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Questions tagged [physics]

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

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1answer
52 views

Is Mathematical Biology analogous to Mathematical Physics? [on hold]

Mathematical Physics seeks to create mathematical tools and methods to solve physics problems. Is mathematical biology roughly analogous? Is mathematical biology the discipline that seeks to create ...
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0answers
31 views

Understanding the Following Integral Notation

I'm a little confused on the notation my professor used for the following integral. \begin{equation} \int \bar{Y}_{l_f}^{m_f} \left( \dfrac{-Y_1^1 + Y_1^{-1}}{\sqrt{2}}, \dfrac{iY_1^1 + iY_1^{-1}}{\...
1
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1answer
57 views

feynman lectures physics vol 1 chap 13 13-4 prove

Hi guys I've recently into this Feynman's book and I have a question while reading it. Last part of chap 13 he proves that the force produced by the earth at a point on the surface or outside it ...
5
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1answer
243 views

Proving that any solution to the differential equation of an oscillator can be written as a sum of sinusoids.

Suppose you have a differential equation with n distinct functions of $t$ where $\frac{d^2x_1}{dt^2}=k_{11}x_1+...k_{1n}x_n$ . . . $\frac{d^2x_n}{dt^2}=k_{n1}x_1+...k_{nn}x_n$ I want to show ...
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0answers
16 views

How to create an equation for a “skewed versed-sine pulse”?

I have been reviewing this article on piano hammer dynamics: https://www.acs.psu.edu/drussell/Publications/pianohammer.pdf They describe the impact of a piano hammer to have ideally perhaps a sine-...
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0answers
12 views

Rearranging Formulas - How does this formula turn into this one.

How does $ \Delta E_t = m\times c \times \Delta \Theta $ rearrange into $ \Delta \Theta =\frac{\Delta E_t} {m \times c } $ Would prefer if you could break it down step by step if possible.
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0answers
27 views

Does it make sense to speak in a total derivative of a functional?

I would like to consider the problem of the total derivative of a given functional \begin{equation} \mathcal{L}\big[\phi\big(x,y,z,t\big),\theta_r\big(x,y,z,t\big),x,y,z,t\big],\tag{1}\label{eq0} \end{...
0
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1answer
19 views

Calculate free-fall time of object with initial velocity

For the life of me I can't work this one out. I need to calculate the time for an object to free-fall when it has an initial velocity vector. See below for explanation image: I am trying to ...
0
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0answers
17 views

How to tell when a state variable violates a bound during a numerical ODE solve?

Is there a good way to tell when a state variable violates a bound during a numerical ODE solve? For example, say we're simulating an object flying through the air with an ODE solve, it'd be nice to ...
0
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1answer
31 views

Calculate initial velocity based on displacement, time and constant acceleration.

"A car has a constant speed along a road. It goes down a hill at a constant acceleration. 50s after it goes down the hill the speed is doubled and 50s later it reaches the end of the 200m hill and is ...
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0answers
40 views

Why are all physical quantities tensors? [on hold]

I have been struggling for years to understand what a tensor is. I know all physically meaningful quantities are to be described as tensors but why? What is the link between a "p+q-linear form on ...
0
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1answer
34 views

Probability distribution of a moving particle

I am having a issue with the wording of this question. Find the probability of the following. The velocity $v$ of a randomly selected particle, whose distribution obeys the probability density ...
2
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0answers
19 views

What is the matrix of inertia of a thin rectangular plate? [closed]

I only want to get sure how the matrix looks like, Is it : $\begin{bmatrix} \frac{Mb^2}{3} &0 &0 \\ 0&\frac{Ma^2}{3} & 0\\ 0& 0 & \frac{M(a^2+b^2)}{3} \end{bmatrix}$ Or ...
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0answers
24 views

Examples of quadruple integrals in physics

As the title implies, I was looking for practical applications of quadruple integrals in physics but couldn't find any. Do you have any examples? In particular I'd like to understand what could ...
0
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0answers
21 views

Nested integral with same function at every integral being multiplied an integrated again.

$$\int_z^{\infty}f(z_1)\int_{z_1}^\infty f(z_2) \cdots \int_{z_{n-1}}^\infty f(z_n)dz_ndz_{n-1}\cdots dz_2dz_1$$ Just for reference we could also write it as $$\int_z^\infty \int_{z_1}^\infty\cdots\...
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1answer
17 views

Space explosion [closed]

A shell of mass M is at rest at a point in space. It bursts into two fragments with a combined energy of E (ignore radiation losses). 1. Show that the relative speed of the two fragments after ...
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0answers
24 views

What is the operational way of discovering scale invariance of differential equations?

