Geometric object with magnitude (length) and direction.

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1answer
186 views

What is the physical interpretation of the dot/inner/scalar product of two vectors?

What is the physical interpretation of the dot/inner/scalar product of two vectors? See, if we multiply two scalars like 2*3 we say two times three is six. I also do understand multiplication of ...
2
votes
1answer
432 views

Line of action force

The task is to reduce the two forces into a single net force and then find the equation of its line of action. I chose to find the net force and momentum with respect to the origin. The magnitude of ...
2
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1answer
420 views

The curl of a special cross product

When given two vectors $\mathbf{A}$ and $\mathbf{B}$, the curl of the cross product of these two is given by ...
2
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1answer
91 views

$\hat{\imath}$ component of force exerted on an electron by a magnetic field?

The magnetic field over a certain range is given by $\vec{B} = B_x\hat{\imath} + B_y\hat{\jmath}$, where $B_x= 4\: \mathrm{T}$ and $B_y= 2\: \mathrm{T}$. An electron moves into the field with a ...
2
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2answers
423 views

Sum of all forces

Let us glue up these two images, where we get closed loop thrust of water. Force $F_3$ has direction $-x$ and force $F_2$ has $x$ direction. What is the sum of all forces? Can it be more than zero? ...
2
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1answer
191 views

Vector transformation in special relativity

Please note that I am very new on this website so have some difficulties in writings as required here but trying really hard to learn quickly. La-Tex is the main problem but please understand me that ...
2
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2answers
84 views

Another question about Shankar's notation

I have another question on the notation in Shankar. I think it's sloppy, but I also may just be misunderstanding it. Again, this is at the very beginning of the math intro. He has: $$a\left| V ...
2
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1answer
57 views

The subtle differences between angular momentum and centrifugal force?

I am a mathematician wanting to understand the differences between the concepts of angular momentum and centrifugal force. The following two ideas are clear to me from a physical point of view, but ...
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2answers
44 views

Another condition of calculating work

Let's imagine that there is a box placed at the corner of a table, and I push it so that my applied force makes an angle of 30° from the table's surface. The box would move and, due to the effect ...
2
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1answer
114 views

Understanding vectors in an example

I just read an example of vectors in my book which is confusing me. Three particles A,B and C are at the vertices of an equilateral trinagle ABC. Each of the particle moves with constant speed v. ...
2
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1answer
766 views

Laws of addition of Vectors

How Triangle Law and Parallelogram law of addition of Vectors are different?Ain't they. Please don't tell me the things written in book......give me the appropriate reason.And how do i distinguish ...
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2answers
822 views

I don't understand the idea of perpendicular vectors being independent of each other?

So problem 71-75 is about vectors. The problem says: A river has a current flowing with a velocity of 2.0 meters per second due east. A boat is 75 meters from the north riverbank. It travels at ...
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1answer
34 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
759 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
569 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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2answers
70 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
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2answers
554 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
106 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 ...
2
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3answers
157 views

Force vs. impulse: what is the math description of their interaction?

In this image there are two forces acting on the same body, and we can decribe them mathematically and geometrically using vectors and the palallelogram rule. NOw, suppose the box (stone, ...
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2answers
106 views

Differentiating a vector product

$$m_i\mathbf{r}_i\times\frac{\mathrm{d}^2\mathbf{r}_i}{\mathrm{d}t^2} = \frac{\mathrm{d}}{\mathrm{d}t}\biggl(m_i\mathbf{r}_i\times\frac{\mathrm{d}\mathbf{r}_i}{\mathrm{d}t}\biggr)$$ I do not ...
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7answers
24k 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
563 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
1k 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
929 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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1answer
222 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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3answers
12k views

Why work is a scalar and not a vector?

Work (in physics) is a scalar but why? and why not a vector?
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2answers
150 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
151 views

A simple way of calculating Euler Angles from Rotation Matrix — help!

This is a follow up of this question : I have the rotation matrix $$ \left( \begin{matrix} a_{11} & a_{12} & a_{13}\\ a_{21} & a_{22} & a_{23}\\ a_{31} & a_{32} & ...
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2answers
496 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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1answer
44 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
69 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
71 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
201 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
1k 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
3k 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
125 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
267 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
263 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
330 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
5k 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
35 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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1answer
24 views

How can kinetic energy be conserved in an elastic collision

How can kinetic energy be conserved in an elastic collision as collision is said to occur between two bodies if they physically collide against each other or if the path of one of then is affected by ...
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1answer
71 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
103 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
137 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
217 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
169 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
104 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
526 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
17 views

Computing the Initial Velocity of an orbiting body

I'm working on a simulation program that replicates the movement of planets around a large celestial body (the sun). This is a three dimensional simulation that uses vectors. At present, I'm ...