Geometric object with magnitude (length) and direction.

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2answers
28 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
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4answers
4k 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.
0
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1answer
37 views

Would equations for a spinning top be an (x,y,z) vector [duplicate]

I am following the equations on this page, and for torque it is $mgr\sin\theta$, but I am curious about $r$. I am working on a game and I want to correctly model the top, and am curious if $r$ should ...
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2answers
132 views

Inner products with orthonormal bases

Probably a stupid question here - I think it's a case of me not having sufficient mathematical background to follow this through. In Leonard Susskind's Theoretical Minimum book, he represents the ...
2
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2answers
44 views

Why should an area vector point normal to the surface?

Why is it that the direction of an area vector should be always along the normal drawn to the surface? Can't it also be some other angles with the plane?
7
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3answers
226 views

Why is the cross product between two vectors calculated by the determinant of a matrix

The cross product $\vec{a} \times \vec{b}$ can be written as the determinant of the matrix: $$\left| \begin{matrix} \vec{i} & \vec{j} & \vec{k} \\ a_i & a_j & a_k \\ b_i & b_j ...
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1answer
50 views

Parallel Transport and covariant derivative

I have been trying to understand the notion of parallel transport and covariant derivative. I am unable to see why the change in a vector when it is parallel transported from one point to another ...
3
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5answers
218 views

Forces as vectors in Newtonian mechanics

I seem to be confused about the nature of forces as vectors, in the basic Newtonian mechanics framework. I know what a vector is as a mathematical object, an element of $R^3$. I understand that if a ...
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2answers
48 views

Is the cross product of two vectors always perpendicular to both? [closed]

Does the cross product of two vectors result in a vector perpendicular to both of the vectors or does the cross product of only two perpendicular vectors result in a vector perpendicular to both of ...
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1answer
30 views

Vectors-Can anyone explain me the concept of sense in vectors?

Is it same as the direction?Then , why another term "sense"is used ,instead of direction? Can anyone illustrate it?
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4answers
73 views

Find a central force given the orbit

I've been trying to solve the following problem for a long time. Let's consider a particle of mass $m$ in $\mathbb{R}^3$ with polar coordinates $(r,\theta,\phi)$. The particle moves on the orbit ...
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0answers
37 views

What is the concept behind …? [migrated]

Could someone kindly explain the concept behind this statement " Vector A is perpendicular to both Vector B and Vector C. So Vector A is parallel to VectorB x Vector C " Is there any rule like if a ...
0
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1answer
27 views

Determining the moment of force [closed]

A force $F = 3i + 2j$ passes through through a point $P$ with respect to an origin $O$. How do I determine the moment of the force at the origin.
2
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1answer
244 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 ...
2
votes
4answers
168 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
73 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 ...
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3answers
102 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
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2answers
75 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?
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5answers
697 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 ...
0
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4answers
88 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
55 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
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2answers
41 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 ...
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1answer
58 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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5answers
622 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 ...
1
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0answers
22 views

How to derive the function from its gradient? [migrated]

Let $a$ be a vector and $a= \nabla\phi$ where $\phi$ is a scalar. How to find $\phi$ when $a$ is given? My approach: $a_1dx=a_2dy=a_3dz=d\phi$ So, $\phi=\int a_1dx=\int a_2dy=\int a_3dz$ but the ...
2
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1answer
53 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
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1answer
46 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. ...
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2answers
85 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 ...
0
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1answer
52 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
46 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
72 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
676 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 ...
3
votes
3answers
134 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
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4answers
69 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
26 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
votes
1answer
96 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
3answers
133 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
55 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
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2answers
46 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 ...
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votes
1answer
32 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
173 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
83 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} & ...
-1
votes
1answer
48 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
43 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?
4
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1answer
37 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
4k 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
92 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
34 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 ...
0
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4answers
248 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
votes
1answer
424 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 ...