Geometric object with magnitude (length) and direction.

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21 views

Can a vector be defined by invariance of some algebraic operation to translations rather than rotations?

Every physics book I've come across defines a vector as an n-tuple of numbers that can be combined via an inner product that's invariant to rotations. Is it possible to instead define a vector via ...
2
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1answer
27 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 ...
1
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1answer
65 views

Interpretations of (r,s) tensors [duplicate]

A tensor of type (r,s) on a vector space V is a C-valued function T on V×V×...×V×W×W×...×W (there are r V's and s W's in which W is dual space of V) which is linear in each argument. We take (0, 0) ...
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3answers
644 views

How to determine direction of forces in a static problem?

I am consistently getting this wrong. To me, in the picture below, it would make sense that the structure would be pulling downward, and the cable BD would be pulling upward - thus the system is in ...
-1
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0answers
23 views

Vectors-a tricky problem [duplicate]

A particle subjected to two equal forces along two different directions. If one of the forces is halved, the angle which the resultant makes with the other is also halved. The angle between the forces ...
3
votes
3answers
120 views

How to understand the definition of vector and tensor?

Physics texts like to define vector as something that transform like a vector and tensor as something that transform like a tensor, which is different from the definition in math books. I am having ...
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1answer
52 views

An interesting problem on vectors [on hold]

A particle subjected to two equal forces along two different directions. If one of the forces is halved, the angle which the resultant makes with the other is also halved. The angle between the forces ...
2
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4answers
2k 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
63 views

If the velocity vector of a moving particle is always perpendicular to the position vector, is the path a circle?

A Newtonian physics question: If the velocity vector of a moving particle is always perpendicular to the position vector, is the only possible path a circle? What if the magnitude of the velocity ...
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1answer
19 views

Flow rate is calculated only using the parallel component of the velocity vector

Flow rate is calculated using only the parallel component of the velocity vector to the area vector. Why is this? How can I mathematically prove this? Namely, how do I prove any perpendicular ...
0
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1answer
92 views

Quantum states and state vectors

Does a state vector correspond to only one quantum states and the components in the state vector correspond to different states of this quantum state or is it that the components of the state vector ...
2
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1answer
206 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 ...
1
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3answers
131 views

Gradient is covariant or contravariant?

I read somewhere people write gradient in covariant form because of their proposes. I think gradient expanded in covariant basis $i$, $j$, $k$, so by invariance nature of vectors, component of ...
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3answers
126 views

Relation between component and algebraic definition of covariant vectors

I studied contravariance and covariance concepts in following way: For any vector if we get its components by parallelogram way we achieve contravariant components, and if we want to get its ...
3
votes
1answer
51 views

Show that getting parallel transported does not change angle between them- Tensors [closed]

I must tell you that I have never seen this kind of question in Tensor Analysis. Our professor had set up this question in our exam, but I don't know whether it belongs to tensors or not. The question ...
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2answers
41 views

How do I find the perpendicular velocity of a particle to a varying magnetic field?

I am trying to find the component of velocity perpendicular to a magnetic field. This was easy when the magnetic field was static and pointing in only one direction (the $z$ axis), but now I need to ...
-2
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1answer
31 views

How can I get average numbers of days wind flow from 16 direction? [closed]

Wind flow from North direction a nos. of days, Similarly from North East b nos. of days, East c nos. of days, South East d nos. of days, South e nos. of days, South West f nos. of days, West g nos. of ...
3
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2answers
168 views

Position Representation in Quantum Mechanics

How does the 3d position operator look like in position representation? I know that in 1d the position operator $\hat{x}$ is just multiplication by $x$.
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2answers
72 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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1answer
45 views

Determine the number of days with North-East wind direction from the number of days with North and East wind direction? [closed]

I have some data like: Wind flow from north direction = “X” Numbers of days. Wind flow from east direction = “Y” Numbers of days. Then is there any formula to know numbers of days wind flows ...
1
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1answer
37 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
40 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
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0answers
9 views

Understanding the use of Minimum Translation Vector (MTV) for an elastic collision response [migrated]

So, I'm trying to simulate polygon physics, both linear and angular. To calculate the MTV is easy in SAT (Minimum Translation Vector), and to use it to adjust position is also easy: ...
4
votes
1answer
36 views

Can we directly measure vectors' quantities?

Can we perform some kind of experiment that will give us, for example, the $p_x$, $p_y$ and $p_z$ of a particle in a single measurement? I'm aware that they commute so one measurement will not ...
4
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4answers
3k views

Why is current a scalar quantity?

