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Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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Tension of rope over frictionless edge obstructing block

Consider the diagram below. All corners are assumed to have no friction. Is it true that the tension throughout the rope is equal in all sections? The section over the edge of the building, the ...
Bucephalus's user avatar
1 vote
5 answers
104 views

What does it mean when vector quantity is negative?

I’ve seen in some problems that vector quantity is negative. For example, negative Coulomb means that two charges attract… negative acceleration means that object is slowing down. However, magnitude ...
Alexander Djurovich's user avatar
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What does $v$ actually represent in pulley problems?

Let us consider the problem of two pulleys with boxes attached to their ends. One pulley is movable, and the other is not. The problem requires us to find a relationship between velocities of these ...
Alexander Djurovich's user avatar
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Error in reasoning for electric field outside a cylinder

Suppose we have a cylinder of length $L$ with uniform charge density that has its central axis on the $z$ axis and the center of its bottom face located at the origin. Let $P_z$ be any point that lies ...
Joa's user avatar
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2 answers
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What is the correct way to think of position?

How accurate would it be to think of position (along some axis) as the component of radius vector. Example: $$ \textbf{r} = x \hat{\textbf{i}} + y \hat{\textbf{j}} $$ And if that is correct, we could ...
Alexander Djurovich's user avatar
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5 answers
123 views

Direction of impulse

My textbook has the following problem: A batsman deflects a ball by an angle of 45° without changing the initial speed which is equal to 54 km/h. What is the impulse imparted to the ball? (Mass of ...
archthegreat's user avatar
1 vote
1 answer
142 views

Physical intuition for the Minkowski space?

As the title suggests, I am looking for physical intuition to better understand the Minkowski metric. My original motivation is trying to understand the necessity for distinguishing between co-variant ...
user10709800's user avatar
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1 answer
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How does this proof of Gauss’ law generalize from $1$ to $n$ charges?

I am having trouble seeing how the proof of Gauss’ law for one charge generalizes to hold for multiple charges in Griffiths’ introduction to electrodynamics. Gauss’ law is proved for one charge (for ...
Joa's user avatar
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Split Pauli Four-vector as quadratic terms of spinors

If I have the Pauli Four-vector $$x_{\mu}\sigma^{\mu} = \left(\begin{array}{cc} t+z & x-i y \\ x+i y & t-z \end{array}\right)$$ with $\sigma^0$ as Identity Matrix. Is there some way to write ...
Alexandre Masson Vicente's user avatar
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51 views

Can sum of two vectors be a unit vector? [migrated]

I stumbled upon a question which states the following - If vector $A = 0.6\bf\hat{i} + N\bf\hat{j}$ is a unit vector, find the value of $N$. On solving, the value for $N$ would be 0.8 . But my real ...
Agog 0615's user avatar
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How to find the resultant speed component, and finding the angle in which the trajectory had hit the ground?

When having a trajectory traveling over a projectile, both the vertical and horizontal velocity components must be obtained in order to calculate the resultant velocity. The question is: Why the ...
Mohammad Osama's user avatar
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1 answer
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How to go from a vector operator to its components?

(I'm sorry if this question is a duplicate, I couldn't find anything that answered my question.) I'm doing an exercise where I'm supposed to get the matrix elements for the vector operator $D$ (the ...
Hector Freire's user avatar
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3 answers
64 views

$z$-component of electric field due to a static square loop

I am having trouble finding the $z$-component of an electric field discussed in problem 2.4 of Griffith’s introduction to electrodynamics. Suppose we have a square loop of side length $a$ carrying a ...
Joa's user avatar
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5 votes
2 answers
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Why do we need unit vectors in a differential bit of area?

I was reviewing the section on spherical coordinates in Griffith’s’ introduction to electrodynamics and I noticed that he includes unit vectors in the definition of an infinitesimal bit of area but ...
Joa's user avatar
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Covariant and contravariant velocity [migrated]

I'm facing the following problem in tensor calculus: I want to calculate the velocity of a mass particle in spherical coordinates. So I'm using the following coordinate functions for spherical ...
Hans-Friedrich Pfeiffer's user avatar
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Can a vector tangent to a spacelike surface be null?

I'm studying the peeling-off behaviour of zero rest-mass fields, as described in Penrose's paper. In it, he talks about the boundary $\mathscr{I}$ of the conformal completion of an asymptotically ...
Smikkelma's user avatar
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2 answers
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Complete unit of vectors and their scalar counterparts [closed]

I'm aware that we use m/s as the SI unit for both speed and velocity. My question then is, we use units to define the magnitude of the vector (velocity), why not add units for the direction too? For a ...
PANAV SINGH's user avatar
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How can we find the angle between areal vector and magnetic field?

