Geometric object with magnitude (length) and direction.

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1answer
17 views

Differentiation of a vector with respect to a vector

Does differentiation of a vector with respect to a vector make any sense? Even if it makes sense, how does it make any physical meaning? I mean what is the physical interpretation?
-1
votes
1answer
18 views

Statics Vector Question [on hold]

I need help with this problem image of problem: http://postimg.org/image/87o0tyfyp/ I could answer the question if I had a second angle but I don't even know where to begin to solve the question. ...
0
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3answers
49 views

Curl of a vector

What is the physical interpretation of curl of a vector? Please give some common examples in Physics. Just as divergence implies flux through a surface.
3
votes
1answer
316 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 ...
-1
votes
2answers
61 views

Very basic question about vector

The vectors $a = (2,-1,-2)$ and $b = (0,-3,4)$ are given. Determine $a$:s parallel and normal vector to $b$. Obviously the parallel vector should be the dot product $a \cdot b$ times the unit vector ...
0
votes
1answer
47 views

Basic Notation Help Needed : Classical Mechanics, Unit Vectors

Can someone help me with some basic notation? Here's a situation where I'm surely missing some trivial piece of the puzzle: Example 1: given $W = \frac{1}{2}cpAv^2$ (air resistance), adding a unit ...
-1
votes
0answers
67 views

Proof for parallelogram law of vector addition [migrated]

The Statement of Parallelogram law of vector addition is,If two vectors are considered to be the adjacent sides of a Parallelogram, then the resultant of two vectors is given by the vector which is a ...
0
votes
0answers
23 views

Using the dipole moment to calculate the electric potential

I have the following defintion of dipole moment given: $$ \vec{p} := \int\vec{r}'\rho(\vec{r}')dV $$ Where $\rho$ is a charge density function and $\vec{r}'$ traces out the body of charge. I am ...
13
votes
5answers
635 views

What does it mean for a physical quantity if its mixed second partial derivatives are not equal?

This goes for every problem (either in electromagnetism or fluid dynamics) that has to do with vector fields. Say we have a fluid flowing in a closed circular pipe (or an electromagnetic field, the ...
1
vote
3answers
436 views

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

Couyld anyone explain how the lecturer concluded that $$(\underline{r_2} - \underline{r_1}) \times \underline{H} = \underline{p} \times \underline{H}$$
0
votes
2answers
70 views

Transformation of four-velocity in special relativity

I am revising special relativity introducing more matrix form in the equation. Currently I am reading book in which transformation matrix is defined as $${\Lambda= \begin{bmatrix} \gamma & ...
18
votes
6answers
45k views

What is the physical significance of dot & cross product of vectors? Why is division not defined for vectors?

I get the physical significance of vector addition & subtraction. But I don't understand what do dot & cross products mean? More specifically, why is it that dot product of vectors ...
0
votes
1answer
50 views

When will the velocity of a particle be perpendicular to it's initial velocity?

I am learning kinematics with vector analysis. I was given the position equation:$\mathbf{r} = 10t\hat{\mathtt{i}} + (20t-5t^2)\hat{\mathtt{j}}$. It asks me the time when the velocity of the particle ...
0
votes
1answer
44 views

Derivation of vector cross product [duplicate]

Everyone of us know about the vector cross product. But I wonder, how the formula of $AB\sin\theta$ has been derived? Can anyone help?
0
votes
1answer
11 views

Clarification needed:Projection Or Whole Length to be considered during integration

Sometimes in magnetism,electrostatics,friction problems when a force is acting over a curved we usually take the net projection of the curved path as the distance(to avoid integration).But it certain ...
2
votes
2answers
50 views

Geometric definition of the Lorentz inner product

In Euclidean space one can define the dot product as projecting one vector to the other and multiply the length of the projected vector with the length of the other vector. This definition doesn't ...
6
votes
6answers
594 views

Is there a physical interpretation of a tensor as a vector with additional qualities?

