# Questions tagged [physics]

Questions on the mathematics required to solve problems in physics. For questions from the field of mathematical physics use (mathematical-physics) tag instead.

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### What is the fault in this method of finding second moment of area of a circle

I am trying to find the second moment of area of a circle about a diameter using first principles. Place the centre of the circle at the origin of XY-plane. Now consider a tiny circular sector with an ...
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### Some details concerning projective representations in Wienberg's book

I have a question from the book "the quantum theory of fields" by S. Weinberg in page 89: How can we get $[U(\Lambda )U(\bar{\Lambda})U^{-1}(\Lambda \bar{\Lambda})]^2=1$ from the fact that ...
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### Magnitude of Instantaneous Velocity $=$ Instantaneous Speed Rigorous Proof [closed]

In physics, for an infinitesimal time period $\lvert dr \rvert = ds$ Where $dr$ is displacement and $ds$ is the distance covered. I understand this idea intuitively but am eager to know a rigorous ...
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### Finding the optimal surface enclosing a given volume

I would like to find, over the set of continuous surfaces that enclose a volume $V$, the one(s) that lead to the maximal value of a certain cost function. I'm working on a physics problem which ...
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### Physics Kinematics Equation Derivation

I was wondering how you can derive the physics kinematics equation $\Delta x = v_f\Delta t - \frac 12 a \Delta t ^2$ algebraically. I understand where this equation comes from geometrically (when a=...
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### Does a generalization of the Sokhotski-Plemelj Formula to four (or higher) dimensions exist?

The Sokhotski-Plemelj Formula states $$\frac{1}{x \pm \textbf i \eta} = \mathcal{P} \left(\frac1x\right) \mp \textbf i\pi \delta(x)$$ where this expression has to be ...
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I was reading a physic text, and I don’t understand how to transform their non rigorous argument. The part where I don’t get it is when they write $d\theta=d\phi=0$. It means nothing as $d\theta$ and $... • 319 0 votes 0 answers 35 views ### Proof of Schur-Weyl duality$\newcommand{\ket}[1]{|#1\rangle}$I am reading an article (Joy Lie, 2019, "The Quantum Schur Transform and its Applications"), about the quantum Schur transform. There, it is stated that ... • 23 0 votes 0 answers 23 views ### Diffraction cone visualization I have a problem visualizing the diffraction cone for rays coming from different sides: Although I've read multiple papers on the topic, my math skills aren't strong enough to fully grasp it, as I'm ... 1 vote 0 answers 44 views ### Can this property that I formulated be used to find solutions to Navier Stokes in cylindrical coordinates? Let's say I want to derive a vortex flow function $$\psi (r,t)$$ using a scalar field bell surface of the form below, where$W(t)$controls the width (but is not actually the width) as a function of ... -1 votes 3 answers 53 views ### How to untangle the ODE$\frac{dx}{dt} = c + \frac{px}{l_0 + pt}$? [closed] In working on this problem, I came up with the following differential equation: $$\frac{dx}{dt} = c + \frac{px}{l_0 + pt}$$ where$x$is the dependent variable,$t$the independent, and all others ... • 4,450 4 votes 0 answers 170 views ### Dynamics of a sliding cube on the$XY$and$YZ$planes A cube with side length$a$, is initially placed with one vertex at the origin, and its faces parallel to the coordinate planes ($XY, XZ, YZ$) and totally lying in the first octant. Then its rotated ... • 24.3k 0 votes 0 answers 18 views ### Series Solution of Laplace Equation in Spherical Coordinates I am a physics student and this question was asked on the Physics stack exchange as well. I just want you to go through the derivation first. I was recently Studying Griffiths Electrodynamics after a ... 3 votes 1 answer 63 views ### Mach equation algebraic manipulation I'm trying to go from: $$M^2 = \frac{M_S^2 + \frac{2}{\gamma-1}}{\frac{2M_S^2 \gamma}{\gamma-1} - 1}$$ to: $$M^2 =1 - \left[\frac{\gamma +1}{2 \gamma} \right] \left[ \frac{M_S^2-1}{(M_S^2-1) + \frac{... 0 votes 1 answer 66 views ### Proof of a mathematical step involving trigonometric functions On a scientific paper I found a strange step, from this (\theta and \phi are time-dependent; \gamma, g, and l are constants):$$ \ddot{\theta} - \ddot{\phi} - \ddot{\theta} \, \cos(\phi) + \... 0 votes 0 answers 20 views ### Alternative definition of ergodicity for physical systems Imagine we have a physical system whose dynamics are given by its hamiltonian H, defined in a space A. My question is whether the following definition is equivalent to saying that the system is ... 0 votes 0 answers 37 views ### Inverse of a matrix sum and difference in terms of known inverses I have been working on a problem related to the inverses of matrices and would appreciate any insights or solutions. The problem is as follows: Given two invertible matrices$A$and$B$with known ... 0 votes 0 answers 57 views ### Is "work" a natively physical or natively mathematical concept? I recently watched a wonderful video explaining the Cauchy and Residue theorems, and how a complex integral's components relate to work done by and flux from the Polya vector field of the function ... • 157 0 votes 1 answer 75 views ### Integral transformation that I don't understand. I am confused about an integral transformation used in a certain algorithm. The purpose of the algorithm was to obtain distance when accelerating/decelerating without the need to explicitly know how ... 2 votes 1 answer 46 views ### Decomposition of function into products Given a single variable function$f(x)$, is there a way of decomposing it into the product of a family of function. Something similar to, $$f(x) = \prod_n p^{a_n}_n(x)$$ I am trying to find the ... 1 vote 1 answer 62 views ###$\ddot x$vs.$\dot x^2$I'm working on a physics assignment and am having some trouble. I need to integrate$r\dot\theta^2$with respect to$t$. However, my trouble lies in the definition of the upper-dot format. Given: $$\... • 13 3 votes 1 answer 71 views ### How to evaluate this definite integral in terms of Bessel functions. In the context of Green's functions for the Free Klein-Gordon field, the following integral occurs:$$\int_m^{\infty}{\rho e^{-\rho r}\over\sqrt{\rho^2-m^2}}\; d\rho.$$Here m, is a positive ... 1 vote 0 answers 62 views ### particle in motion under the influence of friction Let's consider a particle of mass = 1 Kg moving according to the law$$ \ddot x(t) = -V'(x(t))-\frac{2}{3}\dot x(t) = -x(t)^3+x(t)-\frac{2}{3} \dot x(t).$$(The potential energy is$V(x)=\frac{x^4}{4}...
Although I came across this issue doing physics, the underlying nature of the problem is purely mathematical. So, Work is defined as $W_p=\int_{\gamma_{p}}\vec F_p\cdot d\vec r_{pa}$ where $\vec F_p$ ...