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.
6,128 questions
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Do there exist $\alpha, \beta \in (0, \pi/2)$ that are distinct rational multiples of $\pi$ such that $\frac{\sin \alpha}{\sin \beta}$ is rational?
The title says it all, so I'll provide the motivation here in the question body.
In Physics by Halliday, Resnick, and Krane, I encountered the following figure:
Assuming that the oscillating bodies ...
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+50
Exercise in Acoustic Doppler Effect
I am looking for some guidance on the second part of a geometry type problem which I have given a scan on and partial workings below (likely with a procedure error e.g. wrong Maclaurin series). I ...
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If 2 recursion relations have the same coefficients, are the solutions proportional?
In the book of sakurai
Modern Quantum Mechanics they have this $$
\begin{aligned}
& \sqrt{(j \mp m)(j \pm m+1)}\left\langle j_1 j_2 ; m_1 m_2 \mid j_1 j_2 ; j, m \pm 1\right\rangle \\
& =\sqrt{...
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Solving for a diffraction grating's orientation and surface periodicity from its diffracted beams, can the problem be inverted?
Background:
Below is a calculation of the diffracted wavevector $\mathbf{k_1}$ from an initial wavevector $\mathbf{k_0} = -k_0 \mathbf{\hat{z}}$ incident on a planar surface with normal $\mathbf{\hat{...
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Magnetic Field of Cylinder with Uniform Current Density
Though this is a problem from physics, I think it is more about mathematics.
Suppose an infinite cylinder $V$ of radius $a$ with its center aligned in $z$ axis carrying a current density
$$
\...
-2
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0
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parabolic speed of an arrow from a tower
We had an exercise where we needed to calculate a couple of things but here is the question translated:
A guy is standing on a tower at the height of $10$ meters and shoots an arrow. The height can be ...
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2
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Minimizing $f(v_1,v_2)=\frac{1}{2} m_1 v_1^2 +\frac{1}{2} m_2 v_2^2$ over $m_1 v_1 + m_2 v_2 = p_i$ [closed]
How do I minimize $$f(v_1,v_2)=\frac{1}{2} m_1 v_1^2 +\frac{1}{2} m_2 v_2^2$$
when
$$m_1 v_1 + m_2 v_2 = p_i?$$
I want a solution in terms of $p_i , m_1$ and $m_2$.
I am trying to show that an ...
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10
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Maximizing $\int_0^1 f(x) \, {\rm d} x$ given $\int_0^1 x f(x) \, {\rm d} x = 0$
Let $f : [0,1] \to [-1,1]$ be an integrable function such that
$$\displaystyle\int_{0}^{1} x f(x) \, {\rm d} x = 0$$ What is the maximum possible value of $\displaystyle\int_{0}^{1} f(x) \, {\rm d} x$?...
- 459
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Can it be proven that CVT(Continuously Variable Transmissions) are impossible using only smooth rigid bodies?
In mechanical engineering, there are many designs of a CVT(Continuously Variable Transmissions) that is able to change gear ratio continuously, but all of them are unsatisfactory for some reason.
...
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Origins of the Airy function [closed]
The Airy functions $\text{Ai}(x)$ and $\text{Bi}(x)$, first studied by astronomer George Biddell Airy, are linearly independent solutions to the differential equation $$\frac{d^2 y}{dx^2} - xy = 0$$
I ...
- 5,369
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1
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Asymptotics expression in a long-range field theory
In studying a one-dimensional field theory with long-range interactions, I obtain the following scaling function for the two-point correlation function:
$$
\Psi\!\left(\frac{r}{\xi}\right)
= \int_0^{\...
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Deriving a Probability Distribution Function for Speed Function for Velocity.
Consider a probability distribution for velocity $P(\vec{v})$ function that depends only on the magnitude $v$ of the vector. I would like to derive a probability distribution for speed. For this, I ...
3
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Help in ensuring divergence of electric field of a cubic body in free space is zero after finding the electric field : Part 2
I deeply apologize for having to edit the question again. Actually I am currently doing the last part of calculations to prove $\nabla \cdot \vec{E}=0$ after finding $\vec{E}$ of a uniform cubic ...
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Proof of Chasles theorem (Kinematics)
I have been trying to prove Chasles theorem using linear algebra. I am especially doubtful about whether the matrix can be inverted in the plane $\Pi$. And does this theorem also hold for ...
- 465
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2
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The speed of plane wave
Picture below is from Evans' Partial differential equations. I can't understand the red line.
In my view, the speed of (2) should be $\sigma$. And I am sure it is not typo since the red line is used ...
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