What is a tensor? has been asked before, with the most highly up-voted answer defining a tensor of rank $k$ as a vector of a tensor of rank $k-1$. But if a scalar is defined as a physical quantity ...
1
vote
3answers
96 views

Find time-parametrization given path and speed of a particle

Consider a particle in two dimensions with position vector $r(t)=<x(t),y(t)>$ and the shape of the path is described by a function $y(t)=f(x(t))$ (Thus $r(t)$ is a parametrization of $f$ with ...
0
votes
2answers
48 views

What should the brake force in this problem be? [closed]

Alright so I think I know how to do this but I require help in calculating what acceleration would be in terms of some sort of friction coefficient. So model a particle going down a hill. The slope ...
0
votes
2answers
32 views

Distance traveled from displacement

I am currently reading a book called Physics for Scientists and Engineers by Serway. While reading the chapter about 2-dimensional kinematics, I asked myself a ...
2
votes
3answers
139 views

Vector decomposition validity

Is force or field decomposition into component vectors always valid? Lets say a constant electric field $\vec{F}$ is acting in space such that it makes an angle $\phi$ with respect to the horizontal ...
2
votes
2answers
86 views

What coordinate systems allows the magnitude of the basis vectors to change with position?

I'm familiar with coordinate systems where the direction of the basis vectors changes with position, but I haven't come across any where the relative magnitude of the basis vectors themselves are ...
0
votes
2answers
121 views

Orientation of a rocket going in a circle?

This problem is from my physics homework: A rocket is moving at constant speed in a perfect circle in deep space, far away from any planets or stars. The diagram below shows the circle the ship ...
0
votes
3answers
89 views

Difference between $|d{\bf r}|$ and $d|{\bf r}|$

What is the difference between $|d{\bf r}|$ and $d|{\bf r}|$ and why are both of them not always equal to each other? My question might seem stupid to some and will probably get downvoted but I have ...
0
votes
2answers
68 views

Is torque still a vector in 2 Dimensions?

In 3D, torque is defined as $\vec{r} \times \vec{F}$ which is a vector, therefore having both a direction perpendicular to the plane of $\vec{F}$ and $\vec{r}$ and a magnitude of ...
6
votes
2answers
816 views

Understanding the difference between co- and contra-variant vectors

I am looking at the 4-vector treatment of special relativity, but I have had no formal training in Tensor algebra and thus am having difficulty understanding some of the concepts which appear. One ...
2
votes
1answer
552 views

Relative wind velocity explanation - understanding Irodov problem 1.6

I am having trouble understanding the reasoning behind the solution in this Irodov General Physics problem. The problem is 1.6: 1.6. A ship moves along the equator to the east with velocity vo = ...
0
votes
2answers
167 views

Cross product and the right hand rule - what is the intuition behind it? [duplicate]

I understand that by convention, the cross product is defined to be the vertical projection of vector $A$ on $B$ in the case of $A \times B$. But the vertical projection of $A$ on $B$ would still be ...
1
vote
3answers
72 views

Is there a general rule for determining the direction of tension force?

Tension, for me, is a tricky thing. After finishing a related chapter of my book and watching a video, I still can't get a hang of it. Here is a situation: My knowledge is that tension, just like ...
0
votes
2answers
35 views

Is the displacement vector tangent to the circular path?

My book says that when a mass travels in a curved path, like a circle for example, the instantaneous velocity and displacement vectors are both tangent to the path. I agree that velocity vector ...
0
votes
1answer
30 views

How do I get the angle for the $x$ and $y$ component of the electric field for four equidistant particles?

Four particles form a square of edge length $a= 5.00\ cm$ and have charges $q_1= +10\ nC$, $q_2=-20\ nC$, $q_3=20\ nC$, and $q_4=-10\ nC$. In unit vector notation, what is the net electric field the ...
1
vote
1answer
62 views

Coulomb's law with an $r^3$, not $r^2$, in the denominator [duplicate]

I am reading an older physics book that my professor gave me. It is going over Coulomb's law and Gauss' theorem. However, the book gives both equations with an $r^3$, not $r^2$, in the denominator. ...
0
votes
1answer
26 views

Co-ordinate rotations

I need help transforming a magnetic field vector from one co-ordinate system to another. I have the components of the Earth's magnetic field in a co-ordinate system with z facing radially into the ...
5
votes
2answers
309 views

How does one write Newtons 2nd Law using the language of forms?