Current has both magnitude and direction. As per the definition of vector defined in encyclopedia, current should be a vector quantity. But, we know that current is a scalar quantity. What is the ...
2
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2answers
87 views

“Vectors” (i.e. 1-tensors) their definition and motivation for relativity

I'm reading Einstein Gravity in a Nutshell (by Zee) and here he defines a vector as an object which is invariant under coordinate representation; concretely, if in one coordinate representation, $V$, ...
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2answers
31 views

How are the angles equal?

At the back of my mind I know they should be equal, but mathematically, how are the two $\Delta \phi$ angles equal? The only explanation present in the text is that, "both velocities are ...
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2answers
77 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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4answers
138 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 ...
7
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1answer
243 views

How to calculate roll, yaw and pitch angles from 3D co-ordinates (Euler Angles)

I have digitized a video of a flying fly in a 3-dimensional space. At all instants I know the x, y, and z co-oridinates of the following points on the fly's body --- The points are my choice, and ...
6
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1answer
73 views

Curvilinear Coordinates and basis vectors

In these notes, $\frac{\partial \vec{r}} {\partial q_i}$ is stated to form a basis set for the vector space. How does this happen? Also, how does one justify this equation from Goldstein's ...
0
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2answers
52 views

Isn't this statement regarding projectile motion wrong?

Isn't this statement regarding projectile motion wrong? If a body is thrown at an angle to the horizontal with initial velocity $u$, then displacement of body as a function of time is ...
1
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1answer
45 views

Kinematics simple question [closed]

Question: In order to protect himself from the rain, a person is standing holding an umbrella at right angle to the horizontal surface. The rain is falling at 10m/s when the velocity of the wind is ...
2
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2answers
66 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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1answer
62 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 ...
1
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1answer
84 views

Rate of change of a vector

I'm studying the book "Classical Mechanics" by Goldstein together with a coursebook my professor provided. I'm having trouble grasping how to intuitively determine what the rate of change of a vector ...
2
votes
1answer
121 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 ...
0
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2answers
92 views

Polar coordinates explanation needed on calculation [closed]

This is the question. Here is the answer. But honestly I cant figure it out. Maybe my lecturer's handwriting is quite illegible too (just kidding). Sorry if I ask too simple question but ...
3
votes
2answers
561 views

Which mathematical operation does the right hand rule for current come from?

I am currently wondering about this famous rule: Where does it come from mathematically that when you point with your thumb in the direction of the current, your curved fingers will point in the ...
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votes
1answer
36 views

Where did I commit a mistake in calculating rotation? [closed]

I did something wrong in my calculation, can somebody tell me what?
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4answers
69 views

The work done by running in a rectangle

This may be quite off-topic but please help me. Is there any work done when I run in a rectangle? I thought that the answer should be no. But my teacher says that we should calculate each side ...
1
vote
1answer
75 views

What are some good resources for learning how to apply vectors in physics?

Although I don't have any problems with vectors when using them in Mathematics but I am having a hard time using them in physics. It is really frustrating me. Can you please recommend me some good ...
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3answers
5k views

Why work is a scalar and not a vector?

Work (in physics) is a scalar but why? and why not a vector?
1
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1answer
60 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 ...
0
votes
2answers
60 views

How is it that the cross product of two vectors is always perpendicular to the given vectors? [duplicate]

Vector addition, subtraction and dot product seem logical enough, but I don't understand how two vectors acting on the same plane maybe, can give a perpendicular resultant.
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2answers
89 views

Stellar Power(Luminosity) Flux

So I was applying some mathematical techniques I learned to physics, and one thing that captured my interest, is the power or luminosity flux of a star. So modeling the situation, taking the scalar ...
0
votes
1answer
42 views

Question about resolving forces

Say, in the example below, the weight $mg$ of the object is $800N$. To find $R$, the conventional method is to use $R\sin(28^\circ) = 800$. But why isn't it possible to use instead the component of ...
3
votes
2answers
242 views

Why the generators of boosts transform like a vector under rotation?

$$\left[J_i,J_j \right]=i\epsilon_{ijk}J_k$$ $$\left[J_i,M_j \right]=i\epsilon_{ijk}M_k$$ $$\left[M_i,M_j \right]=-i\epsilon_{ijk}J_k$$ where $J_i$ is the generator of rotation of Lorentz group, $M_i$ ...
1
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1answer
84 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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5answers
1k views

Can we divide two vectors?

Can we divide two vector quantities? For eg., Pressure( a scalar) equals force (a vector) divided by area (a vector).