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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2
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1answer
28 views

Velocity as a function of position, given velocity as a function of time

Knowing the expression for the acceleration as a function of time: $$ \frac{dv}{dt} = - c v^n$$ (for some constant c >0 and n >1), one needs to find the velocity as a function of time and as a ...
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0answers
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How to compute fourier transform of the function knowing its spectral density function?

I have the following function (where W denotes displacement of cylindrical shell under some force): $S_w(x_1, x_2) = W(x_1, x_2)W(x_1, x_2)^* = \sum_{m_1, m_2 = 1}^{\infty}C(m_1, m_2) \cdot\sin^2{\...
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2answers
17 views

Center of Mass for a Lamina. Why is the value inside the integral $x$ and not $x/2$?

TLDR Why is the center of mass formula for a lamina equal to $A_1$ but not $A_2$? (Specifically the $0.5$ in the $x$-coordinate integral). $$ A_1=\left(\frac{\int_a^bxf(x)dx}{\int_a^bf(x)dx}, \frac{\...
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0answers
16 views

How does the lie exponential map act on tangent vectors?

I'm currently attempting to understand a little bit about how the exponential map works in general. I'll try to lay out what it is I think I've understood and where I think the problem lies. If I have ...
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0answers
22 views

Poincaré sections for a harmonically forced system

I'm investigating a system of second order differential equation representing the discrete physical system illustrated in the figure below. The idea is to prescribe sinusoidal motion to the surface (...
2
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2answers
30 views

Why relative velocity must be perpendicular to velocity of one of the bodies for closest approach

I came across this question that asked the same, but I couldn't understand the reasoning. I feel it wasn't answered clearly, and the OP also sought clarification. The answer stated, From a physics ...
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0answers
14 views

Error in Derivation of Tsiolkovsky Rocket Equation? [migrated]

Can someone point out where the error is in the following derivation of the Tsiolkovsky rocket equation? According to the Newton's second law combined with his third law, we know that the net external ...
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0answers
11 views

How does the magnitude of curl of a vector field relate to magnitude of vector potential?

So, suppose I have a vector field $ \vec{F}$ which is 'nice', then by helmholtz theorem, I can write: $$ \vec{F} =- \nabla \phi + \nabla \times \vec{A} \tag{0}$$ Now, suppose that I measure that: $$ \...
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2answers
24 views

Application of the principle of conservation of angular momentum and the principle of conservation of energy

A satellite is launched in a direction parallel to the surface of the earth with a velocity of $36900km/hr$ from an altitude of $500km$. Determine (a) the maximum altitude reached by the satellite. (b)...
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0answers
24 views

Work and Energy, how to solve? [closed]

A metalball weighing 5N is thrown vertically upward with a velocity of 39.2 m/s². Calculate it's potential energy, kenetic energy and the maximum height reached using conservation of energy principle. ...
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1answer
36 views

What is the meaning of this formula (y2-y1) * cos ((x1+x2) /2)? [closed]

Can anyone please explain the meaning of the cos((y1+y2)/2) in this formula please? Note: the constant 6371 is the earth's radius
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15 views

Get relative position of object from moving camera.

I have a moving webcam trying to track an object and I want to get the relative position of where it is from the camera. My setup is a webcam on a robot tracking a stationary object. The robot knows ...
5
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1answer
61 views

Polynomial integral calculation, maybe residue theorem

When evaluating a loop correction for a certain field theory, I arrived at the following integral $$\int\limits_{\mathbb{R}^{1,3}}\frac{d^4 k}{(2\pi)^4}\frac{1}{\left((k^0)^2-\dfrac{|k|^4}{M^2}-m^2+i\...
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1answer
16 views

Does the work required to lift an object depend on the acceleration of the object?

I'm confused by an example in Stewart's (8th edition, early transcendentals) Calculus textbook. Example 1, Section 6.4: "How much work is done in lifting a 1.2kg book off the floor to put it on ...
2
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1answer
40 views

Divergence of magnetic field $B = \frac{\mu_0 I}{2\pi r}$

I have to show that the divergence of this magnetic field is 0. I can do this pretty easily using the divergence theorem; however, if I try using try computing the divergence directly $\nabla B$ does ...
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0answers
42 views

Using a Partial Differential Equation to find the dynamics model of physical intearctions

I don't know a lot about Partial Differential Equations (PDEs) but I think they are used to find solutions to complex interaction problems. So my first question does solving a PDE enable us to obtain ...
2
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3answers
87 views

Why, when we impose restrictions such as the ones of our physical world, new properties arise? [closed]

Unfortunately I am not and expert mathematician nor a philosopher so I don't have the right words to phrase the concept, but the following example should be able to make the question clear: Take the ...
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0answers
29 views

Calculating Light Fall-Off from a Large Source [closed]

"the inverse square rule is often still a useful approximation; when the size of the light source is less than one-fifth of the distance to the subject, the calculation error is less than 1%"...
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0answers
34 views

Improper Integral of a general function in $x>0$

I'm a first year Physics student and currently practicing questions from our 'Introductory Mathematics for Physicists' course. I ran into a problem dealing with a proof of improper integral of a ...
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2answers
40 views

Is this angular momentum derivative always true?

