Geometric object with magnitude (length) and direction.

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3
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3answers
543 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
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3answers
165 views

Confused about the direction of friction force

I'm really confused about the direction of friction force. I think about collision of two balls and think that "friction force is opposite to the relative speed of the contact point of the two ...
0
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3answers
227 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 ...
2
votes
2answers
97 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
votes
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 ...
1
vote
2answers
52 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 ...
0
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2answers
27 views

Nature of Pressure

Pressure is defined as force per unit area. Therefore, pressure = force divided by area. Since force and area are both vectors, how can we perform this division without violating the rule of vectors? ...
3
votes
1answer
499 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 ...
2
votes
1answer
724 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 = ...
1
vote
1answer
33 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 ...
1
vote
1answer
24 views

Laboratory fixed-vector components

What are laboratory fixed-vector components? I have an effective Hamiltonian derived from a 40-something year-old Chemical Physics paper. The article mentions the term laboratory fixed-vector ...
1
vote
1answer
41 views

Speed with wind resistance

This is probably a basic question, but it has been a while since I did anything like this. If a boat is sailing forward at speed $x$ and the direction of the wind, with magnitude $y$, is either equal, ...
0
votes
1answer
43 views

Why trajectories approach to origin tangent to the slower direction?

I am reading non-linear dynamics from Strogartz. Suppose, I have two solutions of a non linear system: $x(t) = x_0e^{at}$ and $y(t) = y_0e^{-t}$, where $a\in \mathbb{R}$. Now it is clear that,for ...
0
votes
1answer
46 views

Deriving Konopinski's Operational Definitions of Scalar and Vector Potential

In "What the electromagnetic vector potential describes", E. J. Konopinski asserts: Operational definitions of Φ, A should now be expected to stem from the equation of motion (2) when it is ...
0
votes
1answer
65 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 ...
0
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1answer
42 views

Electric Flux - Vector Components

How is $vcos(\theta)$ the perpendicular vector? I think I'm missing something fundamental in my trig and vector knowledge...
0
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1answer
51 views

Torque on shaft

Consider a generator which supply power using a shaft to a turbine. The torque applied on shaft by generator is $T$. As the shaft has constant angular velocity the turbine should also be applying ...
-1
votes
1answer
22 views

Vectors finding direction include the difference between “north of east” and “east of north”

In what direction is your friend from the starting point after skiing 3 km east and then 1.5 km north? so far I know that angle= tan-1(opp/adj)=(1.5/3.0) angle= ...
3
votes
0answers
109 views

Sound - for purposes of vibration

What is the best way to distribute noise from more than one source (I'm envisioning a system with many), within a dome, with the ground as its primary target, at optimal frequencies and volumes to ...
2
votes
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
votes
0answers
152 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
votes
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 ...
1
vote
0answers
27 views

How to find tangential and normal unit vector to a trajectory from the equation?

Considering a 2D motion in a plane and the equation of the trajectory of a point $y=f(x)$, I don't understand how exactly $\frac{\mathrm{d}y}{\mathrm{d}x}$ can be used. In particular if I'm looking ...
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0answers
45 views

Defining a room that is equally lit at every point

Imagine you were in a room designed such that no matter where in the room you stand, a sphere of volume 1 liter held at 2 meters above the ground would be exposed to the same amount of light. How ...
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0answers
40 views

Calculus/Vector Calculus and so on in special relativity book recommandation

I want to learn calculus 1,2,3 vector calculus, analysis and so on in special relativity. But I never found a good and clear book/source on it. Can someone recommend an easy book or internet source on ...
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0answers
35 views

What does 'vector-like' mean?

What are properties of vector-like field/particle? What's the counterpart of it? Chiral like?
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0answers
41 views

Why is the angular average of the direction of the momentum squared a third instead of one?

In the article http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf (in going from eq. (6.13) to eq. (6.14)) it is stated that ...
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0answers
68 views

Can you explain what's meant by “Effective Force” here?

A small cart is being pulled horizontally to the right with a $20$ lb force $\vec{F}$ making $45^\circ$ angle to the floor. What is the effective force moving the cart forward? Answer: since $\vec{F} ...
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0answers
34 views

What is a diffusionless fluid?

