Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
0
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0answers
19 views
Equilibrium of forces acting on a lifted car
Assuming there is a car that lifted by a tow cable such that only the rear wheels are in contact with the ground, how does the tension in the tow cable, the weight of the car and the contact forces ...
-3
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0answers
20 views
River crossing with pointing method [on hold]
A river is $b$ meter wide and the water is flowing with $u$ velocity. A man with $v$ velocity respective to the river water want to get to the straight other edge point (means that point is just front ...
2
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5answers
98 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?
-1
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1answer
42 views
Calculating work in a two dimensional space [closed]
I am struggling to understand how to solve the following question:
I can't figure how to use the integrals properly, and I can't understand how to get rid of the unit vectors. I was given a solution, ...
2
votes
1answer
57 views
Why the basis of vectors and one-forms can not be related through the metric as a vector and one-forms?
I know that basis vector and basis of one-forms are related through
$$ \tilde{e}^\mu \cdot \vec{e}_\nu = \delta^\mu _\nu .\tag{1}$$
However, the metric has the property that allows to convert ...
3
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4answers
106 views
Why does this line integral give the wrong sign?
I've been trying to find the error in this approach to calculate the work of a uniform gravitational field on an object falling to the ground in the $-y$ direction.
$$\begin{align}
W
&= \int_{i}^{...
2
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0answers
40 views
Is 1/vector is a vector or not? [duplicate]
Let $\vec { A } = a \hat { i } + b \hat { j } + c \hat { k }$. Is $\frac { 1 } { \vec { A } }$ a vector or not, and if it is, then what are its components?"
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1answer
58 views
Incline Paradox?
Suppose I have an inclined plane as shown
If I have a body kept on the incline and released . If I break it's weight into two components , I can break it into one perpendicular to plane and the other ...
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1answer
62 views
Why do we write pressure as $\frac{F\cos\theta}{A}$, and not $\frac{F}{A\cos\theta}$?
If you can follow from the diagram, the latter should be equally correct.
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1answer
19 views
Scalar field and 2 types of line integrals
Consider the line integral,
$\int _ c$f(x,y)$\vec dr$ , where $f(x,y)$ is a scalar field, and it is evaluvated on a curve $c $. After integration we get a vector let it be $\vec I$ .
$\int _ c$f(x,...
1
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4answers
87 views
The change in magnitude of centripetal acceleration
When an object (e.g. racecar) moves around in circles with constant tangential velocity, constant centripetal acceleration is present.
What happens to the centripetal acceleration when the racecar is ...
0
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2answers
61 views
Can we sum accelerations to get a total acceleration?
I was looking at this question (from the picture below) the other day and I did it by adding the forces in the $x$ direction using Newton's second law and I got the right answer.
My friend on the ...
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1answer
55 views
Acquire gradient data of a surface from deflection measurement
.
In the figure above, a laser beam with source at point $I$ falls on a surface (DUT) at point $P$ and gets reflected. The reflected ray falls on the center of camera at point $R$. From the figure it ...
0
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1answer
99 views
Using $v_f = v_0 +at$ for objects in free fall [closed]
I have a question about the difference of using $v_f = v_0 +at$ and $s = v_0t + \frac{1}{2}at^2$ for objects in free fall. I'm trying to solve a problem where there's a ball rolling along an inclined ...
0
votes
2answers
53 views
How to specify the orientation of an area vector?
We all know that the area of a triangle having consecutive sides as $\vec { a }$ and $\vec { b }$ is $\frac { 1 } { 2 } | \vec { a } \times \vec { b } |$, but what is the direction of that area vector?...
4
votes
3answers
185 views
Angular momentum of a system about the center of mass
Let $\boldsymbol{R}$ be the center of mass of a system of particles. Then the angular momentum of the system is
$$\begin{align}
\boldsymbol{L} &= \sum \boldsymbol{r}_i \times \boldsymbol{p}_i\\\\
&...
4
votes
6answers
106 views
How can static friction depend on the normal force, but be directed orthogonal to it?
According to my understanding:
two orthogonal forces aren't related and two orthogonal vectors don't affect each other
the force of static friction $F_s$ depends on the normal force $F_n$, so $$F_s = ...
1
vote
2answers
92 views
Positive work along path [closed]
Consider I have a simple formula for the work along some path (in 1 dimension):
$$W~=~\int_{x_0}^{x_1}\vec{F}\cdot d\vec{x}.$$
If I now move from left to right ($x_1 > x_0$) along the axis (...
