Geometric object with magnitude (length) and direction.

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221 views

A whole lot of doubts on Lorentz representation

Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on ...
2
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1answer
110 views

Considering the theory of special relativity: Is torque still a vector?

Considering the theory of special relativity: Is torque still a vector? In classical mechanics it is easy: You have 3 axes and thus 3 planes. Every plane has its own torque so torque has 3 ...
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2answers
6k views

split gravitational force into x, y, and z componenets

I am writing a program for a computer science class in which I am doing an n-body simulation in 3-dimensional space. Currently, I have figured out the gravitational force along the hypotenuse between ...
2
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3answers
286 views

Why are triangles drawn like so when working with gravity on an inclined plane?

This is my first year as a physics student, and I've never learned about vectors past a basic level, so this is confusing me. When we have gravity on an inclined plane, we separate it into two ...
2
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2answers
239 views

Reflection - reaction force direction

Let's say an object hits a wall. When the object is reflected does the direction of the reaction force caused on the wall look like the red arrow? Does that direction depend on how "strong" object is ...
2
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2answers
356 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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4answers
14k views

What is the difference between dot and cross product?

What is the difference between dot product and cross product? Why do we use cross product to find torque, why can't we use dot product? Also we use dot product to find work done and not cross ...
2
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4answers
2k views

Sum of acceleration vectors

If a point mass has some accelerations $\mathbf{a_1} $ and $\mathbf{a_2} $, why is mathematically true that the "total" acceleration is $\mathbf{a}= \mathbf {a_1}+\mathbf {a_2}$?
2
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2answers
139 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 ...
2
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1answer
84 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. ...
2
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1answer
181 views

What type of mathematical structure is a physicist's definition of a vector space?

A vector space as defined by a mathematician lacks the invariant scalar product that lies at the heart of what I would define as a physicist's definition of a vector space that models the physical ...
2
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3answers
20k views

Vertical and horizontal components of forces and vectors

I'm getting a bit confused when finding components of vectors and forces. In problems for vectors, I've always known that if you want to get the components of a vector, you would use the following: ...
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2answers
585 views

About vector form of friction

I read a text on mechanics and in the chapter on friction, there written that the kinetic friction is in the form $$f_k = \mu_k F_N$$ where $f_k$ is the kinetic friction, $\mu_k$ is the kinetic ...
2
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2answers
352 views

Coordinate transformation from earth to solar

I am building a 3d model of the solar system and need to figure out the position of the pole stars of each planet in order to tilt the planets in the correct direction the correct amount. I've already ...
2
votes
1answer
93 views

What's the difference between classical and quantum vector superposition?

$(1)$Since quantum-mechanical states between two consecutive measurements are represented as superposition of orthonormal basis vectors in a vector space, at first glance it seems like it makes sense ...
2
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4answers
325 views

Normal Vectors to these Hypersurfaces on a Lorentzian Manifold

With respect to the coordinates $(x^{0},x^{1},x^{2},x^{3})=(v,r,\theta,\phi)$, we have the following components of the metric tensor: $\begin{bmatrix} g_{00} & g_{01} & g_{02} & ...
2
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2answers
137 views

How do you pronounce $\vec{A} \cdot \vec{B}$ and $\vec{A} \times \vec{B}$? [closed]

I'm French. I would like to know: How do you pronounce $\vec{A} \cdot \vec{B}$ : "A scalar B" or "A dot B" ? How do you pronounce $\vec{A} \times \vec{B}$ : "A vectorial B", "A vector B", "A cross ...
2
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2answers
98 views

Orthogonality in curved space/spacetime

When are two vectors orthogonal in curved spacetime? From wikipedia: "In 2-D or higher-dimensional Euclidean space, two vectors are orthogonal if and only if their dot product is zero, i.e. they ...
2
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2answers
886 views

Why do smaller objects become harder to break?

When grabbing a typical tree branch of at least two feet, it's so easy to snap with a less than one inch circumference that even a toddler can do it. However, after breaking it, the smaller halves ...
2
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1answer
2k views

Which are other anomalies like Divergence of 1/r^2?

