Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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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 ...
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1answer
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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 ...
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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 ...
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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.
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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 $\...
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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{...
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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 $\...
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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 ...
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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{...
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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 ...
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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-...
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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'...
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1answer
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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 ...
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4answers
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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 ...
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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 ...
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1answer
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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. ...
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1answer
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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 ...
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3answers
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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 ...
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2answers
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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 ...
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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 ...
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3answers
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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}{\...
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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 (...
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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 ...
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1answer
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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? (...
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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 ...
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1answer
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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 ...
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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} ...
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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 ...
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1answer
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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 ...
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1answer
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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 =...
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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 ...
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2answers
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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?
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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 ...
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1answer
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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 ...
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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?
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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 ...
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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?
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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 ...
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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 ...
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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?
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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 ...
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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 ...
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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 \...
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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 ...
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2answers
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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 = $\frac{\boldsymbol{\hat{\mathbf{r}}}}{r^2}$...