Geometric object with magnitude (length) and direction.

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577 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
726 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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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
14k 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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1answer
41 views

Component of Component of a vector [duplicate]

NOTE : By perpendicular component of $\vec{F}$, I mean a vector which is a component of $\vec{F}$, but perpendicular to it. In the image above, the red vectors are a possible set of rectangular ...
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2answers
65 views

What is the power given by centripetal force?(in circular motion)

A particle of mass $m$ is moving in a circular path of constant radius such that the centripetal acceleration is varying with time as $a_c = k^2rt^2$ where $k$ is constant. The power given to ...
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2answers
95 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
80 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
122 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
1k 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
175 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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1answer
218 views

What are some good resources for learning how to apply vectors in physics?

Although I don't have any problems with vectors when using them in Mathematics but I am having a hard time using them in physics. It is really frustrating me. Can you please recommend me some good ...
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5answers
140 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
262 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
277 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
119 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
707 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
52 views

What is the difference between a tensor, vector, and a matrix? [duplicate]

I'm currently going through notes on a physics course and I'm having trouble understanding the difference between a tensor, a vector, and a matrix. I know that a vector is a kind of tensor and that a ...
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1answer
39 views

Probable mistake in the derivation of the vector form of Biot-Savart's Law

In the course of "Classical Electrodynamics", our professor stated Biot-Savart's Law as follows: $$\vec {dB}=\frac{\mu_0}{4\pi}\cdot \frac{i\vec {dl} \times \vec r}{r^3}$$ Then he proceeded to derive ...
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2answers
48 views

Motivation for usage of 4-vectors in special relativity

I understand that if one considers a 4-dimensional space-time from the outset then 4-vectors are the natural quantities to consider (as opposed to 3-vectors as in Newtonian mechanics), since the ...
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1answer
58 views

what is the energy required to change only direction of a vector? [closed]

Does change in velocity vector change Kinetic energy of a system? Does any energy change when we change direction of a vector of a system?
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1answer
41 views

Correct way to write Pauli matrices

This is purely a question of notation for the Pauli matrices. What is the correct way to write them for use as operators? Would I just write the vector of the matrices as a vector i.e ...
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2answers
94 views

Physicists definition of vectors based on transformation laws

First of all I want to make clear that although I've already asked a related question here, my point in this new question is a little different. On the former question I've considered vector fields on ...
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1answer
75 views

Understanding elastic collisions of objects with the same velocities

I am having trouble understanding the following statement from my book: The law of cosines tells us that if the sides of a triangle obey the Pythagorean formula, they must form a right triangle. ...
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1answer
28 views

Is it possible to determine when an accelerometer is in a vibrating state compared to a non-vibrating state?

I would like to know if so, how raw 3-axis accelerometer data could be analyzed and manipulated real-time to register periods of vibration. The device being used has a max sample rate of 62Hz (I ...
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1answer
133 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 ...
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1answer
79 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 ...
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2answers
90 views

Clarification on meaning of scalar in math and scalar in physics

When a mathematician says something is a scalar, say on the plane, they mean that it associates to points on the plane real numbers. When a physicist says something is a scalar, they mean that if we ...
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3answers
811 views

Why do we need both dot product and cross product?

I was looking for an intuitive definition for dot product and cross product. I have found two similar quesitions in SO, but I am not satisfied with the answers. Finally I found a possible answer here. ...
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2answers
403 views

Derivation of Jefimenko's Equation in Jackson's EMT book

I have been trying to understand the derivation of Jefimenko's equation in Jackson on p.246-247 which can be seen in the photographs attached. First of all I did not fully comprehend the ...
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1answer
2k views

Difference between Speed and Velocity

What is the difference between Speed, Velocity and Acceleration? Could any one describe it pictorially?. I am more over confused even after investigating many times. I am unable to relate myself ...
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2answers
227 views

Relation between Vector space $V$ and its dual $V^{*}$ [closed]

I asked the same question in Math.SE, but I was suggested to ask it here as well. I am studying relativity, and as you know the theory extensively uses the notion of covariant and contravariant ...
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2answers
75 views

Can one representation of a projector operator be re-arranged to get another?