0
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4answers
91 views
Angular Momentum Derivation without Vector products - is it possible? [closed]
I am trying to prove myself the formula for angular momentum:
$$L = mvr = pr$$
without use of any vectors.
I started by considering the comparison between $E = \frac{1}{2}mv^2$ and $E = \frac{1}{2}...
1
vote
3answers
96 views
if a vector has a magnitude equal to zero, can that thing exist? Can that thing be measured? [closed]
consider a vector (a vector is a physical quantity ) having magnitude equal to zero.Now, if something has a magnitude equal to zero, can that thing exist? Can that thing be measured?
if net force on a ...
1
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2answers
84 views
Proof that $\vec {r(t)}=\vec r_0 + \vec v_0 t + \dfrac{1}{2} \vec a t^2$ for uniformly accelerated motion
Displacement of a particle moving through $ x $ axis is given by $$ x(t)= x_0 + v_0 t + \dfrac{1}{2} at^2 $$ Can we deduce from it that $$ \vec r(t)=\vec r_0 + \vec v_0 t + \dfrac{1}{2} \vec a t^2$$ ...
1
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1answer
39 views
Unit vector in displacement
When we use vectors in physics why does the unit vector (for displacement) equals magnitude of 1 or magnitude of 1m?
4
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5answers
157 views
Why we use vectors?
When we say that the position of an object is +5m on x axis why we need to use vectors? I mean could we don't use vectors and just say +5m on x or y or z axis instead of writing 5*unit vector either $...
1
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0answers
31 views
Expressing Fresnel Equations in terms of $\mathbf k$-vectors
Write the Fresnel Equations in terms of the k-vectors (or the propagation constants $\gamma$). Assume that the x-direction is normal to the interface, and the z-direction is parallel to the interface, ...
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3answers
47 views
Coriolis force decomposition of angular velocity [closed]
I can’t for the life of me understand how the $\omega$ in this is decomposed to
$$\vec{\omega}= \omega (-\sin(\theta),0, \cos(\theta))$$
Any help would be greatly appreciated!
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1answer
47 views
Is this Question correct? Newtonian Motion - Relative Motion of Rain
There is a question in a textbook which states:
"A cyclist is riding north at 12km/h when it starts to rain. The rain appears to be falling towards her at an angle of 10 degrees relative to the ...
0
votes
3answers
80 views
What is the real notion/feel of a tensor quantity? [duplicate]
I have been just introduced to the term tensor while studying Rotational Dynamics, particularly about Inertia. But I just don't get a clear line separating vector from a tensor. What does someone mean ...
3
votes
1answer
1k views
Isn't the velocity in an orbit always tangential, not radial and tangential?
In this video the person resolves the momentum vector into two components, tangential and radial. But isn't the velocity at every point on the orbit tangential?
0
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0answers
24 views
What is the direction of velocity at different points in an elliptical orbit? [duplicate]
Consider an elliptical orbit. We know that the direction of velocity is fully tangential at periapsis and apoapsis. But what is the direction of velocity at other points on the elliptical orbit?
2
votes
1answer
64 views
The action of Lorentz transformations on 4-vectors in special relativity
So I am studying special relativity and have been introduced to basic tensor calculus used in the theory. Recently, I came across a statement that is confusing me: $$\Lambda^\mu_{\,\,\nu} x^\nu = x^\...
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1answer
48 views
Is $\nabla=\nabla'$? Nabla operator acting on $r^n$
I have been taught that
$$\nabla r^n =\text{gradient of }r^n =n r^{n-1}\ \hat{\boldsymbol r}$$
but in introduction to electrodynamics by Griffith (4th edition) on page 173, $\nabla' r^n$ is given by $-...
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3answers
332 views
Is spinor the sum of scalar, vector, bi-vector, pseudo-vector, and pseudo-scalar?
Is spinor $\psi$ actually the sum of scalar, vector, bi-vector, ..., pseudo-scalar?
Before talking about spinors, we have to differentiate two kinds of spacetime, demonstrated with the example of ...
1
vote
1answer
48 views
Banking of road
If a car is moving on a banked frictionless road one of the component of normal reaction force acts as the centripetal force required for the turn. But normal reaction force is a reaction force. ...
1
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2answers
60 views
Why does tangential acceleration change in value?
I don’t understand why tangential acceleration changes in value in a parabolic movement with constant acceleration (gravitational acceleration). Since acceleration is constant, tangential and ...