I'm taking a course in astrophysical fluid dynamics and have come across a problem involving "small diffusionless disturbances" of a fluid. Based on the nature of the course I expect the examiner to ...
1
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0answers
55 views

how to rotate scaled-vector (orientation) by scaled-vector (rotation)

Recently I seem to have gotten the physics-engine portion of my 3D simulation/game engine [apparently] working correctly. The most convenient way to store and compute position and orientation are in ...
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0answers
34 views

How do I show $e_r$ and its first- and second time derivative?

What does a charge q moving in a circular orbit with a constant velocity (a "rotating charge") and a stationary observer that measures the E field look like? And how do I show $e_r$ and its first- and ...
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0answers
138 views

Understanding unit vectors

Trying to understand how the unit vector ${\mathcal{\hat{r}}}$ defined as $\frac{r' - r}{|r' - r|} $ (where $r'$ is the source point) works in this problem: Work out the electric field, $E$, at point ...
1
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0answers
151 views

Phonon vectors and characteristic length interpretation

Basically I have a set of vectors of unit length, $\{\nu_i\}$, describing the movement of phonons (all orthogonal to each other), $\{\omega_i\}$. Lets say I only have two atoms, $m_1$ and $m_2$. In ...
0
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0answers
38 views

What is the meaning of “closure is lost” for a set of kets (or any members of a vector space)?

This is the closure relation in Quantum Mechanics: $$\sum_i |i\rangle \langle i| = 1 $$ which I understand as "the sum of the projections onto the basis vectors leaves the projected vector ...
0
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0answers
14 views

Relations between unit vectors in polar and curvilinear coordinates

I'm a bit confused about the relations between unit vectors in curvilinear and polar coordinates in a plane. Let $u_{R}$ be the radial unit vector in polar coordinates and $u_{N}$ the normal unit ...
0
votes
0answers
45 views

Direction vector for gravity

I have co-ordinate axes on the earth's surface (and I've been told these are the axes I have to use). Ignoring z, I have x and y axes. The question asks me to calculate the acceleration due to ...
0
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0answers
30 views

Why does the angular average of the divergence result in a factor 1/3?

In going from eq.(6.13) to (6.14) in http://www.nano.northwestern.edu/intranet/pubdocs/quasiclassical.pdf it is assumed that ...
0
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0answers
133 views

Accelerometer Pitch and Roll Calculation

I am developing an application for a device that needs to know its tilt/orientation, specifically, pitch and roll. Roll is positive if the right side of the device is elevated, and pitch is positive ...
0
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0answers
78 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 ...
0
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0answers
28 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 ...
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0answers
30 views

How do I evaluate this general magnetic dipole equation for this given setup?

This shouldn't be too hard a question (mostly focused on vector multiplication) but I'm still not confident in my answer. Basically, I am looking at the force between two magnetic dipoles and using ...
0
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0answers
38 views

The first term of Stokes Vector of natural light is zero?

Consider the electric field of a beam of natural light: $$ E(r,t) = E_0 \cos(k·r+wt) $$ Since this beam of light is natural, the vector E has all the components possible that satisfies: ...
0
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0answers
121 views

Four-momentum, four-velocity, energy

If given the four-momentum of any particle monitored by an observer as: p = $p^\hat{α}e_\hat{α}$ using unit vectors in observer’s reference frame and u = $e_\hat{0}$ then I get I'm just ...
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0answers
56 views

Vector Equilibrium

I'm trying to understand more about this 'vector equilibrium' apparently coined by R.Buckminster Fuller. In this site (http://cosmometry.net/), it claims: "The Vector Equilibrium, as its name ...
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0answers
61 views

How to interpret the factor $\frac{(\vec v\cdot \hat n)}{|\vec v| 4\pi r}$?

There is a small area element of size $da$ and normal vector $\hat n$. I understand that the particles with speed $|\vec v|$ that hit this area element in the time interval $(t,t+\delta t)$ lie in a ...
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0answers
14 views

vector addition and subtraction

. Vector A has a magnitude of 20 m and makes an angle of 30∘ above the positive x axis. Vector B has a magnitude of 12 m and is oriented 60∘ to the left of the y axis.? Part 1: Find the magnitude ...