I have a vector space $V$ and a subspace of $V$, $W$. Let $P$ be the projection operator for subspace $W$. Also let the dimension of $W$ be $d$. Also I have two orthonormal basis $(a_1,a_2,...a_d)$ ...
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2answers
41 views

Change of vectors [closed]

We have two vectors $F1$ and $F2$ as shown in figure. The change of vectors is shown as $F2-F1$. Why it is it rather than taking negative of vector $F2$ i.e. $-F2$ and then adding it by head-to-tail ...
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5answers
4k views

How to find total force on an object?

If there are a multitude of forces acting on an object in different directions, how do we find the TOTAL force? I know we add up the $ x $- and $ y $-components of the forces individually, but how do ...
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2answers
619 views

Free vs bound vectors and torque

When considering basic Newtonian mechanics, we can treat vector as free and move their point of application at will. This is consistent with the affine nature of Euclidean space. However, when ...
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1answer
631 views

Rate of change of a vector

I'm studying the book "Classical Mechanics" by Goldstein together with a coursebook my professor provided. I'm having trouble grasping how to intuitively determine what the rate of change of a vector ...
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2answers
726 views

Angle needed for object A to intercept with object B

Object B is 15 degrees East of North at a distance of 20km/h. Object B is moving at an average speed of 30km/h in the direction 40 degrees East of North. If object A is capable of moving at 100km/h, ...
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1answer
121 views

Commutation of abstract $O(3)$ generators and vectors [closed]

I've been given the following problem, and I'm quite lost with it. Let $L_1$, $L_2$, and $L_3$ denote the abstract $o(3)$ algebras. You are given that $\vec{A} = (A_1, A_2, A_3)$ and $\vec{B} = ...
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1answer
329 views

Spinor formalism in QFT

We can describe fields by two formalisms: vector and spinor. This is the result of possibility of representation of the Lorentz's group irreducible rep as straight cross product of two $SU(2)$ or two ...
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1answer
2k views

Relative Velocity problem

I was solving many problems on relative velocity and observed that when the question asks, "what is the minimum time taken by the boat/man to cross the river.?" so the solution says that he ...
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1answer
159 views

How to add magnitude data in an ENU coordiante system

I have water velocity data taken in an ENU (East, North, UP) or XYZ coordinate system. The data is contained in 3 columns like this: ...
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1answer
873 views

Resultant vector problem

$\newcommand{\v}[1]{\vec #1}\newcommand{\i}{\hat i}\newcommand{\j}{\hat j}$ Problem statement (1,2) A shopper at the supermarket follows the path indicated by vectors $\v A, \v B, \v C, \v D$ in ...
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1answer
1k views

Is it possible to prove that the curl of a gradient equals zero in this way?

If $(\nabla\times\nabla\Phi)_i = \epsilon_{ijk}\partial_j\partial_k\Phi$, where Einstein summation is being used to find the $i$th component... Using Clairaut's theorem $\partial_{i}\partial_{j}\Phi ...
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1answer
795 views

Bra space and adjoint vectors

If I'm not wrong, a bra, $ \langle \phi_n | $, can be thought as a linear functional that when applied to a ket vector, $| \phi_m \rangle$, returns a complex number; that is, the inner product it's a ...
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2answers
1k views

What is the physical meaning of a dot product and a cross product of vectors? [duplicate]

My teacher told me that Vectors are quantities that behave like Displacements. Seen this way, the triangle law of vector addition simply means that to reach point C from point A, going from A to B ...
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1answer
51 views

Why is the spatial term for contravariant 4-gradient negative, whereas for other 4-vectors it is the covariant part that is negative spatially?

The contravariant 4-displacement is: $${x}^{\alpha} = (ct,\mathbf{r})$$ And the contravariant 4-gradient is: $${\partial}^{\alpha} = (\frac{1}{c}\frac{\partial}{\partial{t}},-\nabla)$$ From what I ...
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1answer
47 views

Vector Navigation and equations [closed]

So I am taking a grade 12 physics online course and I am getting stuck on the Vector Navigation equations as there isn't much explanation in my course. The following text is found in my online ...
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2answers
58 views

Time dependent ODE involving cross product

Let $\vec{A}$ be any time dependent vector quantity, and $\vec{\alpha}$ any constant vector. I was told that a solution to the differential equation $$ \dot{\vec{A}} = \vec{\alpha}\times\vec{A} $$ is ...
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3answers
102 views

How to apply a force vector to a position vector?

A particle is present in the two dimensional space. It's position is given by the vector: $$x = \begin{pmatrix} |x| \cos(\theta) \\ |x| \sin(\theta) \end{pmatrix}$$ It experiences a force of: $$ F = ...