Geometric object with magnitude (length) and direction.

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1answer
35 views

How would you go about solving this graphical mass problem? [on hold]

I've tried finding the x and y components of the vectors created by each mass to find the resulting vector's magnitude. However, my answer of 0.354 N keeps getting marked wrong. Any ideas on how to ...
2
votes
1answer
40 views

Cable wakeboard raley

Illustration of the problem: http://www.youtube.com/watch?v=OWRixptJaRo The non physics solution: http://www.youtube.com/watch?v=FRwHcJjfCR4 My first approach to learn this was to follow youtube ...
1
vote
1answer
21 views

How can I calculate the torque on a body resulting from a spinning propeller?

If a quadcopter has all of its propellers spinning on the same direction, the body of the quad will obviously start spinning in the another direction. I know how to calculate the torque acting on a ...
0
votes
2answers
48 views

Simple change in velocity question

The hand of a clock is 1cm long. find the change in velocity of the hand in 15 seconds. The question is pretty simple, $v=2\pi R/T$ and then using the vector addition one can easily get answer which ...
0
votes
1answer
65 views

Unit Vector vs. Basis Vector

When reading about vectors I sometimes have seen unit vectors multiplied by the components and other times I've seen basis vectors used instead. $$v=x \hat i+y \hat j+z \hat k$$ $$v=xe_x+ye_y+ze_z$$ ...
0
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1answer
96 views

Expressing virtual force in terms of muscle contraction force

Two bodies connected with a hinge joint with axis in J. They also connected with a muscle at points M and M`. I’m trying to express virtual force Fv in terms of muscle force Fm acting at the point M ...
0
votes
2answers
50 views

What is the difference between real value and abs value? [closed]

I am confused here, though I have been reading about it for years. What is the difference between a real value and an absolute value? For example, when do we take the absolute value of pressure or the ...
5
votes
2answers
185 views

Why do we use orthogonal axes?

I have been asked several times that “why do we use orthogonal axes in coordinate systems?” and I was always replying that “because of simplicity”. But, today morning, someone asked me that question ...
0
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3answers
84 views

What is the Direction of area vector?

In case of closed surfaces the area vector is directed outwards the surface. But what is the direction of the area vector in case of an open surface e.g. A thin lamina type of surface. Does it depend ...
2
votes
1answer
65 views

Why does the divergence of the Ponyting vector have energy flux density?

The poynting vector is defined as $\vec{S}=\mu_{0}^{-1}\vec{E}\times \vec{B}$ Taking the divergence of the poynting vector, one arrives at $\vec{\nabla} \cdot \vec{S}=-\frac{\partial u}{\...
0
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1answer
111 views

Elemetary Rotations -imagining differential rotations - intitutive proof of such rotations being vectors

I was reading and extract from "Fundamentals Laws of Mechanics", 1980, by I.E Irodov, § 1.2. 'Kinematics of a Solid' and came across this insane text where the author asks me to imagine a 'solid ...
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votes
1answer
45 views

Why is the absolute value of the side in this problem taken to find theta?

To find the resultant magnitude and its direction (theta) in this problem, one must perform the following procedure: However, my point of confusion is why they took the absolute value of Rx at the ...
-1
votes
1answer
65 views

Does a resultant magnitude always have to be positive?

If components vectors can be positive OR negative, why must resultant vectors always be positive?
1
vote
1answer
44 views

Notations used to express direction [closed]

We express direction relative to a reference point and call a certain direction positive and it's direct opposite direction negative, by convention. But, what notation should we use to express a ...
0
votes
1answer
65 views

Four Vectors in SR and QFT

I'm covering both special relativity and quantum field theory in the summer. I'm currently using Spacetime Physics by Taylor and Wheeler to cover SR. Since I'm covering SR on the side with QFT, I'm ...
0
votes
1answer
31 views

What would be the resultant of two vectors at 180°?

