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
26 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
24 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
21 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
63 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
26 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
27 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 ...
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1answer
19 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
86 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
13 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
17 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
17 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
53 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, ...
0
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1answer
43 views

Connection between Functional Analysis and Quantum Physics [closed]

Hi does anyone have an idea of which specific areas of Functional Analysis and Topology have a strong connection with the study of Quantum Mechanics and Quantum Field Theory? Thanks.
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0answers
24 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
52 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 ...
-1
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2answers
48 views

Integrating to find deceleration, and finding ball height? [closed]

1) A ball is thrown straight up from a height of 8 ft with an initial velocity of 40 ft/sec. How high will the ball go? (Take g = 32 ft/sec2.) How would I do this? Wouldn't I need to find a velocity ...
1
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0answers
23 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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0answers
14 views

Source sound position mutiple point

i want find sound source position like this picture : ![find source][1] But i just konw the delay I know the delay for position 2 and 3 (or more) from source after hits the first point. I don't ...
0
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1answer
21 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
56 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
31 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
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2answers
79 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
44 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 ...
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0answers
52 views

how to solve this integral involving any square root

how to solve the integral $\int\sqrt{\alpha+\beta e^{\gamma t}}dt$ i got this integral from the problem Given that the velocity $v$ of a body $t$ segonds after passing a point $O$ is found by ...
0
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1answer
38 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
56 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? ...
-1
votes
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
votes
1answer
48 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
40 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
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1answer
23 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
350 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
27 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
votes
2answers
33 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
19 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
votes
1answer
19 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
59 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
votes
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 ...
1
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2answers
25 views

Calculate work done using integral

A chain lying on the ground is 10m long and its mass is 80kg. How much work is required to raise one end of the chain to a height of 6m? So im working in MKS system since its m and kg so the work ...
3
votes
1answer
34 views

Inequality involving sums and products (related to multi-stage rockets)

Let $a_i$ and $b_i$ be strictly positive real numbers for $i=1,\ldots, n$. I wonder whether the following inequality holds in general or does not:$$\frac{\sum_{i=1}^n a_i+\sum_{i=1}^n ...
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2answers
29 views

At 2:00pm a car's speedometer reads 30mph, and at 2:10pm it reads 35mph. Use the Mean Value Theorem to find an acceleration the car must achieve.

I'm only assuming that f(a) and f(b) are assigned to each respective velocity, but I'm not sure how the mean value theorem can be applied to distance rate and time.
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0answers
34 views

How do you get the curvature tensor of the Schwarzschild Solution?

So, on the Wikipedia page on the derivation of the Schwärzschild solution , I get everything up to the part about the Ricci tensor. What were the components of the tensor that were used? Could ...
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2answers
57 views

Need help with integral to evaluate electric field around a spherical shell.

I was trying to prove that the electric field at a distance $x>R$ from the centre of a charged shell is $\dfrac{kQ}{x^2}$. I did the physics part but I got stuck when I encountered the following ...
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0answers
34 views

Identities with dirac deltas

How are you supposed to verify or derive common physics text 'identities' involving dirac deltas like $$ \lim_{t \to 0} \mbox{sign}(t) \frac {\partial}{\partial t} \frac{\partial}{\partial x^i} ...
0
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1answer
18 views

Equilibrium Of Forces - Vector Condition

A body is in equilibrium under 3 forces A,B,C.Show that A x B = B x C = C x A (x represents cross product). Well I know the longish method of writing A= a i + b j + c k form and then balancing along ...
0
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1answer
7 views

Finding the velocity $v$ for which the total time the object moves from its initial position to the position where it stops is minimal

A body first moves with a constant velocity $v$ along a track with a length of $L=5 \ [m]$ and then decelerates with an acceleration $a=2 \ [\frac{m}{s^2}]$ till it stops. How to find the velocity $v$ ...
0
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2answers
80 views

Proof that Electromagnetic force is much stronger than gravity [closed]

The electromagnetic force is given by this formula: $$Fl=q(v\cdot\,B)$$ and gravity is given by $$Fz=m\cdot\,g$$ Now do I've to proof that the electrmagnetic force is much stronger than gravity but ...
0
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1answer
36 views

Application of differential equation (wave equation)

I am not 100% sure what is "steady-state solution w(x)". I tried to solve the question by first making equation (1) equals to zero; then integrate it twice with respect to x and substituted u=0,x=0 ...