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
50 views

Prooving Kepler's Second Law through vectors.

I am taking a multivariable calculus lecture online provided by MIT OpenCourseWare. ...
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1answer
37 views

Integral equation involving Planck radiation formula

I am stuck in solving the following integral equation: $$\sigma T^4=\pi\int_{\lambda_0}^{\lambda_1}d\lambda W_{\lambda,T}$$ where: ...
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0answers
38 views

Tension on the string of a drawn bow.

An archer's bow is drawn at its midpoint until the tension in the string is 0.881 times the force exerted by the archer. What is the angle between the two halves of the string? *Edit: some context, ...
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17 views

What force should be applied to each axis given a forward angle and a left/right direction?

I have three parameters: up/down angle, left/right angle, and power. The up/down angle can range from 0-90. It determines the forward force applied to my object. 0 means it moves straight forward ...
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1answer
36 views

Invertibility of inertia matrices

The inertia matrix is defined, for a discrete body composed of material points $P_i$ of mass $m_i$ whose position vector $\overrightarrow{CP_i}$ with respect to the centre of mass $C$ has Cartesian ...
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2answers
88 views

Velocity and Acceleration

I'm currently studying applications of calculus to the physical world in mathematics. I don't understand how a particle with zero velocity can have a positive acceleration. If the particle is at rest, ...
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1answer
43 views

Physics/Math conversion

I'm having difficulties solving this conversion. I know what to do at first but the way to set this up is a bit confusing:
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2answers
72 views

Mechanics problem. [closed]

A bottle is dropped from a blimp whose height is 1200m. Assume that a= 9.81m/s/s, find the time it takes the bottle to reach the ground.
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0answers
35 views

Notation for Christoffel symbols used by Gödel in “An example of a new type of cosmological solution of Einstein field equations of gravitation”

I have difficult to understand the meaning of the notation used by Gödel in the article cited in the title of this post. You can find it here: http://www.lygeros.org/10552b.pdf In the second page ...
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0answers
27 views

Algebraic determination of asymmetric unit (aka irreducible wedge) in Brillouin zone of lattice

In Solid State physics the reciprocal space is of utmost importance to predict the band structure and thus most of the electrical transport parameters like effective mass, etc. The First Brillouin ...
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1answer
40 views

Impact of weight of the dice

If you throw a 6-sided die there is a probability of 1/6 to throw any specific value. However, this assumes that dice are exactly symmetrical, and we all know that they are not, in reality. Let's ...
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1answer
25 views

Calculate a jetplane's distance from my location

So i was sitting outside my workplace and saw this jet flying. I was really curious if there is a way to calculate the jet's distance between the jet and my location. (I have very little knowledge ...
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1answer
74 views

Trouble with a Statement in Arnold's “Mathematical Methods of Classical Mechanics”

On Pg 6 of Arnold's Mathematical Methods of Classical Mechanics (2nd Edition), there is a line which reads One can speak of two events occuring simultaneously in different places, but the ...
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2answers
44 views

Physics- Horizontal Displacement

Currently working my way through a maths problem, and I've hit a brick wall. A circus acrobat is launched from a cannon that is aimed at 75 degrees above the ground. He leaves the barrel at a ...
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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 ...
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1answer
75 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
45 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 ...
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1answer
72 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 ...
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0answers
31 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 ...
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1answer
51 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 ...
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0answers
46 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
25 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 ...
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1answer
84 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
82 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 $$F_x = (60\mbox{ lb})\cos20^\circ$$ ...
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1answer
31 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 ...
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2answers
59 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 ...
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3answers
49 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 ...
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1answer
33 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 ...
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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 ...
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0answers
28 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
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1answer
88 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 ...
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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
38 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 ...
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1answer
40 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
22 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.) ...
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2answers
89 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 ...
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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 ...
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0answers
18 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 ...
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2answers
96 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, ...
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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 ...
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1answer
116 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
31 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 ...
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0answers
29 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 ...
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1answer
24 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 ...
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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 ...
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4answers
61 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 ...
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2answers
59 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 ...
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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. ...