For finding torque we need to find the angle between areal vector and magnetic field. But areal vector makes an angle 37° with the x axis and that means it makes 53° with magnetic field because that's ...
android's user avatar
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3 answers
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Why is angular velocity vector perpendicular to the velocity vector and position vector in uniform circular motion?

I am unable to understand if the angular velocity vector is always perpendicular to both the velocity vector and position vector how does it influence anything at all and what is it's significance. ...
Madly_Maths's user avatar
2 votes
0 answers
63 views

Possible ambiguities of quantization

Quantization means to replace $p$ (the momentum) in the expressions of classical physical quantities with $-i\hbar\nabla$, so we get an operator belonging to each physical quantity. However, an ...
mma's user avatar
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2 votes
2 answers
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Confusion with treatment of unit vectors in electrostatics

I am reading Griffiths’ Introduction to Electodynamics and there are two problems where the methodology for treating unit vectors in integrals seems inconsistent to me. When we are trying to find the ...
Joa's user avatar
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5 votes
3 answers
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Is obeying the parallelogram law of vector addition sufficient to make a physical quantity qualify as a vector?

I know that obeying the parallelogram rule of vector addition is a necessary condition for vectors. But is it sufficient? In other words, can there be a quantity that is added using the method but ...
HerrAlvé's user avatar
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1 vote
2 answers
100 views

Why must a constraint force be normal?

If we impose that a particle follows a holonomic constraint, so that it always remains on a surface defined by some function $f(x_1,x_2,x_3)=0$ with $f:\mathbb{R^3}\rightarrow\mathbb{R}$, we get a ...
16π Cent's user avatar
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1 answer
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Question about the geometry of the normal force [closed]

Let's say a man is pushing a box over a ramp with angle $\theta$ with the horizontal. By opposite adjacent angles, I think the normal force would be $mg\sin\theta$ why is the normal force $N = mg\cos\...
samsamradas's user avatar
3 votes
7 answers
847 views

Physical Quantities Sign Convention

I see that almost all physical quantities carry signs. But the confusion I have is what they really mean. Does negative velocity mean decreasing velocity or velocity in the opposite direction? Does ...
Singing Account's user avatar
0 votes
4 answers
82 views

What is the tangential component of any vector?

There's a statement I discovered in the book I am reading which says Kinetic energy changes only when speed changes and that happens when the resultant force has a tangential component. Does that ...
android's user avatar
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-1 votes
1 answer
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Invariance of Acceleration vs Invariance of Magnitude of Acceleration and help with proof

This question is a half-rant, half-question, as I am genuinely curious as to what the standard physics view is on this question. As someone who has studied math extensively (but not physics), please ...
atonaltensor's user avatar
1 vote
1 answer
61 views

What happens to $\frac{d}{dt}\left(\hat{v}\right)$ at the highest point a projectile reaches when launched vertically upwards?

Acceleration is given by $\dot{\vec{v}} = \frac{d}{dt}\left( v \hat{v}\right) = \dot{v} \hat{v} + v \dot{\hat{v}}$. What happens to $\dot{\hat{v}}$ when the direction of velocity flips by $180^o$? E....
Anis Manuchehri-Ramirez's user avatar
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1 answer
73 views

Deriving the properties of the Dirac matrices

I am working on the properties of the Dirac matrices, but I cannot figure out the derivations. For example, on proving $\gamma^\mu {\not}{a} \gamma_\mu = -2{\not}{a}$, we first prove that $\gamma^\mu \...
user174967's user avatar
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1 answer
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Showing the Lorentz Invariance of Integral measure $dp^4$ using Levi-Civita Symbols

It's probably being a bit pedantic. I understand that since the transformation of $p^\mu$ is $p^\mu \rightarrow \Lambda^\mu_\nu p^\nu$. The integral measure transforms as the determinant of the ...
Lost_Soul's user avatar
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1 vote
0 answers
60 views

Vector potential of Weird loop

I have to calculate the vectorpotential of a current flowing through the loop at the origin: where the current is given by $I(t)=kt$ for some $k>0$. Given equations $$\mathbf{A} = \frac{\mu_0}{4\...
want2know's user avatar
-1 votes
1 answer
42 views

Components of velocity in projectile motion [closed]

I came across this question in my physics textbook (Gr12) and I was hoping someone could explain the solution to me A ball is thrown horizontally off a building at $8.2\,\text{m}/\text{s}$. At a ...
Nathan's user avatar
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-1 votes
2 answers
67 views

Problem with resources, Walter Lewin's third lecture

I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec ...
0 votes
1 answer
86 views

Do gamma matrices commute with 4-vectors?

