Geometric object with magnitude (length) and direction.

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2
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2answers
56 views

How to define pseudovector mathematically?

The textbook describes pseudovector like this: Let $a,b$ be vectors and $c=a\times b$, $P$ be the parity operator. Then $P(a)=-a,P(b)=-b$ by definition. But $P(c)=c$ since both $a$ and $b$ reverse ...
1
vote
2answers
116 views

If an asteroid were threatening the Earth, could I deviate it just by jumping on it?

An impact by a 10 kilometres asteroid on the Earth has historically caused an extinction-level event due to catastrophic damage to the biosphere. There is also the threat from comets coming ...
0
votes
1answer
33 views

Reflection - reaction force direction

Let's say object hits a wall. When the object is reflected does the direction of the reaction force caused on the wall looks like the red arrow ? Does that direction depends on how "strong" object is ...
-1
votes
0answers
26 views

addition of a component of a vector to the same vector [on hold]

I am having a problem in the last part of this question-(D).My book says that it is not meaningful. I think that supposing a vector for instance 2i^ has a component 2i^. so when they are added it is ...
3
votes
4answers
808 views

Can we add any two vectors?

Can we add any two vectors? If not, why is that so? I think this is not true, but I am not sure. My book says it is true, but I guess it is a misprint. For example, adding acceleration to velocity.
0
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1answer
40 views

The meaning of: “a vector quantity has magnitude and direction” [on hold]

At a tutorial the teacherasked a student if he could explain vector and scalar quantity in concepts of everyday life, not by using any formula. they answered ''it is a vector because it has magnitude ...
-4
votes
0answers
34 views

Position Vector confusion [closed]

I am having a little trouble understanding why the position vector r in calculating the $v_a$ is given by $225/\sqrt2$ (-i -j) If it is the position of C with respect to A shouldn't it just be $225$ ...
0
votes
1answer
45 views

Finding resultant and direction of resultant

In this question- A motorboat is racing towards north at 25km/h and the water current in that region is 10km/hr in the direction of 60 degree east of south. Find the resultant velocity of the ...
-1
votes
1answer
34 views

A particle has $\overrightarrow{r}(0)=4m(\hspace{2pt}\hat{j}\hspace{2pt})$ and $\overrightarrow{v}(0)=(2m/s^2)\hat{i}$ [closed]

I am having trouble with these problems, and I want to gain a understanding of how to solve these. I'll put what I have tried at the end, even though I don't think it'll be of help. A particle has ...
-2
votes
0answers
27 views

Particle Acceleration in three dimensions [closed]

So here is the problem I dont know how to approach it.
0
votes
0answers
26 views

A vector field $\vec{F}$ from cartesian to spherical [closed]

I have a vector field F that has the same magnitude and directions at all points in space. If I choose $z$-axis parallel to $\vec{F}$, so the cartesian coordinate of $\vec{F}$ is $\vec{F}=F\hat{z}$, ...
1
vote
1answer
51 views

Vectors in non-orthogonal systems

In a non-orthogonal coordinate system, what is the physically significant difference between the components of a vector on the skew axes and its projection onto each axis? Why would one want to find ...
0
votes
1answer
27 views

The vector r points from $P'(x',y',z')$ to $P(x,y,z)$ [closed]

For some reason this question is giving me a hard time :( The vector $r$ points from $P'(x',y',z')$ to $P(x,y,z)$. (a) Show that if $P$ is fixed and $P'$ is allowed to move, then ...
2
votes
1answer
30 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 ...
0
votes
2answers
35 views

Find net force on a mass centered between four other masses

I'm not going to post the full question, I just want a general idea of how I should go about solving this type of problem. There is a square with 4 charged masses on each of the corners, in the ...
3
votes
1answer
152 views

How is weight distributed when legs are astride?

Is there a simple and quick formula to find the weight (the force acting) on each leg, especially when legs are astride and they are not equally stretched? (or, better) not equally distant from the ...
2
votes
2answers
158 views

A whole lot of doubts on Lorentz representation

Can someone tell me in layman's language how the $(1/2,1/2)$ represents a vector field and $(0,1/2)$ or $(1/2,0)$ represents spinors and $(0,0)$ represents scalar field. Please don't be pedantic on ...
1
vote
1answer
54 views

4-vector velocity to Newtonian?

The four-vector condition for a particle free of forces is: $\frac{du}{dτ} = 0$ and the equivalence of this to the statement of newton's first law follows from the expression for four-velocity: ...
0
votes
1answer
33 views

Average acceleration when more than two different velocities occur [closed]

Suppose a car travels at 5m/s north for 5 seconds, it then turn east and travel at 7m/s for 10 seconds, finally it turns north east and travel at 10 m/s for 20 seconds. What is the average ...
0
votes
2answers
70 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 ...
0
votes
1answer
40 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 ...
2
votes
2answers
49 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?
1
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2answers
143 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 ...
7
votes
3answers
252 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 ...
5
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1answer
55 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
votes
5answers
226 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 ...
-1
votes
2answers
53 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 ...
1
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1answer
31 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?
-2
votes
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
votes
4answers
76 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 ...
0
votes
1answer
32 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.
1
vote
3answers
80 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
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3answers
103 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
77 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
89 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
64 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
48 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
639 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
78 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 ...
14
votes
5answers
749 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
54 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
48 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
53 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
73 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
103 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
36 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
148 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
102 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
57 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 ...