Geometric object with magnitude (length) and direction.

learn more… | top users | synonyms

1
vote
3answers
91 views

Why should multiplication of a ket vector by a complex number change only its “direction”?

Dirac argues on page 17 of his book, The Principles of Quantum Mechanics, that multiplication of a ket by a complex number shouldn't change the state this ket represents. But then concludes: Thus ...
1
vote
3answers
104 views

Integral ambiguity

I'm a bit confused with some notation I encounter in physics calculus. Consider this: Taken from here. Integration operates on functions, correct? What does it mean to integrate $\frac{d{\bf ...
0
votes
2answers
86 views

Is there a difference in handwritten nabla $\vec{\nabla}$ with an overset arrow and typeset nabla $\nabla$?

According to some physicist at KIT it is usual to write the following when using pen and paper: whereas in typeset texts you write $\nabla$. Is that true? Are there sources for this convention?
0
votes
4answers
98 views

Dot product of vector and its derivative with respect to time? How does $L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$? [closed]

How does: $$L \cdot\frac{dL}{dt} = \frac{1}{2}\frac{d(L^2)}{dt}$$ where L is a vector (I dunno how to make it bold in the equation). How do they reach to this right hand side equation? And what is ...
3
votes
3answers
89 views

What is the relative velocity of this plane relative to the helicopter? [closed]

There is a plane moving 100 m/s due east relative to the ground without vertical motion. There is a helicopter facing north moving straight up at 20 m/s. From the perspective of the helicopter, is the ...
1
vote
2answers
66 views

Free vs bound vectors and torque

When considering basic Newtonian mechanics, we can treat vector as free and move their point of application at will. This is consistent with the affine nature of Euclidean space. However, when ...
7
votes
5answers
687 views

Where am I confused about force addition?

As far as my knowledge is concerned, a vector quantity should possess magnitude and direction & more over it should also obey the laws of vector addition. As we all know that the vector sum of 3 ...
0
votes
0answers
80 views

Acceleration of a unit vector in the Feynman Lectures

In the Feynman Lectures on Physics chapter 28, Feynman explains the radiation equation $$\vec{E}=\frac{-q}{4\pi\epsilon_0 c^2}\, \frac{d^2\hat{e}_{r'}}{dt^2}$$ The unit vector $\hat{e}_{r'}$ is ...
15
votes
5answers
802 views

When is it useful to distinguish between vectors and pseudovectors in experimental & theoretical physics?

My understanding of pseudovectors vs vectors is pretty basic. Both transform in the same way under a rotation, but differently upon reflection. I might even be able to summarize that using an ...
2
votes
1answer
56 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 ...
0
votes
1answer
58 views

Torque definition and right hand rule not arbitrary

I have read the following: http://www.feynmanlectures.caltech.edu/I_20.html#Ch20-S1 The formula for $\tau_{xy}$ is derived in this chapter: http://www.feynmanlectures.caltech.edu/I_18.html#Ch18-S2. ...
0
votes
1answer
58 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
votes
1answer
47 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
vote
1answer
77 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) ...
0
votes
4answers
165 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 ...
0
votes
1answer
43 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 ...
3
votes
3answers
180 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 ...
0
votes
1answer
111 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 ...
3
votes
1answer
58 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 ...
1
vote
2answers
61 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 ...
3
votes
3answers
140 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 ...
-2
votes
1answer
34 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
votes
2answers
186 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 $x$.
2
votes
4answers
203 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 ...
-1
votes
1answer
55 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
vote
1answer
54 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?
0
votes
1answer
109 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 = ...
4
votes
1answer
40 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 ...
1
vote
2answers
107 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} & ...
0
votes
2answers
35 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 ...
2
votes
2answers
99 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, $V$, ...
6
votes
1answer
83 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
votes
2answers
56 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 ...
7
votes
1answer
1k 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 ...
1
vote
1answer
95 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
votes
2answers
70 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
votes
1answer
240 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
vote
1answer
153 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
133 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
votes
2answers
96 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 ...
0
votes
4answers
982 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 ...
3
votes
2answers
593 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 ...
-1
votes
1answer
38 views

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

I did something wrong in my calculation, can somebody tell me what?
0
votes
4answers
90 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
82 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 ...
0
votes
2answers
70 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.
1
vote
1answer
67 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
1answer
65 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 ...
1
vote
1answer
129 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 ...
11
votes
5answers
4k 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).