One of my exercises was to prove the identity $$\gamma^\mu\displaystyle{\not}a\gamma_\mu=-2\displaystyle{\not}a.$$ Which is trivial if $\gamma^\mu a_\nu=a_\nu \gamma^\mu$, as follows $$\gamma^\mu\...
agaminon's user avatar
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0 votes
3 answers
52 views

Resolving gravitational acceleration

I came across a problem in physics where I had to find the acceleration down an inclined plane. I started by considering $g$ as one of the components, and the one along the inclined plane as the ...
aakansha bahuguna's user avatar
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0 answers
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The length of four-force

Recently, I'm reading the FeynmanLecture II_26 https://www.feynmanlectures.caltech.edu/II_26.html It says that the “length” of the four-vector is an invariant under what is called the “complete ...
Luewis X's user avatar
1 vote
2 answers
66 views

Is the $y$-component of projectile motion independent of the $x$-component or not?

In projectile motion, it is said that both the $x$ and $y$ components are independent of each other but according to the equation of the trajectory, $$y = x \tan\phi - \frac12 g x^2/(u^2\cos^2\phi)$$ $...
Sai Varun 's user avatar
1 vote
0 answers
72 views

Angular velocity versor

I am going back through the definitions of good old Euclidean vectors and trajectories to see whether when i was younger i missed important concepts. In my notes, and reference book, i found that for ...
LolloBoldo's user avatar
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2 answers
44 views

Equations of motion for constant acceleration

I read that the equations of motion for a constant acceleration can be represented in a scalar form as well as a vector form, but what's the need to do them in vector form what extra can we do by ...
Manish's user avatar
  • 51
1 vote
2 answers
119 views

Calculating the net forces in multi-mass dynamic system

I am trying to figure out a generalized method for finding the net force of each mass in a multi-mass dynamic system. We have learned methods in highschool but those don't work for more complex ...
Khalil Burns's user avatar
4 votes
5 answers
193 views

Where does the four-vector potential $A^\mu$ originate?

Now the default answer to this may be, "It has no origin because it's a definition", but let me just try to justify my concern here. On page 842, equation (22.91) of "Modern ...
Electra's user avatar
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-1 votes
1 answer
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Can distance traveled by a body be zero?

I had seen a teacher saying on YouTube that we must note that distance traveled can not be zero then I searched for the same on net and surely some sources say same e.g. the below link https://byjus....
Shinnaaan's user avatar
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2 votes
2 answers
85 views

How to compensate tilted accelerometer?

First of all, I only have accelerometer to solve this problem. I have tilted accelerometer mounted in a vehicle, and I like to get the output values of this accelerometer as if this accelerometer is ...
Hong's user avatar
  • 23
1 vote
2 answers
59 views

Euler Rotation Equations and invariance of vectors in different reference frames

Consider two frames, one which is inertial and the other one rotating w.r.t. to the inertial frame. Say there is a rigid body having angular momentum which is same/invariant in both frames. How is it ...
JAY YADAV's user avatar
0 votes
2 answers
85 views

Linear velocity on a circle

Consider a ball rotating around the z-axis with constant angular velocity $\vec{\omega}$, then the linear velocity $\vec{v}$ is given by $\vec{v} = \vec{\omega} \times \vec{r}$. It is easy to ...
Chuan Huang's user avatar
0 votes
1 answer
42 views

Velocity Formula in SHM

In Simple Harmonic Motion in one dimension, if we assume $$\text{Displacement}=x=A \text{sin} (\omega t+\phi)\implies \text{velocity}=v=A \omega \text{cos} (\omega t+\phi)$$ From here by substitution ...
Starlight's user avatar
  • 347
4 votes
1 answer
82 views

How can I formalize better this proof that angular momentum is conserved for a small impulse?

The book I am studying is discussing Lagrange stability of circular orbits, which assumes fixed angular momentum $L$, hence in an introductory paragraph explains why, when studying stability of a ...
ebenezer's user avatar
  • 130
0 votes
1 answer
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A change in the unit vector over a finite time interval

how we can write the change in unit vectors over a finite time interval, the change in unit vectors in an infinitesimally small-time interval 'dt' is given by the magnitude of the really small angle ...
Manish's user avatar
  • 51
0 votes
2 answers
59 views

Vectors in inertial and non-inertial frames

Trying to understand how vectors change in inertial and non-inertial frames Am I right in saying vectors are defined by their invariance under coordinate transformations? My main question is are ...
ED2468's user avatar
  • 75
3 votes
6 answers
168 views

Why can't rotations in general be associated with vectors?

In my textbook, there's a question: A vector has both magnitude and direction. Does it mean that anything that has magnitude and direction is necessarily a vector? The rotation of a body can be ...
archthegreat's user avatar

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