Geometric object with magnitude (length) and direction.

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2answers
81 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 ...
-1
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1answer
20 views

Calculating uniform angles between 2 vectors [on hold]

If I have two vectors, say: [100] and [101] and I want to calculate two angles between them, uniformly distributed, would it just be: [1 0 0.33] and [1 0 0.66]? So, [100] = 0 degrees [101] = 45 ...
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0answers
26 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 ...
3
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3answers
17k 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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0answers
19 views

Geometric and algebraic aspects of geometric vectors [closed]

I'm writing some notes for a honors physics class and I am having some trouble with some proofs. Say $\vec{A}$ and $\vec{B}$ are some geometric vectors. Then we defined the dot product ...
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0answers
22 views

Displacement Vectors [closed]

Displacement vectors of 3m and 5m in the same direction combine to make a displacement vector. How long is it? What is a displacement vector and how do I calculate this?
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2answers
38 views

Why taking components of a component of a vector is invalid?

Suppose there's a force $F$ of magnitude 10 newtons in the direction of positive y-axis acting on a particle A. I know that the particle would not experience any force in the positive x-direction ...
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2answers
30 views

Finding the magnitude of Two Vectors [closed]

Vector C has a magnitude 23.4 m and is in the direction of the negative y-axis. Vectors A and B are at angles α = 44.4° and β = 27.7° up from the x-axis respectively. If the vector sum A+B+C = 0, what ...
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2answers
62 views

When does $\mathbf n\times(\nabla V_2-\nabla V_1)=0$ imply $V_1=V_2$

I was reading a paper on electrohydrodynamics which has the following sentence (in my own words): At the interface/boundary, the requirement of continuity of the tangential component of the ...
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2answers
32 views

Direction of electric field lines and electrostatic force

Direction of electric field and electrostatic force should be same by the equation $$\vec{F} = \frac{k q q_0}{r^2}$$ Electric Field $$\vec{E} = \frac{k q}{r^2}$$ Let us suppose that there is a ...
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0answers
22 views

How to convert $V \otimes W^*$ to a matrix space? [migrated]

Namely let's say we have chosen basises $e_1, e_2, ... e_k$ for $V$ and $j_1, j_2, ... j_n$ for $W$. Now, since we can always just convert them separately, and then add the matrixes, how we represent ...
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7answers
2k views

Quaternions and 4-vectors

I recently realised that quaternions could be used to write intervals or norms of vectors in special relativity: $(t,ix,jy,kz)^2 = t^2 + (ix)^2 + (jy)^2 + (kz)^2 = t^2 - x^2 - y^2 - z^2$ Is it ...
0
votes
1answer
16 views

How to find one of the vectors when we know the other, the angle between the vectors and the result? [closed]

We're given that the result of the two vectors $a$ and $5$ is $7$ and the angle between the two vectors $5$ and $a$ is $60$ $degrees$. How do we calculate the of the vector $a$ ? I used $R^2 = P^2 + ...
3
votes
1answer
224 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 ...
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3answers
353 views

Why does the moment of force (aka. torque) depend on the perpendicular distance?

Couyld anyone explain how the lecturer concluded that $$(\underline{r_2} - \underline{r_1}) \times \underline{H} = \underline{p} \times \underline{H}$$
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2answers
138 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 ...
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0answers
17 views

Vector Problem - Resultant [migrated]

This was a problem asked to me in a science quiz: Given |A|=10,and R=A+B.Hence what are the possible values of |B| ? I said that since the angle between vector A and vector B can be anything ...
2
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2answers
6k views

Derive vector gradient in spherical coordinates from first principles

Trying to understand where the $\frac{1}{r sin(\theta)}$ and $1/r$ bits come in the definition of gradient. I've derived the spherical unit vectors but now I don't understand how to transform ...
2
votes
1answer
35 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) = ...
0
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1answer
26 views

Resolution of force vectors

For example in a simple pendulum problem.. the forces that act on the bob are tension and gravitational force. but while the resolving the vectors to find T(tension) at any given angle x with the ...
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3answers
63 views

Tension on a string

A string is attached at both extremities and put under tension $T_0$ at rest. We know that if we pull the string upwards from the middle, the tension will increase. But why is it that, admittedly, ...
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1answer
46 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
92 views

Is a vector and a unit vector dimensionless

Lets say I have a position vector $\vec r$. Is it dimensionless or does it have a dimension of length i.e $[L]$. Also does the unit vector $\hat r$ have a dimension?
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1answer
33 views

Is the Mass flow rate (Mass flux) a scalar quantity?

