Questions related to mathematical physics which include application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories

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1answer
38 views

Uniform Circular robot motion

Here is the initial diagram: The robot is moving counter-clockwise around the circle. I am having trouble seeing how they derived the centers of the circles. They have defined the center of a ...
0
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1answer
122 views

2 Second Pendulum Length on The Moon [closed]

This was a physics bonus assignment. I have been trying to solve it for the last 2 hours. Let's say that the density of The Moon and The Earth are the same. Moon radius:Earth radius is $0.273:1$! How ...
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1answer
50 views

(Integration) Physics problem to find the time before a collar comes to rest on a ring with friction.

If unclear, scroll to the end integral which needs to be evaluated. I need to find $\tau$ from this integration/differential equation but I'm stuck. $$\int\frac{-{\rm ...
1
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1answer
73 views

Group theory argument

I'm reading Group Theory in Physics by Wu-Ki Tung and on page 69 in the proof of Theorem 5.3 he makes a group theory statement that I don't get. Let me try give some notation and explanation ...
0
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0answers
33 views

determining the fermi velocity via density of states

The problem is to determine the Fermi velocity for a fermion gas at absolute zero. the problem using integrating a function that looks like $$ v = \frac{4\pi V}{h^{3}} m^{3} \int_{0}^{\infty}{ ...
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0answers
28 views

How does the Schrodinger's potential transformer if the metric conformally transformers?

Given Schrodinger's equation $$ (-\nabla^2+V)\psi=E\psi $$ and the conformal transformation $\tilde{g}_{mn}=e^{2\phi}g_{mn}$, how does the Schrodinger's potential $V$ transformer if the metric ...
1
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1answer
62 views

Coordinate systems in physics problem (damped pendulum)

A simple pendulum of lenght $\ell$ is vibrating freely (with small oscillations). The pendulum is set into forced vibration by moving its point of suspension horizontally with a Simple Harmonic ...
1
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0answers
52 views

How to solve an overconstrained system of equations?

What is the easiest codeable way to solve an overconstrained static model? How does Force Effect https://forceeffect.autodesk.com do it? Given a 10m long bar angled as the hypotenuse of a 3, 4, 5 ...
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0answers
28 views

Calculating line of motion based on turn-rate acceleration

Given initial time, velocity, position, forward acceleration, and (uniquely to my question, it seems) turn acceleration; and given max forward and turn acceleration; and given the time that has ...
1
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1answer
86 views

Proving that $\int \delta \dot{x} dt = \delta x$

Everytime I've seen this I've assumed it was true. It seems plausible. But I would like to rigorously prove it. I think this is correct, but I would like another opinion because my mathematics is very ...
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2answers
122 views

Determine the resultant force of the inclined plane

So I was given this problem for my statics subject. I'm just having problems getting the x and y components of the force $120$ lb. I know that $60$-lb Force $$F_x = (60\mbox{ lb})\cos20^\circ$$ ...
0
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1answer
32 views

Pendulum tension force

I realize this is physics related, although the problem is really about math so I thought it would be a good fit for this site. My illustration is supposed to depict a pendulum and the forces ...
1
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2answers
65 views

How to verify how good my data is?

I'm in an undergrad physics lab right now and I have taken some data. The theoretical curve should be proportional to $\cos^2(\theta)$. How can I quantify how close my data values are to this ...
0
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3answers
50 views

Prove that if the speed of a particle is constant, $\vec a$ is perpendicular to $\vec v$

My train of reasoning (well, not even that, more like "translating") so far: Let $C$ be some constant. $\|\vec {v(t)}\|=C$, so $\frac {d\|\vec {v(t)}\|} {dt}=0$. But, where to go from here? I don't ...
0
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1answer
36 views

How to derive velocity out of acceleration in a circular motion?

A car starts moving in a circle with a radius of 200 meters. It has a constant tangential acceleration of $1{\text{m}\over {\text{sec}}^{2}}$. a. What is the angular acceleration? b. What is the ...
1
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1answer
25 views

If a velocity vector $\vec {v(t)}$ has constant length, must its acceleration also have constant length?

I'm not really sure how arbitrary acceleration is (like, if I can just choose an acceleration that makes the velocity vector erratically change directions while still keeping its length the same, or ...
0
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0answers
29 views

Questions about the mechanics of a spinning CD.

