votes
5answers
762 views
Intuitive methods for representation of Cartesian Coordinates in terms of Spherical Coordinates as basis [closed]
I was going through Griffith's Electrodynamics and came upon an example, where he used that, $$\cos\theta \ \hat{r} - \sin\theta \ \hat{\theta} = \hat{z} $$
Now I admit I was confused for a while ...
-1
votes
0answers
33 views
Converting unit cartesian to spherical coordinates
I was reading answer on this link:
https://physics.stackexchange.com/a/290743/228740
He writes:
$$
\mathbf{x} = \frac{\partial r}{\partial x} \frac{\partial}{\partial r} +
\frac{\partial \theta}{\...
0
votes
2answers
82 views
Relativity geometric analysis without spacetime
I'm an engineer and I'm used to classical mechanics "spatial-vectors" approach, which allows a geometric analysis of rigid bodies motion. In this context, as you know, it is very useful to imagine (...
0
votes
0answers
28 views
Question from Introductory Classical Mechanics by Morin
I understand if the system is to not move then the normal force from the ball to the triangle would have to support the weight of the triangle(or other shape depending on the problem). However, the ...
-1
votes
1answer
32 views
Does the component of vector depend on the orientation of the axes?
the question was:
A situation may be described by using different sets of co-ordinate axes having different orientations. Which of the following do not depend on the orientation of the axes?
(...
0
votes
2answers
52 views
Are there two ways of representing a vector i.e., parrallelogram and resolution?
the question was:
The component of a vector is
(a) Always less than its magnitude
(b) Always greater than its magnitude
(c) Always equal to its magnitude
(d) None of these
...
0
votes
1answer
30 views
Non-uniform circular motion with constant radius of curvature
$\let\oldhat\hat
\renewcommand{\vec}[1]{\mathbf{#1}}
\renewcommand{\hat}[1]{\oldhat{\mathbf{#1}}}$
Suppose we have a car moving on a circular track of radius $b$ and speed $v=ct$, where $t$ is time ...
2
votes
0answers
39 views
What is the meaning of a vector integral over another vector?
Reading Portis's Electromagnetic Fields: Sources and Media I came across this expression for the stored electric energy in a volume in a general medium:
$$ U = \int dV \int \mathbf{E}\cdot d\mathbf{D} ...
0
votes
1answer
95 views
Weird assumption in a paper to prove equation [closed]
Let $M_k$ and $M_{k+1}$ be two successive positions. Supposing the road is perfectly planar and horizontal, as the motion is locally circular, we have:
Where $\Delta$ is the length of the circular ...
-2
votes
1answer
124 views
What is the actual difference between scalar and vector quantities?
We often differentiate them by saying scalar quantity have magnitude while vector have both direction and magnitude. But how's it possible that if an object is moving then it won't have direction in ...
-3
votes
1answer
56 views
Regarding the Lorentz force:
I know that the Lorentz Force law states that:
$\vec{F} = q\vec{E}+q\vec{v} \times \vec{B}$
And then for the magnitude of the force, where $q_2$ is the moving charge:
$E = F/q_2$, and therefore $E =...
0
votes
1answer
35 views
Transformation of a vector's components in a time-dependent transformation
I know how the contravariant and covariant components of a vector transform when the coordinate system is changed (⇒ the known relation between the old coordinate system and the new one, I multiply by ...
1
vote
2answers
44 views
What is the use of Subtracting velocity?
By adding two velocity's direction we get the direction the object has travelled. But what do we get when we subtract vectors?
-1
votes
1answer
23 views
Angular velocity in curved space (2d manifold)
In 3d Euclidean geometry, the velocity of any point of a rigid body is given by the cross product between its angular velocity and the position vector which links the instantaneous rotation center to ...
0
votes
1answer
37 views
Determining the $z$-component of a force to maintain equilibrium?
I came across this problem in vector mechanics wherein I’m asked to determine the value of $d$ such that the tension in cables $AC$ and $AD$ is half the tension in $AB$.
What I initially did was ...
-1
votes
1answer
39 views
Why do forces follow the triangle law of vector addition? [duplicate]
Why do, when two force act on a point their result is third side of triangle formed by the component forces?
1
vote
1answer
50 views
What causes tangential acceleration
The body moves on a circular path and has both tangential as well as centripetal acceleration.
Friction acts outward as shown in figure. If this friction exceeds mv²/r, then shouldn't the body just ...
0
votes
4answers
117 views
Why was the concept of velocity created? [closed]
Why do we use velocity instead of speed for different physics problems?
I recognize how they are different but why use one over the other?
0
votes
2answers
66 views
Why there is no a vector quantity in $P=\sqrt{2mK.E}$
Personally, If I saw this law I would say that momentum is a scalar quantity, because I know that (scalar quantity X scalar quantity = scalar quantity).
Since momentum is a vector quantity, So why ...
0
votes
0answers
32 views
Proof of skewsymmetry of electromagntic function in Minkowski spacetime
I have been studying special relativity from the Gregory Naber's book: "The geometry of Minkowski spacetime" and I found a very strange proof. In Section 2.1, just before of equation 2.1.2. the book ...
1
vote
0answers
40 views
Why should forces add as vectors? [duplicate]
We are supposing in my mechanics course that forces add as vectors. But why, philosophically, should this be the case?
0
votes
0answers
22 views
Current-carrying wire in a magnetic field. Cross product, vectors and scalars
We have a wire with cross-sectional area $A$, length $L$ and current $I$.
If the wire is in a magnetic field $\vec B$, the magnetic force on each charge is $\vec F =q\vec v_d \times \vec B$.
$\vec ...
0
votes
1answer
52 views
Consistent calculation of the total momentum in quantum physics
When we are considering a one-dimensional case in quantum physics, we can calculate the momentum by solving the eigenvalue equation:
$$ -i \hbar \frac{d}{d x} \psi(x, t) = p_x \psi(x, t).$$
If we ...
0
votes
2answers
72 views
Calculating gravitational force with multiple planets [closed]
I have a question regarding the following problem:
Given the following system of planets (see image), calculate the total gravitational force acting on $m_3$.
($m_1 = 2 \cdot 10^{20}kg;$ $m_2 = 1 \...
1
vote
1answer
52 views
Intuitive Understanding of Vectors? [duplicate]
I've recently gotten into physics, since I wanted to start learning it after I self-studied Calculus 1. I'm currently using the textbook "Fundamentals of Physics" by Halliday, however, I'm having a ...
2
votes
2answers
97 views
Divergence of a Vector Field - Surprising Result [duplicate]
I'm following the text Introduction to Electrodynamics by Griffiths, and I came across the following in an in-text problem:
Sketch the vector function v = $\frac{\boldsymbol{\hat{\mathbf{r}}}}{r^2}$...