Context The answer here by @Keenan Pepper gives an instance for what it means for an algebraic or trigonometric formula to be scale invariant. For quick reference, I quote his answer here but with a ...
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0answers
22 views

derivative of a derivative with respect to another variable

This problem comes from my physics lectures so hope i am not wrong here because its still a Mathmatical Problem. So i have to derive a function $W(q(t),\dot q,t)$ that is defined for example as $W =a\...
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0answers
9 views

Find deceleration given initial and final velocity, time, and displacement [closed]

Without friction, I want to slow an object down to 0 velocity over a given distance and time, how do I find the deceleration?
5
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1answer
75 views

Why is symplectic geometry the natural setting for classical mechanics?

I was reading this very nice document, to understand why symplectic geometry is the natural setting for classical mechanics. I more or less understood why there is naturally a 2-form that arises. ...
0
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1answer
28 views

Solving simultaneous logarithmic equations from Newton's law of Cooling

A cup of warm water at $46$ degrees is placed into a refrigerator. 10 minutes later, the water is $39$ degrees, and another 10 minutes later, the water is $33$ degrees. Use Newton's law of cooling ...
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1answer
16 views

Differential in Polar coordinates (velocity)

The velocity of circular motion in polar coordinates is like this; $$\vec v(t) = \frac{d}{dt}\vec r(t) = \frac{dR}{dt} \hat u_R (t)\ +\ R \frac{d\hat u_R}{dt} $$ where $R$ is the radius, and $\hat ...
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1answer
31 views

Rigorous explanation of integration involving delta distribution

In a physics class, I saw the following: The charge density of a uniformly charged circle (charge $Q$) of radius $R$ can be described in cylindrical coordinates using the delta distribution as $$ \...
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0answers
53 views

Equations of Motion for Rocket?

Introduction The problem at hand is to have force and two angles as input and the position and orientation of the rocket after a time as the output. This is to be used in an accurate interactive ...
2
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0answers
33 views

Angular Momentum Zero Produce of Irrotational Fluid Proof

A cute problem that I spent a bit time on. Please help. Consider flow domain smooth manifold in $n$ dimension $\Omega$ with boundary and some boundary data. Constant density is assumed. Assume ...
0
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1answer
35 views

Rotation of an ellipse fixed at two points

I have a situation for which I have made a very crude drawing. Let's say we have an ellipse in $\mathbb{R}^2$ that is fixed at $x_0 = -a$ and $x_1 = a$ (as if it were resting on two poles). I am ...
1
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1answer
25 views

Finding $\theta$ that maximizes $\frac{u^2\sin(2\theta)}{g}-\frac{2Fu^2\sin^2(\theta)}{mg^2}$

I am trying to solve a physics problem to do with finding the ideal angle for the maximum range, $x$, of a projectile, with air resistance taken into consideration ($\therefore \theta \neq 45^{\circ}$)...
2
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1answer
49 views

Use the theory of characters to derive the following relation for the representations of $SU_{2}.$

The question is given below: And the hint at the back of the book says: Establish the corresponding equality for characters. And this was a question I was helped on it, which establish the relation ...
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0answers
11 views

Confusion in sign convention of magnification?

A concave mirror forms a real image three times larger than the object on a screen. Object and screen are moved until the image becomes twice the size of object. If the shift of object is 6 cm. Find ...
0
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1answer
43 views

Integral Equation to Differential

Problem Say I have the following equation. $y=f(\theta)$ Where $\theta = \int\int\alpha$ Is it possible to express the equation in terms of $\alpha$ and not the double integral of it? Origin ...
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3answers
56 views

How to decelerate from velocity v to stop time t over distance d?

I'd be grateful for some help with this problem I am trying to solve. Let's say that I have an object travelling at a velocity v. I want that object to come to a halt in time t AND travel exactly ...
0
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1answer
16 views

Notation in wikipedia article about Wick's theorem

The wikipedia article about Wick's theorem can be found here. In that article, they use a rather strange notation: $$\hat{A}^{\bullet}\hat{B}^{\bullet}$$ the bullet superscript isn't defined in the ...
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0answers
23 views

Is the Schrodinger Equation easier to solve in Spherical Coordinates when dealing with the Hydrogen Atom?

Recently, I have been researching the Schrodinger Equation. I am now attempting to derive the solution to the equation for the Hydrogen Atoms potential energy function. What I am wondering is that ...
0
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1answer
22 views

Dividing two equations to find a ratio [closed]

The question is: In the moon, the acceleration due to gravity is $1.6 m/s^2$. Calculate the difference in the period (the ratio) of two identical pendulums if one were on Earth and one on the Moon....
1
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1answer
54 views

Is my proof of first Kepler's Law correct?