A CD is spinning counterclockwise with a radial velocity of $\omega=30\text{rad}/\sec$. The preface of what I did manage to solve and further details: I was asked what is the period time (12 seconds), ...
3
votes
1answer
99 views

What is a good reference for rigorous Electromagnetism and Electrodynamics?

Is there any good book on Electromagnetism from a more mathematical point of view? By this I mean a book which makes use of differential forms and maybe De Rham cohomology. I was also searching for ...
0
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0answers
13 views

Integration of $dR/(d{\alpha}R_0)=-\tan (\pi/N)$

i was doing a physics problem (circular motion's problem) where i had to deal with an object in motion approaching to the center over a regular N-agon and i end up having to integrate this function: ...
3
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1answer
41 views

Differential length of a logarithmic spiral

I am working on a problem that asks to find the magnetic field at the origin of a logarithmic spiral $r = e^\theta$ from $\theta = 0$ to $\theta = 2\pi$, where the angle $\theta$ is measured ...
0
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1answer
41 views

Finding the range of a cannonball- proof verification.

I asked such a question before but I do learn best by mistakes and corrections.(I didn't fully understand it yet.) I could really use your verification: A cannonball is being fired with a velocity of ...
1
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1answer
23 views

How to get a range of a body being shot\thrown? Theoretical question.

I already asked a similar question here, but the answers were technical, leading me to no genuine comprehension of what I am doing.(I am not complaining or anything, I really thanked you then.) ...
4
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2answers
91 views

What are some tips/techniques that might help me solve this (brutal) differential equation?

I've been working on a certain physics problem involving differential equation for two years. I've made some progress on it recently, but I've come across another roadblock, namely an integral that I ...
0
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0answers
18 views

Moment of inertia of lower dimensional bodies and limits

I have noticed that the moment of inertia of an $n$-dimensional body having uniform density $\rho$ is at least sometimes identical to the limit of the moment of inertia of a $(n+1)$-dimensional body ...
0
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0answers
19 views

Express 3 dimensional movement by using 2 vectors?

I have a system that can be described in 3 equations(Lagrange Euler equations) for each coordinate. $L_x, L_y, L_z$: $$\frac{d}{dt} \frac {\partial \mathcal{L}}{\partial \dot{L_x}} = \frac ...
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0answers
18 views

How to prove y component of the field is zero throughout the motion?

This is a pure mathematical question, here is a little background for the interested reader, you can jump directly to the mathematical part if you are not interested. background Imagine we have ...
0
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2answers
132 views

How to calculate the force of tension?

"Three masses are connected by wires and hung vertically. Draw a Force Body Diagram for each mass and determine the tensions in the three wires." I know there are forces only in the y-direction, ...
1
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0answers
28 views

How are 2D collision forces calculated?

Between 2 circles of the same radii, how can I calculate the collision forces to apply to each of the 2 circles? I have position, mass, and velocity for each of the circles. Here's what I have ...
0
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1answer
164 views

How to calculate solid angle of a rectangular detector of 20cm x 10cm?

I have an detector of $20cm*10cm$, how can i calculate the solid angle subtended by the detector if the detector is placed at $30$cm apart? Because directly i cannot use the formula ...
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0answers
37 views

Problem with center of mass in polar coordinates

When we calculate center of mass using rectangular coordinates, we find the average values in each coordinate. Obviously we can't do this very same thing in polar coordinates: if we integrated a ...
0
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0answers
30 views

Can't replicate solution to a non-linear PDE ($- \square \varphi + \lambda \varphi^3 = 0$)

I am trying to replicate the solution of this paper : http://arxiv.org/pdf/0807.2179.pdf Which is, roughly, for the quartic scalar field theory, $- \square \varphi + \lambda \varphi^3 = 0$ a set ...
0
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1answer
27 views

Computing relative directions

I'd like to ask your help for this problem: I have two bearings. These bearings are angle of direction from $-180$ to $+180$ degrees. One is between my current position $(A)$ and a target $(T)$. One ...
0
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0answers
11 views

Selective substitution of parameter

I came across some solutions to a problem which states: $$V_1=V_2e^{j\theta}=V_2\cos{\theta}+jV_2\sin{\theta}=V_2\cos{\theta}+jI_2Z_0\sin{\theta}$$ In this case they just replace the $V_2$ with its ...
2
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4answers
62 views

Physics based trigonometry question

I am working on solving the problem stated in this image: I understand almost everything about this problem. I solved for the magnetic field along the axis of a circular loop, and now I need to ...
0
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2answers
70 views

How to find the range of a cannon ball?

