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.
5,811
questions
0
votes
0
answers
19
views
Making a Fourier Transform converge
Consider for example the following function
\begin{equation}
f(x)=(e^x+1)^{ik_1}\,.
\end{equation}
For $k_1 \in \mathbb{R}$, this is clearly not absolutely integrable and thus its Fourier transform ...
0
votes
1
answer
36
views
Coupled Resonators with sinusoidal coupling
I have two coupled resonators with complex resonance frequencies of $\beta_1$ and $\beta_2$. The coupling between them is varying sinusoidal with time. The time-evolution of their resonant mode field (...
- 11
0
votes
0
answers
36
views
How to prove that $\oint_{C} q[\vec{v}\times \vec{B}] \cdot d\vec{r}=0$
How to prove that $\oint_C q[\vec{v}\times \vec{B}] \cdot d\vec{r}=0$ rigorously, where $q[\vec{v}\times \vec{B}]$ is the magnetic force acting on a positive change q, $\vec{v}$ is the velocity, and $\...
- 115
1
vote
0
answers
21
views
Equivalence of expressions for potential of a line charge between two parallel grounded conductors - method of images and series solution
I am trying to figure out how two expressions for the potential of a line charge between two grounded parallel conductors are equivalent. Showing the equivalence of the two expressions seems more ...
0
votes
0
answers
32
views
Verification of the second law of thermodynamics for liquids? [migrated]
I have a pure math background and I am currently self-learning physics.
To mathematically justify and understand the Second Law of Thermodynamics, mathematicians and physicists have studied the motion ...
- 415
-1
votes
0
answers
34
views
How to integrate the newtons law of gravitation in vector form accounting for acceleration [closed]
Title.
This is the equation of newtons laws of gravitation in vector form, equated to f=ma
$$
\mathbf{a} = -\frac{G M}{|\mathbf{r}|^3} \mathbf{r}
$$
I know that we integrate this equation numerically. ...
0
votes
1
answer
76
views
Electric field in a non uniformly charged sphere
Say you have a solid sphere of radius R and of charge density $\rho(\vec{r})=\vec{r}\cdot \hat{z}$, then what is the electric field at the centre of the sphere.
My Attempt :
Now the standard method ...
- 704
0
votes
0
answers
24
views
How to expand the kernel of a matrix after unitary transformation
As shown the picture. $V_m$ is a rank-deficient initial matrix. Do the unitary transform first and expand the kernel by a set of orthogonal vectors. These operations make the right side of the matrix ...
- 1
0
votes
0
answers
22
views
velocity vs time graph to position vs time graph [closed]
I've been trying to figure out how to transform a velocity vs time graph to a position vs time graph using calculus but to no avail. Is it possible to solve it using calculus or do you just need to ...
- 1
1
vote
1
answer
74
views
whats happening when i do arctan? Mistake or wrong in calculator
I have a problem in a solids course about mohrs circle and its principal forces.
I have solved to its last part and it all checks up when putting the right angle theta which makes the shear stresses ...
- 19
-1
votes
1
answer
116
views
Solve Max Velocity given Distance, Time, Initial velocity and final velocity [closed]
Following is known:
vInitial = 0 mm/s,
vFinal = 100 mm/s,
totalTime = 0.9 sec,
TotalDistance = 100 mm
How can I calculate the maximum velocity that will be reached, considering constant acceleration ...
- 11
-2
votes
0
answers
86
views
Divergence of curl is zero. Why? [closed]
I know that we can prove the statement in the question title by using the following 3D vector identity
$$
A\cdot(B\times C) = (A\times B)\cdot C.
$$ But I had a small scenario in my mind. Let's ...
- 17
0
votes
0
answers
24
views
What will happen if there is no acceleration in circular motion?What will be the deceleration on it? [closed]
suppose there is a ball attached to a rod around a center pivot. I've always read the uniform circular motion is accelerated but what would happen to its velocity over time if it was just given an ...
0
votes
1
answer
55
views
Can an irrep be a tensor product of representations
Consider a unitary irrep of a compact Lie Group $G$ onto a Hilbert space $\mathcal H$, $\pi\colon G\to\mathcal U(\mathcal H)$. Now assume that $\mathcal H$ can be decomposed into a tensor product, $\...
- 29
3
votes
0
answers
83
views
Help with finding N-point functions with some properties
I'm a physicist and I'm working in a problem in general relativity where I end up with N-point functions that have to satisfy equations like this
\begin{equation}
\Big[\nabla_\mu \nabla^\mu +V(x_1)\...
- 187
3
votes
0
answers
143
views
Why is this the method of characteristics?
The following question refers to ref. 1, the equation are numbered alike with a slightly different notation.
The author claims to solve a renormalization group (RG) equation - so the context is ...
