Questions tagged [vectors]

Geometric object with magnitude (length) and direction.

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Vector form of kinematic equation for motion with constant deceleration

Here is the equation for finding the velocity in the case of constant acceleration: $$\vec{v} = \vec{v_0} + \vec{a}t$$ Hence by integrating this equation with respect to t, we obtain position equation:...
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If we want to apply the formula for torque $= pE\sin\theta$. It is given in the problem that theta~0° [closed]

Why do we take sin theta to be theta only and not as sin0° ie., 0?
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What is the absolute Value of Normal force on a block on Wedge?

So i have been solving problems of Newton's Laws of motion and this thing has been quite conflicting for me. I wont complicate my question. I just need one answer. What is the absolute value of normal ...
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Question regarding $dv/dt =$ Tangential acceleration during circular motion [closed]

During Circular motion or really, any kind of motion it is said that $\frac{d|\vec{v}|}{dt} = |\vec a_{tangential}|$ why is it so?, suppose a particle performing circular motion is moving with ...
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Relation between four-wave vector $k^\mu = (k_0, \bf{k})$ and velocity four-vector

Question: how is a (subluminal) wave's wave-vector related to the 4-velocity (phase velocity)? Wikipedia says that $$k^\mu \propto v^\mu \quad\quad\quad (1)$$ as stated in https://en.wikipedia.org/...
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Is Poynting vector $E \times B$ and energy density $(E^2+B^2)/2$, a four vector?

As the title suggests, does the 00th and 0i the components of the electromagnetic energy-momentum tensor viz. Poynting vector and energy density form a four-vector? Answers with both theoretical and ...
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Dirac's Bracket Notation

I have a question on Dirac's bracket notation. In particular, according to this notation, vectors and covectors are represented by $|\psi\rangle$ and $\langle\psi|$ respectively. Moreover, these two ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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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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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