A cannon is positioned with a direction of 60 degrees between the ground and itself. (Sorry, again, for my poor English. I hope you understood that sentence.). The shooting velocity is ...
3
votes
2answers
90 views

How are these definitions of the inertia tensor the same?

I'm looking for some help in understanding the inertia tensor (not the physics, just the math). I'm trying to figure out how to convert between the wedge product and tensor product definitions. ...
2
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0answers
48 views

Question related to the ballistic motion

A point mass will move in the gravitational field of the Earth according to the equation $$\ddot R =-\frac{GM_eR}{|R|^3},$$ where $R$ is the position vector of the point mass measured from the ...
0
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1answer
131 views

Simple Harmonic Motion Formula

The SHM general formula is this: $y(t) = A\sin(\omega t + \alpha) +B$ I have two questions about it As far as I know, there is the cosine formula for when the particle starts at P and sine for ...
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3answers
61 views

Where have I gone wrong? A basic question in physics (Mechanics)

A stone is dropped vertically in a velocity of $15$ minutes per second, from a point $40$ meters above the ground (excuse my poor English.). a. How long will it take to the stone to hit the ground? ...
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1answer
17 views

Is $Cr^a\hat r$ always a conservative vector field?

Is the vector field $\vec r(r, \theta, \phi) = Cr^a\hat r$, where $C, a\in \Bbb R$ are constants and $r \in \Bbb R^+ \cup \{0\}$ is the radial component, always a conservative vector field? I really ...
0
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1answer
65 views

Finding speed of snowballs given initial velocity and angles

You and a friend stand on a snow-covered roof. You both throw snowballs from an elevation of $14$ m with the same initial speed of $12$ m/s, but in different directions. You throw your snowball ...
0
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2answers
58 views

is there any mathematical model how the guitar strings are related?

I'm just curious to know the mathematical relationship between guitar strings and how their frequency changes with the variation of guitar's string length and thickness. Say, I'm vibrating some node ...
0
votes
1answer
24 views

When should I recalculate starting values for my physics engine's multistep integration?

I'm writing a physics engine that uses an Adams-Bashforth and Adams-Moulton predictor-corrector pair for integration, and Runge-Kutta 4 to calculate starting values for their initialization. I am ...
1
vote
3answers
543 views

Solve for velocity, if acceleration is a function of velocity?

Yes, this is a canned question, because canned questions are simply solvable to understand ideas. No, this is not homework. For simplicity, let's assign values. A given object weights 1000 kg, it ...
0
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3answers
37 views

A $1.00 m^3$ volume of iron has a mass of $7.86 \cdot 10^3 kg$, find the length of one side with a mass of $200g$

So this is a relatively simple physics problem, but I'm sort of stumped and need some help finishing this off. The full problem reads: Iron has a property such that a $1.00 m^3$ volume has a mass ...
2
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2answers
49 views

Strange formula for radar horizon, does anyone know where it comes from

I am in Electronics Technician "A" School in the Navy and we are learning the basics of radars. In one module, we were exposed to this formula which confuses me. If someone has an inkling as to why it ...
0
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1answer
28 views

Expression for $dW$ for a 3D position dependent force $\vec{F}(\vec{r})$.

I was looking at the derivation of the infinitesimal element of work done for a 3d position dependent force and I couldn't get over the switching of $\text{d}\vec{v}$ and $\text{d}\vec{r}$ in the ...
0
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1answer
21 views

Little mistake with Levi-Civita symbol property

I have this equation $ \varepsilon_{ijk}B_k = \partial_iA_j - \partial_jA_i $ and I was asked to prove $\mathbf{B}=\nabla\times\mathbf{A}$, where $\mathbf{B}=B^i\mathbf{e}_i$ and ...
1
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1answer
67 views

Planetary Motion: A comet describe a parabola about the sun [closed]

A comet describe a parabola about the sun, show that the sum of the squares of the velocities at the extremities of a focal chord is constant. I have no idea how to solve. Please help. I only ...
0
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1answer
22 views

Rearrangement of harmonic oscillation formulae

Can anyone show me why the following identity is true? $$A\cos(\omega t) + B\sin(\omega t) = \sqrt{A^2+B^2}\cos\left(\omega t + \arctan\left({ \frac BA}\right)\right) $$ I ask this is relation to ...