Questions tagged [vectors]
Geometric object with magnitude (length) and direction.
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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$z$-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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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. ...
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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 ...
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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 ...
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What are the implications of representing basis vectors as directional derivatives? [migrated]
I am pretty new to differential geometry and general relativity. The notion of using directional derivative operators to represent basis vectors is starting to make sense to me, but I am still trying ...
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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 ...
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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 ...
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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\...
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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 ...
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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 ...
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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 ...
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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....
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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 \...
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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 ...
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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
$$\mathbf{A} = \frac{\mu_0}{4\...
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Components of velocity in projectile motion [closed]
I came across this question in my physics textbook (Gr12) and I was hoping someone could explain the solution to me
A ball is thrown horizontally off a building at $8.2\,\text{m}/\text{s}$. At a ...
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Problem with resources, Walter Lewin's third lecture
I've watched Walter's third lecture in 8.01 and I have a small problem with the last part, where he says that $$\vec r_t=x_t\cdot \hat x\ +\ y_t\cdot \hat y\ +\ z_t\cdot \hat z \\ \vec v_t=\frac{d\vec ...
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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\...
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