If two vectors are at 180° to each other, would the resultant be 0 (as per the head-to-tail method), or the difference of the magnitudes of the two vectors? If the former is true, then why isn't it ...
1
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2answers
54 views

Finding if two objects collide

The question that I'm trying to understand is this: This is the part of the solution I don't understand: From my knowledge, if $v_p-v_q$ is due south, this means $r_p-r_q$ is also due south, ...
0
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1answer
31 views

Could we find the overall force and direction of something with a diagram only? (i.e. no calculation)

My friend, who is a geologist, and I were just debating some dynamics stuff. To make this easier, lets come up with an analogy......lets say there's a boat and it's being pulled by two smaller boats ...
0
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0answers
40 views

Vector addition over orthogonal group [migrated]

I am working on a fun problem. The problem is to solve the following equation: $O_1x_1+O_2x_2=x_1+x_2$, where $x_1, x_2 \in \mathbb{R}^2$ are known and $O_1,O_2 \in \mathbb{O}(2)$ are unknowns. [$\...
3
votes
3answers
368 views

Why the $r$ is cubed in the vector notation for of Newton's Law of Universal Gravitation? [duplicate]

I'm learning about astrodynamics on my own and I was wondering why the $r$ is cubed in the vector notation for of Newton's Law of Universal Gravitation: $$\vec{F}_g=\frac{Gm_1m_2}{|\vec{r}|^3}\vec{r}$...
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votes
0answers
41 views

Can someone explain me magnetic potential? [duplicate]

I don't understand why we can write the magnetic field as a potential vector A, and what exactly this potential is. Is it just a mathematical thing? And how can it help me calculate the magnetic ...
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2answers
49 views

Problem with derivation of potential enery of two body in Gravitational energy

Maybe what I'm going to ask sounds stupid but it means a lot to me that's why I'm asking. I've problem with just a single step in derivation. Let's start. I'm keeping in mind the direction of each ...
1
vote
1answer
57 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 ...
1
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1answer
37 views

Calculating relative velocity in three dimensional space

Given two points $\mathcal{A}$ and $\mathcal{B}$ in $\mathbb{R^3}$ whose position and velocity vectors are, respectively: $$\mathbf{r_A}=\begin{pmatrix}r_{A_{x}}\\r_{A_{y}}\\r_{A_{z}}\end{pmatrix}$$ $$...
0
votes
1answer
30 views

Why do we represent the axis of rotation using vectorial notation [closed]

When a body (in pure rotation) rotates along an axis passing through it, why do we represent the axis of rotation in vectorial notation? Wouldn't it be sensible enough to represent the angular ...
0
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1answer
37 views

Subtracting Audio from a Song with Multiple Forms

This question may start oozing into the realm of copyright infringement, but let's discuss the theory first and foremost. I have a song with vocal and orchestral accompaniment from a well-known movie ...
0
votes
2answers
70 views

Am I wrong about the right hand grip rule?

The right hand grip rule (also known as right hand screw rule) tells you the direction of a magnetic field due to a current. If you point your thumb in the direction of the current, your fingers will ...
0
votes
1answer
50 views

Vector Derivative: General Case

From "An Introduction to Mechanics" by Kleppner & Kolenkow, SIE-2007, Chapter 1 (Vectors and Kinematics), Section 1.8 - "More about the derivative of a vector". In this section, towards the ...
0
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1answer
47 views

Norm of the momentum 4-vector

The norm of the momentum 4-vector is $\mathbf{P}.\mathbf{P}$ $= (\gamma mc, \gamma mv).(\gamma mc, \gamma mv) = \gamma mc^2 - \gamma mv^2$ But why is $\gamma mc^2 - \gamma mv^2 = mc^2$?
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0answers
33 views

Adding multiple torque vectors together to determine resultant torque

I am working in a 2D environment, where there are multiple angular forces (torque) applied at an object. The way I calculated 1 torque "application", was by: ...
-2
votes
2answers
33 views

Projectile motion dependency [closed]

I have read that in projectile motion both vertical and horizontal components are independent of each other but i don't get it that how it is possible i think that they are dependent. If they are not ...
0
votes
1answer
76 views

Why does the equality $\int \mathbf{r}\times \nabla f d\nu=0$ holds? [closed]

My question comes from Problem 4. Classical laws for angular motion of Practical Quantum Mechanics. And the Prob.4 is that, To show that the classical relation between angular momentum $\mathbf{...
0
votes
1answer
51 views

A vector in a rotating frame. Find the rate of change of this vector ('particular step derivation') [duplicate]

I am doing a project with the fundamental background not in my major. I am reading the following lecture: How to get the green part? Can anyone show me the detailed derivation or provide ...
1
vote
1answer
30 views

Differences in notation of momentum 4 vector

I have noticed three ways to write the 4 momentum vectors: $P = (E/c, \vec{p})$ $P = (E, \vec{p})$ $P = (E, c\vec{p})$ I know how to derive equation 1, and as far as I know, one can use the ...
1
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1answer
41 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 ...
2
votes
2answers
229 views

How is 4-current a 4-vector?