- 406
1
vote
2
answers
55
views
Motion of midpoint of elastic band connected by two gears
A mechanical device consists of two circular gears, one of radius 2 centered at (0, −2) and
the other of radius 1 centered at (0, 1). The gear of radius 2 rotates clockwise at unit angular
velocity (1 ...
- 95
2
votes
0
answers
37
views
Optical path of a light ray reflected from two mirrors and into a pinhole camera
I have been staring at this problem for longer than I would like to admit.
I am trying to determine the path of a light ray from an object that is reflected from two plane mirrors and into the ...
- 21
2
votes
1
answer
83
views
Finding solution without solving differential equation
I was trying to solve a physics problem and the equation I came up with was: $$F-2kx(t)=mx''(t)$$
It is given that $x(0)=0$ and $x'(0)=0$, and my target is to find the extrema values of $x(t)$
Solving ...
- 98
0
votes
0
answers
24
views
Hamiltonian, Unitary and Matrices Exponential
Suppose I can write my Hamiltonian as above. $J_x, J_y, J_z$ and $Q$, etc. are operators.
It is obvious that I can add the terms as I want: I can add $J_x + J_y + J_z + ...$ or $J_y + J_x + J_z ...$ ...
3
votes
1
answer
31
views
products of real spherical harmonics
Based on the description in wikipedia and the book: Modern Quantum Mechanics (Sakurai & Napolitano), any product of two complex spherical harmonics follows the contraction rule:
$$Y_{\ell_1}^{m_1}...
- 199
0
votes
0
answers
22
views
Calculating Euler Angles form a Moment Equilibrium Equation
I am trying to calculate the Euler angles of a rigid body given 4 force vectors and a location relative to the center of mass.
I know the distance from the center of mass to the four force vectors, $...
- 43
1
vote
1
answer
127
views
The "same old" dy/dx question? Separation of differentials?
I completely understand this question has been addressed one too many times. But I still simply cannot wrap my head around the concept of dy/dx.
Simply put, when can we treat dy/dx as a ratio and when ...
- 159
1
vote
0
answers
36
views
Integral involving Bessel functions, exponential and two Laguerre polynomials
in the context of a physics problem, I encountered the following integral:
$$
\int_0^{\infty} d x J_{N_1+N_2}\left(q x\right) \cdot x^{\left|N_1\right|+\left|N_2\right|} e^{-\frac{x^2}{2}} L_{a_1}^{\...
- 11
0
votes
1
answer
32
views
how to get phase difference between two given functions?
My physics teacher gave a function $y = A\sin(\omega t \pm kx)$ and he gave it a phase shift of $\pi$ and said that the function would become $A\sin(kx \pm \omega t)$.
I wanted to verify it myself so ...
1
vote
1
answer
38
views
integration of second order differential equation about SHM
This is a differential equation of SHM from my book.
$$\frac{d^2x}{dt^2}=-\omega^2\times x$$
Both sides is multiplied by $\displaystyle 2\frac{dx}{dt}$ for simplification. And now,
$$
2\times \frac{dx}...
- 13
3
votes
0
answers
66
views
Height in Stevin's law
In the book Serway-Jewett pag. 420 (file is available via the following URL https://ufile.io/p6qru1g0, free on the net), for the Stevin'law I read:
Now consider a liquid of density $\rho$ at rest as ...
- 6,759
0
votes
0
answers
36
views
How can I find the point of balance of an half ellipsoid with the equation $\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1,\:x\ge 0$
How can I find the point of balance of an half ellipsoid with the equation
$$\frac{x^2}{a^2}+\frac{y^2}{b^2}+\frac{z^2}{c^2}=1,\:x\ge 0$$
As point of balance I mean the point on the surface it stays ...
3
votes
4
answers
201
views
Units and $ax^2L^2+bxL+c=0$ in the real world?
It seems that most math equations that come from the real world usually come with dimensions, even though those dimensions are generally ignored. I'm speaking of general dimensions, which include not ...
- 527
1
vote
1
answer
31
views
Compute vector for a 2D drift
I want to develop a top-down car game that uses the same movement system from a HotWheels promotional one by another developer. I've a car moving based in direction variants (up, up-left, up-right, ...
- 123
8
votes
1
answer
298
views
Prove $n \rightarrow 2^+$ as $a \rightarrow 0$
While studying solids of revolution at college, I came across a problem related to physics that seems to have an answer difficult to prove mathematically, which I have not been able to obtain.
...
- 408
0
votes
0
answers
34
views
Chern-Weil theory for variable rank vector bundles
Chern-Weil theory is the study of the characteristic classes of principal bundles, which in particular (in physics) has lead to the classification of valence bundles in the so-called "10-fold way&...
- 1
1
vote
0
answers
67
views
The fractal dimension of the complementary space
I'm a physicist who specializes in studying the behavior of granular materials. Research has confirmed that certain distributions of granular sizes exhibit fractal characteristics. In simpler terms, ...
