Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
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Find torque around different points
I have a school assignment where I must find the torque about the points $P$, $Q$, $R$ and $S$.
$F = 250N$ and starts in $A$.
Image is not to scale.
My Approach:
Point S:
1. found the degree ...
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0answers
28 views
Angular velocity of rigidly rotating orbit in 3D
Consider a circle in 3-dimensional space. On this circular orbit, a rigid bead moves, thus changing its angle $\phi$ with a reference radius on the circle.
The intrinsic angular velocity is given by ...
5
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3answers
1k views
When does a vector component keep being a vector, exactly?
English is not my native language, so please forgive my errors.
Consider this example:
This is a classic: an exercise requiring you to calculate the electric field produced by a charged ring on its ...
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1answer
67 views
How To Determine The Position Vector [on hold]
The question I have been set is as follows.
A car of mass $m$ is driven at constant speed $v$ around a circular test track of radius $a$, which is banked at an angle $α$ to the horizontal. With ...
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2answers
61 views
A few questions on Gravity [on hold]
What role does the unit vector $ \mathbf{e}_r $ play in $$ \mathbf{F} = - G \dfrac{Mm}{r^2} \mathbf{e}_r$$ and why there's a negative sign?
If the gravitational force always acting in the same ...
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0answers
53 views
Transformation of $4-$velocity
Notation: a greek index indicates four labels; spacetime coordinates $\mu = (0,1,2,3)$. A latin index indicates three labels; spatial coordinates $i = (1,2,3)$.
$$* * *$$
A quantity, to be ...
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0answers
26 views
Torque about a thin line (triple scalar product) [on hold]
given: Force Vector f=2i−3j+k
force acts on the point (1,5,2)
line $x/2=y=z/(−2)$
Known: $T=n.(r\times f)$
'n' is a unit vector in the direction of the given line
r is the position vector
...
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0answers
47 views
Does the proper four-acceleration $A^{\mu} = (0,0)?$
Let the proper four-position vector $x^{\mu}(\tau) = (0, \tau)$. Differentiating this successively wrt $\tau$ I get the four-velocity $u^{\mu}(\tau) = (0, 1)$ and then the four-acceleration $A^{\mu}(\...
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2answers
47 views
Can the world line of a particle be successively differentiated to any order to always give a four-vector?
Starting with the world line of a particle given by $x^{\mu}$, this can be successively differentiated with the particle's proper time $\tau$ to give the four-velocity from the four-position, four-...
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1answer
30 views
Is the disposition of $1$s and $0$s when writing orthogonal ket vectors purely conventional?
If I want to define the basis in the form of $4$-vectors, how do I proceed to make sure they are orthonormal with one $1$ and three $0$ in each vector? Is it just by convention?
Does it matter if I ...
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1answer
35 views
Is gravitational force different from centripetal force in projectile motion?
This has always confused me, in a projectile motion, like a cannon shooting an object, the only force acting on the body is gravitational force, which is facing downwards or more precisely, ...
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0answers
38 views
Speed of plane landing with the wind or against it [closed]
I was solving the following problem in Tipler and Mosca 5th edition chapter 2:
"To avoid falling too fast during a landing, an airplane must maintain a minimum airspeed (the speed of the plane
...
2
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2answers
70 views
Can we know whether it’s a $1D$ or a $2D$ motion just by looking at the position-time relation?
How do I know whether it is a $2D$ or a $1D$ motion, just by looking at position-time, or velocity-time, or acceleration-time equations?
Maybe the question is not very clear, I’m not sure I’m ...
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5answers
70 views
When I divide a vector by a scalar how do we divide a direction by a scalar?
Suppose I divide the net displacement vector of an object by time taken to get the average velocity vector. The displacement vector has both magnitude and direction. How do I divide direction by the ...
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0answers
27 views
Relation between surfaces of an infinitesimal tetrahedron [migrated]
Let $d\sigma_1,d\sigma_2, d\sigma_3$ denote the areas of the faces perpendicular to the axes $x_1,x_2,x_3$ and let $d\sigma_n$ denote the area of the inclined face with unit exterior normal n. My book ...
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4answers
146 views
Different expressions for distance & displacement : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$
I came across these expressions in my book. And the book says that all these are different from each other.
The expressions are : $\int$$d$$|\vec r|$, $\int$$|$$d$$\vec r$|, and $|$$\int$$d$$\vec r|$ ...