As one might have learned in the basic science (ex. Electrodynamic theory), when we apply the divergence theorem to the vector function like 1/r^2 with it pointing in the radial direction (like ...
2
votes
1answer
174 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?
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2answers
156 views

Making sense out of covariance and contravariance

I just read about co- and contravariant vectors and I am not sure that I got it right: If we imagine that we have a n-dimensional manifold $M$ then a tangent space is spanned by the vectors ...
2
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1answer
245 views

Extension of Lami's theorem

I was experimenting with the triple scalar product and forces in equilibrium when I came to this result: Consider 4 forces $ \pmb{F_i}$ for $i=1,2,3,4$. $\pmb{F_i}=F_i\hat{e_i}$ where $\hat{e_i}$ is ...
2
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1answer
73 views

4-vector velocity to Newtonian?

The four-vector condition for a particle free of forces is: $\frac{du}{dτ} = 0$ and the equivalence of this to the statement of newton's first law follows from the expression for four-velocity: ...
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2answers
77 views

Why should an area vector point normal to the surface?

Why is it that the direction of an area vector should be always along the normal drawn to the surface? Can't it also be some other angles with the plane?
2
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1answer
6k views

What does relative to something mean?

I just started learning about vector components and relative motion. I don't understand what relative to something means. I looked online but none of the explanations are helpful. If someone could ...
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1answer
8k views

How do I split a vector into components parallel and perpendicular to a known line?

Given $\mathbf{F}=\langle 7.20,−12.0,28.2\rangle\text{ Newtons}$, find the component of $\mathbf{F}$ that acts perpendicular to member DA such that the vector addition of the perpendicular and ...
2
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5answers
342 views

How does this shell hit the aircraft?

A fighter aircraft is flying horizontally at an altitude of 1500m with speed of 200m/s. The aircraft passes directly overhead an anti-aircraft gun. The muzzle speed of the gun is 600m/s. ...
2
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3answers
1k views

negative vectors (eg velocity)

If you said someone had a velocity of -12mph and they were traveling north? Wouldn't it mean that they were traveling 12mph south? This is a quote from here: if something [object-x] moving to the ...
2
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2answers
87 views

Can an angle be defined as a vector?

In Classical Mechanics angular velocity, angular acceleration, torque and angular momentum can be defined as vectors with clear advantages such as the possibility to use vector product to simplify ...
2
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1answer
68 views

Sign of Gaussian surface that encloses negative charge

I can't solve a contradiction that have appeared in my head. Let's assume we have a negative charge, if we enclose it by a spherical surface and $A$ is surface of the sphere, then we will have ...
2
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3answers
92 views

What is “a vector of $SO(n)$”?

I'm watching (or trying to watch) this lecture from NPTEL on classical field theory. I've understood everything in the series up till this point, including the first half of the lecture on elementary ...
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3answers
231 views

Calculating vector to aim for moving asteroid (3D asteroid game)

Considering we're in a 3D system of coordinates: our ship is at point A, motionless our ship can shoot bullets, the speed of which is known the asteroid is at point B the asteroid is moving on known ...
2
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1answer
80 views

Torque on wire summarized with magnetic moment

The magnetic moment of a current-carrying wire loop $L$ is $$ \boldsymbol\mu = \frac I2\oint_L\mathbf{r} \times \mathrm{d}\mathbf{r} $$ so the torque it experiences under a uniform magnetic field ...
2
votes
1answer
394 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
580 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
119 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
732 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
230 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
votes
2answers
100 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
votes
1answer
105 views

What's the physical meaning of change in momentum vector?

If I there is a initial momentum of 10Ns upwards, and final momentum of 10Ns to the right, I can find the difference in momentum by drawing a triangle and finding the resultant vector. But, how is ...
2
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1answer
645 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 ...
2
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1answer
59 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 ...
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4answers
1k views

Why is force a localized vector and not a free vector?

A vector which is drawn parallel to a given vector through a specified point unlike free vector in space is called a localised vector. The effect of a force acting on a body depends not only on the ...
2
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3answers
185 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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1answer
176 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
2k 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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1answer
1k 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 ...
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2answers
487 views

Angular position vector?

I'm a mathematician, so I like my angular velocities to be vectors. It makes my angular momenta and torques vectors as well, and so they have nice operations I can do on them. Because of that, I pick ...
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2answers
2k 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 ...