Geometric object with magnitude (length) and direction.

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1answer
37 views

Asking about centrepetal acceleration

please look at the fig first 1) How can you claim that the triangle ABC is same as the triangle PQR? 2) How can you claim that the angle between V1 and V2 is same as the angle between AC and AB? ...
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3answers
1k views

What is the general approach to calculating time of impact in 3D?

Given two objects a and b moving at fixed velocities, how would you determine (a) whether they will collide at all, and if so, (b) time of impact? (Let us assume these are spherical bodies each with ...
2
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1answer
760 views

Combined Gravitational Force Vectors in a Spherical Coordinate System

Asking a question here is quite intimidating for me -- while I love Physics, my high-school understanding only allows me to go so far... I've been trying to solve this problem for the last couple of ...
2
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0answers
33 views

Difference between vacuum and pseudovacuum vector?

What exactly is the difference between the vacuum and pseudovacuum vector? In my case the ground state of a system is the vacuum vector and by letting operators act on that vacuum vector magnons are ...
2
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2answers
98 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 ...
2
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0answers
153 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 ...
2
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2answers
73 views

what does magnetic field vector mean?

I am trying to understand what a magnetic field vector tells us about the magnetic field. I understood that a vector is just a representation of a point and how much it is moved in x,y and z direction ...
2
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1answer
44 views

ϕ-component of equation of moition: proving a relationship [closed]

I have the following velocity vector (in spherical polars): \begin{equation} \textbf{v} = u \hat{\textbf{r}} + v_{\phi}\hat{\boldsymbol\phi} \end{equation} Where $u(r) = u$ and $v_{\phi} (r) = ...
2
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1answer
728 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 = ...
2
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2answers
672 views

2D - Kinematics - Linkage System using Vector Algebra [closed]

I have this question that I dont know how to solve correctly : My question is, how do I find $V_B$ ? I will find the angular velocities myself, but I want to know the method to get $V_B$ ? I know ...
2
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0answers
133 views

Surface normal on the earth to the sun at a given point in time

How complicated is it to calculate a surface normal on the spherical approximation of the earths surface pointing towards the sun at a given point in time? What I try do is to highlight a small area ...
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2answers
169 views

Is a vector field not a vector quantity?

I'm trying to make sense of Poisson bracket relation $$\{L_i,A_k\}_{PB}~=~\epsilon_{ikl}A_l,\tag1$$ where $L_i$ is $i$th component of angular momentum, $A_k$ is $k$th component of an arbitrary ...
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7answers
72k views

What does the magnitude of the acceleration mean?

I am a little confused as to what the magnitude of acceleration is and what it means.
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4answers
983 views

Vectors with more than 3 components

I have some confusion over Vectors, Its components and dimensions. Does the number of vector components mean that a vector is in that many dimensions? For e.g. $A$ vector with 4 components has 4 ...
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3answers
2k views

Can vectors in physics be represented by complex numbers and can they be divided? [closed]

Below is attached for reference, but the question is simply about whether vectors used in physics in a vector space can be represented by complex numbers and whether they can be divided. In ...
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5answers
2k views

What is the direction of a point vector. A vector with magnitude 0? [closed]

A simple question : Can a point on a piece of paper represent a vector ? Can i say that a point "B" ( magnitude =0, because it's a point) , is having direction towards +x axis ? Thanks
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2answers
319 views

Directionality of angular momentum

I was told that the sum of linear and angular momentum is conserved. Given that angular momentum's direction as a vector is completely arbitrary (I believe there is no physical reason for choosing ...
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1answer
643 views

Why consider only direction cosines?

Why are these called direction angles? Why do we consider only direction cosines and not direction sines or tans. What is its actual significance? And How to use them? Why are they called ...
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2answers
84 views

Understanding Tensor-operations, covariance, contravariance, … in the context of Special Relativity

I'm currently learning about special relativity but I'm having a really hard time grasping the Tensor-operations. Let's take the Minkowski scalar product of 2 four-vectors: $$\pmb U . \pmb V = ...
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3answers
903 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 ...
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2answers
116 views

More Vector Product Possibilities?

There seem to be two primary means of "multiplying" vectors in physics, the cross product and the dot product. Assuming the angle between vectors is defined as $(a)$, the dot product between vectors ...
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2answers
262 views

If an asteroid were threatening the Earth, could I deviate it just by jumping on it?

An impact by a 10 kilometres asteroid on the Earth has historically caused an extinction-level event due to catastrophic damage to the biosphere. There is also the threat from comets coming ...
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2answers
152 views

Inner products with orthonormal bases

Probably a stupid question here - I think it's a case of me not having sufficient mathematical background to follow this through. In Leonard Susskind's Theoretical Minimum book, he represents the ...
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2answers
282 views

Question on notation in Shankar's Quantum Mechanics - math intro on vector spaces

I'm just beginning Shankar's 2nd edition Quantum Mechanics and having some trouble with notation. He defines his vectors as "$\left|V\right>$" . And with a scalar multiplier as "$a\left|V\right>$" . ...
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2answers
341 views

Point charge potential (sign problem)

I'm a bit embarrassed, but I'm not able to compute the electric potential at point $P$ (at a distance $R$ from the origin) generated by a positive unitary point charge in the origin with the right ...
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2answers
106 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 ...
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1answer
1k views

Is instantaneous velocity a scalar or a vector?

So this is a simple question that I have been confused about. Last night I was in a discussion with a friend, and we somehow ended up on this topic. He believes that instantaneous velocity is a ...
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1answer
260 views

General definition of vector, spinor, and spin

I am looking for basic and exact definitions of fundamental physical concepts in graduate level. I reach this following definitions. Could you please help to improve these definitions. Spin: ...
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1answer
275 views

What kind of physical quantity is angular displacement?