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1answer
68 views
What does expressing ‘velocity’ as a function of $(x,y)$ mean? [closed]
This is a question from my textbook. We have been given an equation of trajectory (equation of an ellipse), and the question wants me to express the velocity vectorially as a function of (x,y).
I ...
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8answers
736 views
Why is acceleration variable in uniform circular motion?
Acceleration is the rate of change of velocity. In the uniform circular motion the acceleration is produced due to change of direction of the velocity(the magnitude remains same). The direction is ...
1
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2answers
65 views
Dot product in E&M
I'm learning graduate level E&M. Textbook is a famous Jackson book. What I would talk now is about pp.295-298 in 3rd ed. I attached the photo of p.298.
It says (paragraph above eq.(7.15) and ...
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2answers
87 views
How does 4-vector notation work?
In particle physics we are going over 4-vector notation. However, my background on this is a little shaky, and I'm having difficulty differentiating the notation and visualizing what it actually means....
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2answers
84 views
What is the unit vector in electric field formula? [duplicate]
What is the $\hat{r}$ (vector) in the formula $\vec{E} = k\frac{q}{r^2} \hat{r}$ for the electric field ? Why we dont use the vectors $\vec{i},\ \vec{j},\ \vec{k}$? Also why this vector doesn't ...
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0answers
19 views
Why are vector products defined in such a way? [duplicate]
The dot product of two vectors is an scalar but the cross product is vector, why? What is the physical meaning of these scalar and vector products? Why are they defined in such a way?
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1answer
32 views
Representing a wave
I don't know how relevant is asking this but We know that we represent waves by displacement, velocity etc.What about area vectors? I mean what about representing a wave by area vectors or even volume?...
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0answers
365 views
Direct sum in physics [migrated]
I know this has been asked before but the questions tend to be specific to particular examples rather than the general case.
I still am not entirely sure when one needs a direct sum in physics. For ...
10
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7answers
876 views
Can we divide a vector by another vector? How about this: $a = vdv/dx?$
My physics teacher told us that we can’t divide vectors, that vector division has no physical meaning or significance. How about this: $$a = vdv/dx.$$
It says acceleration vector equals velocity (as ...
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1answer
29 views
Can I find out magnitude and direction (+starting point) of a vectror using only one method? (graphical or mathematical)
Let's say I need to find out the magnitude and direction (by the direction i mean "position of a vector"/"starting point + direction") in uniform circular motion.
When I draw it into a diagram and ...
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votes
2answers
74 views
Centripetal Acceleration as a Cross Product
Is it fine to express the centripetal acceleration as a cross product?
a=v X w (where a is centripetal acceleration, v is magnitude of velocity, w is angular velocity)
And is it v X w or w X v?
...
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votes
1answer
34 views
Why should the position vector be noted as $R\hat{R}$ in spherical polar coordinates?
Why should the position vector be noted as $R\hat{R}$ in spherical polar coordinates? Now i did the calculation like this: $\vec R = R \sin\theta \cos\phi \hat{i} + R \sin\theta \sin\phi \hat{j} + R \...
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2answers
56 views
What does it mean for a unit vector to have a magnitude of 1?
Imagine a Cartesian coordinate system whose origin is associated with two unit vectors, ê and â, in a 2D-space. Now, let 0.5 cm be the unit of length in this coordinate system.
The magnitude of a ...
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3answers
98 views
Intuition behind dual vectors ('Bongs of a bell' does not help)
Similar to the post here (How to visualize the gradient as a one-form?), I'm wondering about an intuition behind dual vectors and differential forms (and the link in that answer to Thorne's notes is ...
2
votes
3answers
100 views
The direction of torque is so confusing [duplicate]
When I was studying cross and dot products, I learned that the cross product of two vectors A and B is perpendicular to both A and B. But my mind is unable to understand that. Since both A and B are ...
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votes
1answer
49 views
“Order of magnitude” in vectors?
Hello, I was wondering what that statement in the picture (underlined) means? I’m familiar with the term “order of magnitude”, i.e powers of 10 when a measured value is expressed in scientific ...
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2answers
178 views
Doubts on covariant and contravariant vectors and on double tensors
I'm trying to study tensors. Given a coordinates transformation from cartesian to $u_i$ ones:
$$
u_1 = u_1 (x,y,z) \qquad
u_2 = u_2 (x,y,z) \qquad
u_3 = u_3 (x,y,z)
$$
I can write a vector $\mathbf{...