Newton's second law says that $F=ma$. Supposing that the force is conservative and can thus be expressed in terms of a potential $V$ we have that $F=-dV$. We have that $V$, being a function, can ...
1
vote
1answer
31 views

A way to determine if a body accelerates or loses speed at a certain time

With given vectors for acceleration and velocity, is there a way to determine if a body accelerates or decelerates at a certain time-interval? Can this be determined, for instance, by simply observing ...
7
votes
2answers
235 views

What does it mean to transform as a scalar or vector?

I'm working through an introductory electrodynamics text (Griffiths), and I encountered a pair of questions asking me to show that: the divergence transforms as a scalar under rotations the ...
18
votes
5answers
16k views

How can area be a vector?

My professor told me recently that Area is a vector. A Google search gave me the following definition for a vector: Noun: A quantity having direction as well as magnitude, esp. as determining ...
0
votes
1answer
50 views

Explain how $\Delta v_{\perp}=v\Delta\theta$

In The Feynman lectures, under the chapter entitled Vectors, Feynman writes: My two intimately related questions are: 1) What does he mean by the magnitude of velocity? is he talking about the ...
0
votes
3answers
162 views

Animating an Acceleration Vector - Acceleration of object on a crested path in gravitational field

So I was reading in Chapter 3 of my textbook, Sears & Zemanksky's University Physics with Modern Physics by Young and Freedman, 13th Edition, and the discussion took us to a definition of the ...
0
votes
1answer
78 views

Vector product in a 4-dimensional Minkowski spacetime

I'm studying relativity and I lost track of interpretation along the mathematical formalism. What does vector product mean as an event? I mean, how must one interpret the result of the vector product ...
1
vote
2answers
90 views

What does it mean by saying the generators of translations transform as vectors under the Lorentz Group?

The commutator of generators of Lorentz transformation and translation is as follow: $$[M^{\mu\nu},P^\sigma]=i(P^\mu\eta^{\nu\sigma}-P^\nu\eta^{\mu\sigma} ).$$ Then from this we usually say that the ...
0
votes
0answers
25 views

Does dimensionality determine the net effects of randomly oriented forces on an object?

My question relates to the orthogonality of random vectors in high dimensional space, and the relationship of random vectors as a function of dimensionality. My question can be formulated as a ...
0
votes
1answer
61 views

Why would the norm of these vectors be 1?

Let a Cartesian coordinate system $uOx$ coincides with a vertical plane so that $Ou$ is the horizontal axis and $Ox$ is the axis oriented vertically upwards (see Fig. 1). We are looking for the ...
0
votes
3answers
165 views

resultant of 3 vectors along sides of equilateral triangle [closed]

It is a homework problem, but I really don't quite understand the question. It reads- "3 forces of magnitudes 10N, 20N, and 30N acting on a point are parallel to the sides of an equilateral triangle, ...
6
votes
3answers
1k views

Does spacetime position not form a four-vector?

When one starts learning about physics, vectors are presented as mathematical quantities in space which have a direction and a magnitude. This geometric point of view has encoded in it the idea that ...
2
votes
0answers
43 views

Moment line of action

I am having trouble understanding a moment's line of action. Lets say we have door hinge of $L$ length and push down on it with $X$ force. The moment at the begin $(O)$ of the hinge would then be ...
0
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1answer
69 views

Are perpendicular components special in vectors?

We can split a vector (velocity/displacement vector) along any two directions as long as the resultant of the oblique components of the vector is same as my original vector. Similarly if we have to ...
1
vote
1answer
50 views

Clarifying some notation, the square of a vector derivative

I'm reading a text which asserts that, if $\vec{F}(\vec{x})=-\nabla V(\vec{x})$ then we define $$E = \frac{m}{2} \left( \frac{d\vec{x}}{dt}\right)^2-V(\vec{x}) \, .$$ However, I don't understand how ...
1
vote
3answers
391 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 ...
0
votes
4answers
149 views

Is magnitude of velocity same as speed?

Is magnitude of instantaneous velocity same as instantaneous speed? More specifically, is $$\left|\frac{d\vec{r}}{dt}\right| = \frac{d|\vec{r}|}{dt}\; .$$ Also Is it wrong to say that ...