- 111
7
votes
2
answers
633
views
Negative Numbers in Math & Physics
We say that $-4 < -2$ and that $-3 < 0$ and that $-192 < 24$. I'm aware that there are simple, easily understandable definitions for less than / greater than / equal to e.g. $a < b$ iff ...
- 444
0
votes
3
answers
76
views
limit of $\cos^n(\pi/n)$ as $n\to\infty$ (related to Malus's law)
I am trying to find the limit of $\cos^n(\pi/n)$ as $n$ approaches infinity. Using a graphing calculator it appears that the answer is $1$, however I haven't been able to prove it.
The answer relates ...
- 31
2
votes
0
answers
94
views
Heat from a geothermal well: your take?
Imagine digging a cylinder-shaped (vertical) bore-well of depth $L$ and diameter $r$ ($L\gg r$). The (infinitely thin) cylinder-wall is made watertight and we split the well in half using a kind of ...
- 2,175
0
votes
0
answers
28
views
Significance of circulation of vector field
Is there any direct significance, physical or otherwise, of the circulation of a vector field (when not connecting it to the curl)?
Every application, problem, example, or physical model of ...
- 2,722
0
votes
1
answer
116
views
Which way does a stone move when hit by a wheel/tire? [closed]
I apologize if this question has been asked before, but I haven't been able to find a post which covers this exact question.
Let's say that we have a driving car which is moving forward. At some point,...
- 356
0
votes
1
answer
71
views
Is there a rigorous textbook on step by step development for coming up with the equations of motion of classical dynamical systems?
I was trying to find some references for modelling the equations of motion of a simple dynamical system (say a pendulum on a moving mass) when I realized that the very vast majority of the material ...
- 11.1k
1
vote
1
answer
58
views
Alternative simplified method to mathematically prove Pascal's barrel paradox
The effects of Pascal's principle, discovered by the French physicist in his famous barrel experiment.
In the experiment, also named "Pascal's Paradox," Pascal inserted a $10$ m-long ...
- 6,759
1
vote
1
answer
45
views
Conservative vector field given in polar coordinates
Given a vector field $F$ in polar coordinates, for the example the field $$\vec F(r,\theta)= -r \hat r + (r^2\sin \theta ) \hat \theta $$
I am asked to check if the field is conservative.
is it right ...
- 59
0
votes
1
answer
88
views
How taut must a stretchable, horizontally-oriented string be in order for a straight line to approximate the string to within a given margin of error? [closed]
My question deals with a string that can stretch due to its own weight. If the string is allowed to stretch then I'd assume there would always be a bit of a bulge due to gravity.
The only progress I'...
- 411
0
votes
0
answers
26
views
Does $\kappa = |T \times \frac{dT}{ds}|$?
If $T$ is the unit tangent vector and $\kappa$ the curvature, is it true that $$\kappa = |T \times \frac{dT}{ds}|$$?
I believe this is true (proof below), but am surprised that I cannot find it ...
- 2,722
3
votes
1
answer
112
views
Prove Kepler's second law of planetary motion
An object moves in $\mathbb R^3$ it's position $r(t)$ satisfies $$r''(t) = s(t)r(t)$$ for some scalar function $s$ (a central force field, in which all acceleration is directly towards or opposite the ...
- 2,722
1
vote
1
answer
55
views
Does this example for indeterminacy in classical dynamics translate to real life？
I read the paper Example of indeterminacy in classical dynamics.
I understand the paper: Because the differential equation does not satisfy the Lipschitz condition, its solution is not unique, and ...
- 13
0
votes
0
answers
39
views
Functions which depend on position and time: Functional notation and derivations
In his MIT OCW course, Professor Kleitman explores the derivative of temperature when it depends on position and time:
$T(x, y, z, t)$ ... is a function of position $(x, y, z)$ and time $t$... What ...
- 2,722
0
votes
0
answers
48
views
Electric field flux proportional to the field lines generated by (for example) a static charge
Suppose we have a stationary positive charge at a point in space that we call $+Q$. We know by definition that the flow of the electrostatic field is given by, in its simplified form,
$$\Phi_S(\vec E)=...
- 6,759
0
votes
0
answers
24
views
Vector Method for a Related Rates Question
A standard related related rates question is:
A ladder propped aganist a wall is being moved closer. If the distance between the wall and the ladder reduces by reduces by $a$ m/s, find the rate of ...
- 1,105
1
vote
0
answers
32
views
Where does this factor of $\pi$ come from in the period of small oscillations about equilibrium points?
I am working through some exercises in Arnold's Mathematical Methods of Classical Mechanics book, specifically the second problem on page 20. For context, $T(E)$ is the period of motion along a closed ...
- 43
4
votes
1
answer
96
views
How to find surface area of a wing by integration [closed]
I have a question about aerodynamics. I came across that the wing area of an airplane is calculated with this formula, but I can't calculate the integral. Even if the plane wing area is not ...
- 43