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1answer
61 views
Definition of angular velocity vector of $B$ in $A$ - Strange notation
I found the following definition of angular velocity vector of B in A at page 49 of the book "Thomas R. Kane, Peter W. Likins, David A. Levinson - Spacecraft Dynamics - McGraw-Hill (1981)":
The ...
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1answer
33 views
Deep concept of Rotation Dynamics
If angular velocity about axis of rotation passing through COM is × then why value of angular velocity remains same( i.e ×) If we assume axis of rotation anywhere which parallel to the original one?
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1answer
56 views
Resultant effect of orthogonal motion of electric charges
*If two charges are moving uniformly with parallel velocity vectors that are not perpendicular to the line joining the charges, then the net mutual forces are equal and opposite but do not lie along ...
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0answers
36 views
Mass is ignored in vector product of r(vector) and f(vector), why?
In this solution in the book, the mass is ignored after vector product of position vector and force vector. In both part a and b of the question it is the same.
I was wondering what might be the ...
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5answers
96 views
How to determine the direction of a vector?
I have been learning about vectors and acceleration recently and I still don't understand how to determine the direction of a vector.
For instance, if we consider a freely falling particle and ...
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2answers
32 views
How to change a formula when changing the axis?
I have been lerning about acceleration and free fall recently, and we were told the formula for distance is $s=s_0+v_0t+\frac {1}{2}at^2$ (for movement along $x$-axis) but when we change the axis (to ...
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1answer
50 views
Orthonormality and completeness in infinite dimensions: 2 different definitions [duplicate]
In finite dimensional vector spaces, orthonormality is defined as $\langle x_i|x_j \rangle=\delta_{ij}$ and the completeness relation is given simply by
$$I = \sum_i |x_i\rangle\langle x_i|.$$
To me, ...
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2answers
65 views
Unit Vectors in physics
I'm reading the Massachusetts Institute of Technology: "Review of Vectors"
, and I've found this:
I can't see any relationship between the text that is highlighted in yellow and what's depicted in ...
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0answers
67 views
Orthonormality: from finite ($\delta_{ij}$) to infinite ($\delta(x-y)$) dimensional vector spaces [duplicate]
I've been reading Shankar's book on QM, but I'm unsatisfied with the section on "Generalization to Infinite Dimensions".
Given a finite dimensional vector space with a basis $\{x_i\}$, I understand ...
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2answers
75 views
Doubt about current density [closed]
We are taught in electrodynamics classes that current density is a vector quantity while current is a scalar. I understand why current is a scalar and current density is a vector. But what's troubling ...
2
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1answer
56 views
(Lorentz etc) invariant vector fields
(Background: I know some but not much differential geometry, hopefully enough to formulate this post.)
I want to ask about what physicists mean when they say scalar, vector, etc. The answer in ...
4
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2answers
246 views
Normal force not perpendicular to the surface
In my class about mechanics i had to solve this problem, but it was never really explained. The solution is found beneath in a picture. In the solution they also calculate the angle of the normal ...
4
votes
2answers
200 views
How do we prove the downwards force of a massless rope on a pulley it wraps around is $2T$?
I took this picture out of one of Morin's problem books.
The entire system is under the influence of gravity. The ropes are massless, and the circle is massless.
The original question asks to give ...
10
votes
6answers
616 views
What does vector operator for angular momentum measure?
Consider the vector operator for angular momentum $\hat L=\hat L_x \vec i +\hat L_y \vec j + \hat L_z \vec k$.
Does this mean that if we want to measure the angular momentum of a particle in state $\...
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0answers
17 views
difference between translational and dynamic translation equilibrium
What is the difference between translation equilibrium and dynamic translational equilibrium ?
Also what is the difference between rotational and dynamic rotational equilibrium ?
definitions :
...
1
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0answers
57 views
Vector of acceleration in elipse [closed]
A planet travels in an ellipse around a centre located in the origin with the sun close to the centre. The planet's position in the ellipse is given by:
$$x(t) = a \cos(kt)$$
$$y(t) = b \sin(kt)$$
...
2
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5answers
105 views
Why is torque defined as $r × F$ and not $F × r$?
Is it merely due to popular convention or does it supply any special clarification regarding other physical quantities?