Wikipedia states that mass flow rate is a scalar quantity, however Mass Flow Rate= Density x Cross Sectional Area x Velocity and velocity is a vector quantity, so this would imply Mass Flow Rate is ...
2
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3answers
102 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 ...
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2answers
200 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
294 views

Relative motion. Setting course of closest approach

Let $r_{P/Q}$ be the position vector of $\overrightarrow P$ relative to vector $\overrightarrow Q$ and $v_{P/Q}$ the velocity vector of $\overrightarrow P$ relative to $\overrightarrow Q$. Suppose ...
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1answer
399 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 = ...
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votes
1answer
69 views

A particle is constrained to move around the unit circle in the xy plane according to (x,y,z) = (cos(t^2),sin(t^2),0) t >= 0 [closed]

A particle is constrained to move around the unit circle in the xy plane according to (x,y,z) = (cos(t^2),sin(t^2),0) t >= 0 At what point should the particle be released to hit a target of (2,0,0)? ...
1
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1answer
368 views

How can I calculate the speed of an object knowing its horizontal and vertical velocity components?

Let's say a ball is thrown and it experiences typical projectile motion (moves in a parabolic arc etc.) and the only information we know are the equations for the horizontal and vertical components of ...
2
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4answers
136 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} & ...
3
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2answers
91 views

Why is the “complete metric space” property of Hilbert spaces needed in quantum mechanics?

I have been learning more about Hilbert spaces in an effort to better understand quantum mechanics. Most of the properties of Hilbert spaces seem useful (e.g. vector space, inner product, complex ...
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7answers
248 views

How can a set of components fail to make up a vector?

Many books in Physics insist to define vectors are objects with components with the property that the components transform in a proper way under a change of coordinates. Now, in mathematics, on the ...
0
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1answer
43 views

How can Bernoullis be solved without Vectors [duplicate]

Some time ago I asked a question why Dynamic pressure is considered scalar. Why is the dynamic pressure not a vector quantity? This still puzzles me so I hope to give a scenario that doesn't make ...
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2answers
102 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 ...
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2answers
95 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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0answers
20 views

Write the force as a sum [closed]

We suppose that a force $\overrightarrow{F}$ (for example, the gravity) is applied vertically downwards to an object that is placed at a plane which has an angle of $45^{\circ}$ with the horizantal ...
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1answer
26 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...
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1answer
86 views

Quantities that have magnitude and direction but do not obey the parallelogram law [closed]

Back in college, when I'm learning about Vectors, I remember the text book saying.. There are certain quantities that have Magnitude & Direction but doesn't follow the Parallelogram Law of ...
0
votes
1answer
47 views

vector and position and acceleration [closed]

I really need your help with two problems. Consider a moving object that can be described by the position function r(t) = [(8.00m/s )t-[( 4.50m/s^3 )t^3 ]î +(− 2.00 )t^2+10.0m]ĵ In unit­vector ...
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2answers
5k views

Confused on how to properly use right hand rule

I am having trouble using the right hand rule properly and often find myself putting my hand in awkward orientations. I know you point your hand in the direction of $r$ and then point your fingers in ...
1
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1answer
55 views

Newton's third law of motion versus Work

Newton third law of motion says that "To every action, there is always an equal and opposite reaction". The vector study tells us that if two vectors are of same nature and equal magnitude but ...
3
votes
1answer
33k views

How does force relate to velocity

I had originally asked this question on math overflow and it was suggested that I ask it here. So I know that a force will change the magnitude of velocity if it is at an angle other that 90 degrees. ...
0
votes
1answer
95 views

Basic question about angular momentum

I've learned that the angular momentum of an object rotating about a fixed axis is $I \omega $. Also, in absence of external torques, $I_1 \omega_1 = I_2 \omega_2 $ (meaning, two different events). I ...
0
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2answers
676 views

How can I split a resultant force into its $x$ and $y$ components?

Point charge 3.5μC is located at x = 0, y = 0.30 m, point charge -3.5μC is located at x = 0 y = -0.30 m. What are (a)the magnitude and (b)direction of the total electric force that these charges ...
2
votes
2answers
132 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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1answer
43 views

vector resolutions

I am learning Mechanics - motion in a plane. Is it possible to that a given vector can be resolved in infinite ways into two non-colinear vectors in the same plane? For example, I have a vector ...
0
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1answer
51 views

How the torque/moment-of-force can be mathematically defined?

Given the definition of torque/moment-of-force $\mathbf F$ applied in $P$ with respect to the pole $O$ $$ \mathbf M_O=\vec{OP}\times\mathbf F $$ and given that the vectors $\vec{OP}$ and $\mathbf F$ ...
2
votes
1answer
71 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 ...
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1answer
78 views

Problem on relative motion involving wind speed .Finding the real velocity of wind?

Here is the question For a person running west at 7km/hr wind appears to blow from north-west .But when he walks towards west at 3km/hr the wind appears to blow from the north. What is the true ...