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1answer
19 views
About the EKG and why it's waves are positive or negative.e
So, I understand that the EKG is a way of measuring the electroactivity that happens in the heart through the vectors that are created by it.
Every cardiomyocyte has the ability to change its ...
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0answers
41 views
Solid rotates about $n$ axes
A solid rotates about $n$ axes intersecting at one point. The absolute value of angular velocities of each rotation $|\boldsymbol{\omega}_k|\,(k=1,..,n)$ are constant. Find the angular velocity vector ...
1
vote
1answer
26 views
How to determined the angle of force weight in an incline force vector problem?
today in class I was introduced to some basic incline problems. I know that Force weight can be resolved into 2 components-the parallel and the perpendicular. I was given the angle of the ramp to be $...
4
votes
2answers
274 views
Snell's law in vector form
Snell's law of refraction at the interface between 2 isotropic media is given by the equation:
\begin{equation}
n_1 \,\text{sin} \,\theta_1 = n_2 \, \text{sin}\,\theta_2
\end{equation}
where $\theta_1$...
0
votes
1answer
29 views
Inclined plane vector
I have a question,
I need to find $P$ in the following situation. A box of mass 5kg is in equilibrium on a slope at $pi/6$ from the horizontal. I need to find the magnitude of the force in the ...
0
votes
3answers
83 views
Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$?
Why is $\langle c \cdot f|g\rangle=c^*\langle f|g\rangle$?
$c$ is a complex number and $c^*$ is the conjugate. I think that $\langle c \cdot f|g\rangle=c\langle f|g\rangle$ because that's how scalar ...
-1
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2answers
65 views
Can you anti-dot? (9-22 from Marion Thorton) [closed]
I'm solving a question out of the textbook and it reduces to the following.
a particle of mass 2m with velocity $v_0$ collides with a particle of mass m at rest. The collision is elastic.
So using ...
0
votes
1answer
77 views
What is the difference between a quadrivector and a 4-vector? [closed]
What is the difference between a quadrivector and a 4-vector?
Why is the square of a 4-vector equal to $t^2+x^2+y^2+z^2$ while the square of a quadrivector is equal to $t^2-x^2-y^2-z^2$? Aren't they ...
2
votes
1answer
43 views
Dot product in cylidrical coordinates
I'm given the vector:
$$\vec{V}{(r,θ,z)}=\frac{1}{r}\hat{e_r} + (r\cosθ)\hat{e_θ}+\frac{z^2}{r^2}\hat{e_z}$$
I want the scalar product ${\vec{\nabla}}\cdot{\vec{V}}$
We know that in cylindrical ...
0
votes
1answer
58 views
$mg\cos\theta=N$ or $N\cos\theta=mg$ [duplicate]
I was reading up of centripetal motion when I saw the relation that $mg=N\cos\theta$, as can be seen from http://hyperphysics.phy-astr.gsu.edu/hbase/Mechanics/carbank.html, in the case of a ...
3
votes
4answers
2k views
Is a unit vector really unitless and dimensionless?
According to my textbooks, a unit vector has no units and no dimensions, but is only used to specify direction. It only shows the orientation of a corresponding vector in space. I think it's true, or ...
-2
votes
2answers
76 views
Why Gravity doesn't affect Horizontal acceleration/motion?
It is still hard for me to grasp on why gravity doesn't affect horizontal motion, doesnt gravity causes a change in resultant force and thus cause a change in acceleration $F=m.a$
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1answer
42 views
Prove Von Neumann entropy is invariant under coordinate transformation
https://en.wikipedia.org/wiki/Von_Neumann_entropy#Properties
How to show that von Neumann entropy for $p_k$ with basis $|\psi_i\rangle$ is the same for $p_n$ with basis $|\phi_i\rangle$?
That is, to ...
9
votes
6answers
695 views
Definition of inner product as in the case of work
According to the mathematical definition of "vectors", vectors are simply the elements of a set $V$ which forms a vector space structure $(V,F,+,*)$. The definition of inner product states that it is ...
1
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1answer
63 views
Resolving forces on inclined circular motion
When resolving forces vertically and horizontally in a problem where a car is going around a banked bend, why do you consider the components of the normal force? Shouldn’t the normal force just cancel ...
2
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2answers
59 views
Definition of velocity in classical mechanics
Let $(r_1,r_2,r_3)$ be the coordinates of a particle $r$ in the coordinate system $\phi$. Let $\{\hat{e_1},\hat{e_2},\hat{e_3}\}$ be the coordinate basis of $\phi$. Why do we define the velocity $v$ ...