I recently learned how to use differential equations in physics(just the basics), so I tried to prove First Kepler's Law as a challenge. This is my proof, I would like to know if it is correct: ...
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0answers
23 views

Books about electromagnetism/electrodynamics using the language of differential forms [duplicate]

I’m staring to learn electromagnetism and electrodynamics and I’m not very satisfactory with the language and concepts of traditional vector analysis. I’ve heard about the modern formulation of the ...
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0answers
47 views

Vector Calculus - Evaluating $\nabla \times \mathbf{E} = -\frac{1}{c} \partial_t \mathbf{B}$

For the life of me, I cannot remember how to solve equations similar to the cross product equations in Maxwell's equations. I haven't used vector calculus of this level in quite some time and could ...
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0answers
41 views

Questions about using mathematical methods to prove the Caratheodory's Concept of Temperature

First This is what I have saw in a thermodynamics textbook: ///////////////////Start of discussion///////////////////// "There are three homogeneous system,and their parameters of the equation of ...
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1answer
43 views

Evaluate $\dot{v}=-\frac{\gamma}{m}v+g$

Solve: $$\dot{v}=-\frac{\gamma}{m}v+g$$ Where $\gamma,m,g$ are constants I have to to separate the equation as $\dot{v}=\frac{dv}{dt}$ and got to: $$\frac{dv-g}{v}=-\frac{\gamma}{m}dt$$
2
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1answer
47 views

Does there exist a compactly supported integrable function with infinite Coulomb energy?

The title of the question pretty much says it all. I am looking for a function $f\in L^1(\Omega)$, where $\Omega \subset \mathbb{R}^3$ is a bounded domain, such that $$ E[f] = \iint\limits_{\Omega\...
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0answers
19 views

Equations for Center of Mass with respect to y

My textbook says that for a plate bounded by two curves, $f(x)$ and $g(x)$ for $x\in[a,b]$, given $f(x)\geq g(x)$, to find the center of mass, $(x,y)$, we need the following: $$Density=\delta(x,y)$$ $...
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2answers
29 views

Calculate the difference in wavelength of the Balmer-$\alpha$ line ($n = 3$ to $n = 2$) in hydrogen and deuterium

In order to predict correctly the wavelengths of the hydrogen lines it is necessary to use in the expression for $R_{\infty}$ the reduced mass of the electron:$$\mu=\frac{m_e\,m_N}{m_e+m_N}$$ where $...
0
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1answer
41 views

Evaluating $\frac{d}{dt}(\boldsymbol{r} \times d\boldsymbol{r})$ - time derivative of vector crossed with infinitesimal - Kepler's second law

I am trying to evaluate this quantity where $\boldsymbol{r}$ is a position vector, and $t$ is time: $\frac{1}{2}\frac{d}{dt}(\boldsymbol{r} \times d\boldsymbol{r})$ which is the area of a triangle I ...
2
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1answer
121 views

Lagrange multiplier term in Hamiltonian

My question is about a step in this paper: PhysRevB.65.165113 (X.G. Wen) or arxiv page 6. Or alternatively: PhysRevB.90.174417 or arxiv page 3. All papers on spin liquids and the projective ...
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2answers
40 views

Physical meaning and significance of third derivative of a function [duplicate]

Given a physical quantity represented by a function $f(t,x)$ what is (if there is any) the actual meaning of the third derivative of $f$, $\frac{\partial^3 f}{\partial t^3}$ or $\frac{\partial^3 f}{\...
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1answer
47 views

Particle Time Taken

A lecturer of mine gave me and my colleagues this question to solve. A particle is attracted towards a fix point $O$, with a force inversely proportional to its instantaneous distance from $O$. If ...
1
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1answer
53 views

Why is a cylinder not perfectly symmetric as a sphere?

I have read that a cylinder not being perfectly symmetric is the reason behind Rayleigh instability: the process that makes bubbles out of a stream of water. But a cylinder seems also perfectly ...
3
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3answers
78 views

Why does $\vec{F(t)} \cdot \vec{v(t)} = 0$ lead to a circular motion?

Here is a mathematical proof that any force $F(t)$, which affects a body, so that $\vec{F(t)} \cdot \vec{v(t)} = 0$, where $v(t)$ is its velocity cannot change the amount of this velocity. Further, ...
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0answers
20 views

Absence of Pressure gradient in Boundary Layer?

Could someone with knowledge in fluid mechanics please help me in understanding the argument for why dp/dy, the pressure gradient in the boundary layer, equals zero? I have watched his video for a few ...
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0answers
19 views

Struggling with Proof of Prandtl's Boundary Layer Equations

Would someone with knowledge in fluid mechanics please help me in understanding this man's argument for why dp/dy, the pressure gradient in the boundary layer, must equal zero? I would greatly ...