Recently, when asking for the derivative of angular momentum, I gave my own solution $$ \frac {d \vec L} {dt} = \frac {d \vec r_{(t1)}} {dt} \times \frac {d \vec r_{(t2)}} {dt} + \vec r_{(t1)} \times ...
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99 views
+100

Proving an Identity involving sums related to the $Z(N)$-Ising model

Background: I am trying to construct meromorphic functions satisfying a number of axioms, so-called form factors which are important objects in integrable quantum models, following this paper. ...
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0answers
25 views

Solving a first order ODE with two Dirac-deltas

Let's suppose we have a following equation, where $\mathbf{a},\mathbf{b}$ just some 2-dimensional vectors: \begin{equation} \dfrac{d G}{dz}= f(z,\mathbf{a},\mathbf{b}) \cdot G+\delta({z})\delta(\...
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0answers
21 views

Surfaces that maintain constant mean curvature under uniform outward flow

Over on Physics.SE there is an interesting question about electrostatic configurations where all electric field lines are straight. Clearly, setups with spherical, cylindrical, or planar symmetry are ...
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0answers
11 views

Prove that the derivative of a vector with constant module is perpendicular

I am told to prove that the derivative of a vector with constant module is perpendicular to the vector. Here is my approach, though I'm not sure about if it's correct or not: Let $A(t)$ be a constant ...
5
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5answers
201 views

“All models are wrong, but some are useful”. George E. P. Box Question [closed]

“All models are wrong, but some are useful”. George E. P. Box What is the meaning and context of this statement? Is it math, physics, the universe, our limited capacity as humans, probability, the ...
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0answers
15 views

How to find uncertainty of slope and y-intercept of linear fit from uncertainty of data

I know how to find the slope and the y-intercept of a linear fit of some data by least squares. What I can’t find is how to calculate the uncertainty of these two quantities given the uncertainties of ...
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0answers
27 views

How do I solve the wave equation (WITH interaction)?

I am unsure how to approach the added F(x,t) part of this partial differential equation. $$\begin{cases} \partial_t^2u=\partial_x^2u+F(x,t),& x,t\in\mathbb{R}\,\\ u(x,0)=f(x)\\ \partial_tu(x,0)=g(...
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0answers
19 views

Quaternion and vectors for a project [closed]

I need to learn all about Quaternions to realize a project. I'm zero on this, but I have knowledge of linear algebra. I need to find resources on this subject, can you help?
3
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1answer
67 views

Passivity of a dynamical system

Let a dynamical system , in particular a RLC circuit. I want to study the passivity of this. In general the notion of $\textbf{passivity}$ comes out form the statics physics for which by a ...
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3answers
124 views

Do (some) mathematicians think that beauty is evidence of truth in mathematics? [closed]

Some physicists have argued that (other things being equal) a beautiful theory is more likely to be true than an ugly one. Dirac famously took this view: "A theory with mathematical beauty is ...
2
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0answers
46 views

Dissipation of energy for a dynamical system

$\textbf{1)}$When I consider a dynamical system what tells me that there is a dissipation of energy? For instance if I have a RLC circuit and I consider with $E$ the total energy absorbed in a period ...
1
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1answer
19 views

Given a plane, is there a vector that points towards the highest dz when moving by dx and dy? What is that vector called?

The question came to my mind when trying to explain snowboarding up a ramp. When you don't use an edge and the snowboard is flat, it is only stable if your momentum is going straight up the ramp. You ...
4
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1answer
96 views

Physics books recommendations

I’m a maths PhD student looking for recommendations for physics books. I haven’t really done much physics, and I’m wanting to learn the main topics, mechanics (Euler Lagrange etc), electromagnetism ...
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3answers
36 views

Proving that $\frac{\text{d}\vec{v}}{\text{dt}}=\frac{\text{d}|\vec{v}|}{\text{dt}}\hat{v}+\frac{\text{d}\hat{v}}{\text{dt}}|\vec{v}|$.