Angular Displacement is neither a vector nor a scalar. What type of physical quantity it is? Are there any other examples of that physical quantity?
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1answer
92 views

Curl of a vector field with two different systems of coordinates

Let $$\mathbf{H} = H_x \mathbf{u}_x + H_y \mathbf{u}_y + H_z \mathbf{u}_z$$ be a vector field whose components are defined with respect to the unit vectors $\mathbf{u}_x$, $\mathbf{u}_y$ and ...
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1answer
1k views

Intuitive meaning of Dot Product [duplicate]

I know intuitively that the Cross Product of two vectors $\vec{A}$ and $\vec{B}$ represents another vector $\vec{A \times B}$ perpendicular to it. In study of physics we come across this situation a ...
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2answers
2k views

Electromagnetic wave propagation through two lossless dielectrics

In Elements of Electromagnetics (Sadiku, 3rd edition, Section 10.8), the author says to consider two lossless dielectric materials joined at an interface $z=0$. Here two lossless dielectric materials ...
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2answers
4k views

Angular displacement and the displacement vector

I've been recently introduced to angular displacement, and I'm a little bit confused about it. I think that displacement which is a vector and which is defined as the shortest distance between any two ...
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2answers
133 views

Points in Spacetime

Assume there are two points in spacetime $a=(t,x,y,z)$ and $a'=(t',x',y',z')$. Let's say that the first one is in the origin of spacetime i.e. $a=(0,0,0,0)$. The point $a'$ has two possibilities ...
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2answers
328 views

Conservation of Linear Momentum with respect to a given direction

Is linear momentum conserved in any direction? More specifically, if you project all momentum vectors in a system onto another vector, will momentum be conserved? I know that momentum is conserved ...
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2answers
536 views

Why no basis vector in Newtonian gravitational vector field?

In my textbook, the gravitational field is given by$$\mathbf{g}\left(\mathbf{r}\right)=-G\frac{M}{\left|\mathbf{r}\right|^{2}}e_{r}$$ which is a vector field. On the same page, it is also given as a ...
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2answers
697 views

Vectors, Component Addition, and Significant Figures

I have two vectors $\vec{A}$ and $\vec{B}$ and I need to find the x- and y-components of $\vec{C} = \vec{A} + \vec{B}$. Here's what I have so far: $$|\vec{A}| = 50.0 \mathrm{m}, \theta = ...
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2answers
1k views

Acceleration vector - deceleration vs direction

If acceleration of something $= - 10 \text{ m s}^{-2}$ And forwards is define as north. Does that mean the object is getting slower (decelerating) or accelerating in the reverse direction (south) ...
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2answers
12k views

The resultant of two forces acting at any angle?

I am studying about forces as vectors. And they give me this equation: $c^2 = a^2 + b^2 - 2ab \cos C$ Can anybody explain me the second part of the equation? I perfectly understand $c^2 = a^2 + b^2$ ...
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2answers
94 views

Two different formulas

My problem is simple : given a particle of mass $m$, charge $q$ and velocity $\bf{v}$. If $\bf{A}$ denotes the magnetic potential satisfying $\bf{B}= \nabla \times \bf{A}$. I want to etablish the ...
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1answer
68 views

When to use a whole vector approach vs an energy approach?

My professor has just introduced two new ways to solve projectile motions. One approach involve using trigonometry and vectors and the other involves using the idea of conservation of energy. My ...
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2answers
112 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 & ...
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1answer
747 views

Vectors in non-orthogonal systems

In a non-orthogonal coordinate system, what is the physically significant difference between the components of a vector on the skew axes and its projection onto each axis? Why would one want to find ...
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3answers
164 views

Why should multiplication of a ket vector by a complex number change only its “direction”?

Dirac argues on page 17 of his book, The Principles of Quantum Mechanics, that multiplication of a ket by a complex number shouldn't change the state this ket represents. But then concludes: Thus ...
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5answers
127 views

Why is the independence of orthogonal vector-quantities always implicit in books/lectures?

The "theorem" that I can "just" separately deal with orthogonal quantities (like horizontal and vertical force or velocity, etc), I never found explicitly mentioned, but just implicitly in the ...
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1answer
250 views

Understanding vectors in physics: notation

We have the formula for the Lorentz force $$\textbf{F} = q \space(\textbf{E} + \textbf{v} \times \textbf {B})$$ This is a simple formula you learn in high school, but I'm interested to self-study ...
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1answer
259 views

rotation matrix - why am I thinking this wrong?

The rotation given in Question 1 part ii) doesn't match with this wikipedia link http://en.wikipedia.org/wiki/Rotation_matrix. $$ \begin{array}{lcl} x' &=& x \cos\theta - y \sin\theta \\ y' ...
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3answers
118 views

Currents and magnets

I've watched this video on YouTube by Sixty Symbols entitled "Currents and Magnets". In the video, the professor demonstrates the expansion of a wire due to current heating it up and he also ...
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2answers
664 views

Potential of surface charge

I have a question about the $ \hat{n} $ in this formula $\sigma = P \dot{}\hat{n}$. Why do sometime in my book they get $\sigma = P \cos{\theta}$ for a sphere. Isn't $\hat{n} = r$ ? And then in ...
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1answer
457 views

Is there a more clever way to apply the cross product of two vectors to magnetism?

I am just beginning to learn magnetism and my book used two ways to define the force caused by the magnetic field, brushing over the latter. The first: $$F = q v B \sin (\theta).$$ And: ...