I am looking at Jackson sec 11.9, where he states that the $\rho,\bf{J}$ form the 4-current $$J^\alpha=(c\rho,\bf{J})$$ Jackson says this is from the invariant of the 4-divergence $\partial^\alpha ...
1
vote
0answers
45 views

Centripetal acceleration [closed]

I know if a particle is accelerating around the earth it has $$a= \omega*v$$ My question is how do I express this in terms of the unit vector. Would it go something like this. $$|a| = |\omega*v| $$ $...
1
vote
0answers
24 views

Wire with current in magnetic field $\vec{B}$has force $\vec{F_1}$. When rotated, $\vec{F_2}$. Find $B$ [closed]

I have the following question: In a wire with $10cm$ there is a current $4A$ going 'upwards' in the $z$ axis. The force over this field, under a constant magnetic field $\vec{B}$ is $F = -0.2\vec{i} +...
-2
votes
1answer
80 views

Area as a Vector [closed]

Why can we take area as a vector? And say if we take it as a vector why not on the plane why only perpendicular? What is positive or negative area or what the area has to do with direction?
1
vote
2answers
51 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 ...
0
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0answers
29 views

What are the components of r-hat in spherical coordinates?

so I've found a lot of identities that relate the spherical unit vectors to cartesian unit vectors. What is the expression for the spherical unit vectors IN spherical coordinates? I'm tying my brain ...
1
vote
0answers
69 views

Zeroth component of 4-momentum and relativistic energy-momentum relation

As I understand it one is forced to use 4-vectors since we require objects that transform as vectors under application of Lorentz transformations and 3-vectors do not (technically they do under ...
2
votes
2answers
63 views

How do we determine if a certain physical quantity is a vector?

For instance in Newtonian physics we treat position of objects, displacements, velocities, forces, momenta, angular velocities etc all as vector quantities (little arrows in space which have a certain ...
2
votes
4answers
146 views

Rotation of a vector

Is a vector necessarily changed when it is rotated through an angle? I think a vector always gets changed because its projection will change, and also its inclination with axes will always change. ...
2
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2answers
106 views

Is multiplication in physics purely mathematical or is there a physical explanation to it?

Here is what I mean: We always use mathematics in physics, which is pretty powerful, but I still need to ask whether multiplication in physics has a better explanation to what I already think. For ...
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2answers
101 views

Unitary operators evolving the set of Pauli matrices

Consider the Heisenberg picture of Quantum Mechanics. For a two state system we have the Pauli matrices evolving according to the relation $$\sigma_i(t)=U^+\sigma_i(0)U$$ where $U=e^{-iHt/\hbar}$ and $...
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votes
2answers
81 views

How can gravity have a horizontal component?

$mg$ obviously has no horizontal component, but on resolving it into components it seems to have a horizontal component $mgcos\theta sin\theta$. I know I'm doing something wrong here. How is this ...
0
votes
3answers
78 views

Dot product approaches zero as the magnitude of the vectors increase?

Is there such thing? I'm doing some computations on mathematica and I noticed the dot product between two vectors are getting smaller and smaller as I increase the magnitude of the vectors, I'm not ...
0
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0answers
37 views

Electron in a Magnetic Field: Force parallel to velocity?

According to the four-force given in this question, Force is parallel to velocity. But the Lorentz Force is perpendicular to velocity in a constant magnetic field. Is this a contradiction? [a ...
4
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2answers
86 views

What does $(\delta\vec{r}\cdot\nabla)^2$ mean in the derivation of the Lamb shift, and how do you find its expectation?

The Wikipedia page on the Lamb shift includes the following first steps: $$\Delta V = V\bigl(\vec{r}+\delta \vec{r}\bigr)-V(\vec{r})=\delta \vec{r} \cdot \nabla V (\vec{r}) + \frac{1}{2} \bigl(\delta ...