We were taught the following equation on a physics lecture: $$\frac{\text{d}\vec{v}}{\text{d}t}=\frac{\text{d}|\vec{v}|}{\text{d}t}\hat{v}+\frac{\text{d}\hat{v}}{\text{d}t}|\vec{v}|$$ where $\vec{v}$ ...
2
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0answers
63 views

Ant Slipping classical mechanics

Suppose we have on a horizontal timetable $m\textbf{a}_{rot}=\textbf{F}-\textbf{F}_{corialis}-\textbf{F}_{centrifugal}$ where $\textbf{a}_{rot}$ is the acceleration in a rotating frame. Suppose an ant ...
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1answer
36 views

How can I calculate using parallel axis theorem the moment of inertia of a cylinder relative to a main body?

The problem is the following. There is large body A to which we know the center of gravity coordinates relative to the center of gravity of a shape (that is part of A), specifically a uniform density ...
0
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1answer
32 views

How to compute the multivariable limit of a multivariable function as the variables approach infinity.

Consider a particle in a three-dimensional potential $$V(x,y,z)=\frac{A \left(x^3+2 y^3+3 z^3+4 a^3\right)}{\left(x^2+y^2+z^2+a^2\right)^2}$$ This particle has scattering states if $E>E_0$, where $...
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1answer
37 views

Total work compressing a conical spring

A conical spring's stiffness varies linearly with displacement from rest. Its stiffness when uncompressed is 45 N/m, and 150 N/m when fully compressed. The uncompressed spring stretches 30 cm further ...
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0answers
33 views

Trying to derive the path integral from first principles (step 1)

I was recently told in the physics forum (https://physics.stackexchange.com/questions/616186/deriving-the-path-integral-from-the-time-slice-approach-for-a-general-hamiltonia) that it is not possible ...
0
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1answer
49 views

$\Delta$ operator is it as a differential operator?

Consider the second law of dynamics written in terms of both momentum, momentum of a force and angular momentum, $$\bbox[5px,border:3px solid #F5B041]{\overline{F}=\frac{\Delta\overline{p}}{\Delta t}} ...
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3answers
50 views

How do I refactor this sailboat transform to solve for apparent wind direction for my sailboat plotting algorithm?

The core problem I would like assistance with is this: How do I refactor this formula to transpose $a$? $$\sin(a_0)\sin(a) \biggl(\frac{ \sin(\frac{a}{2})}{\sin(a_0 - a)}\biggr) ^2 = VW \cdot \eta$$ ...
2
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0answers
55 views

Work done in submerging a weightless sphere, I am getting exactly half the correct answer, can someone point out my mistake!

This is the question: A sphere of radius 0.4 m and having negligible weight is floating in a large freshwater lake. How much work is required to completely submerge the sphere? The density of the ...
0
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1answer
48 views

What does capital A mean in vector field notation?

This might be a dumb question but I am stuck halfway through an assignment where I am supposed to draw a bunch of vector fields because I don't understand an element of the notation. The equation that ...
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1answer
32 views

The solution to the differential equation doesn't work? Help?

I have the differential equation: $$\frac{dN_b}{dt}=\lambda_aNa(0)exp(-\lambda_at)-\lambda_bN_b(1)$$ I am given that the solution to this is: $$N_b(t)=\frac{\lambda_a}{\lambda_b-\lambda_a}\cdot Na(0)[...
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0answers
37 views

Using complex numbers to rotate vectors in 3-D space

I was recently attempting to solve some optics problems based on refraction. Refraction is the principle that when light rays hit an interface between mediums of different refractive index, the light ...
2
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0answers
35 views

Composition of Dirac delta function with a function in two variables

I have a Dirac delta function of two variables: $\delta(s-z_{1}(1-z_{1})-z_{2}(1-z_{2}))$ which I need to solve. I know how to solve when there is only one variable: $\delta(s-z(1-z))$, in which case ...
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0answers
23 views

Does this second-order system of nonhomogeneous ODE have bounded solutions?

The equations of motion for a bead on a smooth, freely rotating rod with unit length are $$ \left\{\begin{aligned} 0&= \omega_0^2\sin\theta - x\dot{\theta}^2+\ddot{x}\\ 0&=3\omega_0^2\cos\...
2
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0answers
30 views

Derivation of Coulomb's Law in Higher Dimensions [migrated]

How could one go about deriving coulomb's law for an n-dimensional space. For example, a 9D space (I would like to know how for these higher dimensions)? I know in 3D space the volume and radius only ...
4
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2answers
75 views

How would the mathematics relevant to physical theory be different if it didn't use real numbers?

Real numbers assume we can have infinite precision and some of the theory behind them uses infinite processes to establish certain proofs. A small band of mathematicians–eg ultrafinitists–disagree ...
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1answer
30 views

Quick question about ODE solutions (trigonometry equality)

After solving an ordinary differential equation, I got this solution: $$ A\cos(\omega t + \phi) $$ where A and $\omega$ have fixed values (I don't see the relevance to bring them in, thus I won't). My ...

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