# Tagged Questions

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

22 views

### Expression for nano scale crack propogation

The following image is of a nano-scale self replicating crack on a thin film/substrate pair. I want to construct a "position" function for the crack front's propagation. So far the only way I can ...
16 views

### shifting integration variable and taking derivative seemingly giving problem

I am doing loop integral in quantum field theory, and an issue in shifting integration variable is giving me a problem. Let me illustrate with an example. I have an integral that looks approximately ...
31 views

### Clarification about consequence of physics' first principle of thermodynamics

I'm reading the book Physics, by Tipler, and I'm confused at the following statement: [...] From the first principle of thermodynamics, $\Delta U = Q+ W$. Suppose an ideal gas is given heat while ...
22 views

### Deriving E=mc^2 from hollow box with mass M and photon

I'm working on a problem to derive E=mc^2 using conservation of momentum and center of mass. We have a hollow block of length L and mass M. A photon passes through taking mass m and adding it to the ...
39 views

### Work required to align pieces in a plane.

Given two piecewise continuous functions f(x) and g(x) and that $\lim_{a -> x^-} g(a) - f(a) = \lim_{a -> x^+} g(a) - f(a)$ at all points, find the work used to shift each of the planar slolids ...
13 views

### pressure field calculation from velocity field

Velocity field $v = (kx, -ky, 0)$. Initial condition is that pressure is $P$ at origin. I have to find pressure field, which is easy in this case. My problem is the gravity. In part a of the ...
20 views

### Confused with the reexpression of a Hamiltonian in eigenbasis

In the section 4.1 of Quantum Computation by Adiabatic Evolution, Farhi et al proposes a quantum adiabatic algorithm to solve the $2$-SAT problem on a ring of spin chain. To compute the complexity of ...
9 views

### Centre of pressure [on hold]

I am reading about Centre of pressure and have got one confusion : I read that Centre of pressure is independent of inclination with horizontal for a plane figure. In that case, by rotating the plane ...
22 views

### Understanding elastic collision between two rocks with unknown masses

I have this problem here that goes like this: Two curling rocks of equal mass, one red and the other yellow, are involved in a perfectly elastic, glancing collision. The yellow rock is initially at ...
25 views

### What is the angular velocity in an inertial frame given the angular velocity in a body fixed frame?

At a given time t, the rotation matrix R has the value: $$R= \begin{pmatrix} 0.675 & −0.1724 &0.7174\\0.2474 & 0.9689& 0 &\\−0.6951& 0.1775&0.6967. \end{pmatrix}$$ The ...
27 views

### Make a mathematical model from the given temperature problem

Find the temperature $u(x,t)$ in a laterally insulated bar of length $L=3.14$ $m$ having the material property $k=c\rho$ whose ends are kept at temperature $0$ degree Celsius, assuming that the ...
45 views
+50

24 views

### By which the Heisenberg group is introduced? [closed]

I want to know who was the first who introduced the Heisenberg group and in what year. In the Wikipedia there is just an indication that this group was named in honor of the famous German physicist ...
1k views

### Displacement vectors

You walk $53$ m to the north, then turn $60$ degrees to your right and walk another $45$ m. Determine the direction of your displacement vector. Express your answer as an angle relative to east. So ...
43 views

### Central force is planar in n-D

So in 3-D the differential equation $$\ddot{\bf{r}} = -\frac{f(r)}{m}\bf{r}$$ is shown to be planar by noting $$\bf{r} \times \dot{\bf{r}}$$ is constant. But isn't the differential equation planar (...
411 views

### Centre of Mass and Moment of Inertia of a sphere - spherical cap

I have been given a sphere of radius a, from this sphere a cap of hight h is cut off. 1) What is the centre of mass of the rest of the sphere? 2) What is the moment of inertia regarding the axis of ...
34 views

### differentials in physics [migrated]

Often I find the following expressions in physics books: Say we have a current density $\vec{j}=\rho\vec{v}$ through a surface $\vec{F}$ of particles $N$ in the volume $V$ with the density $\rho=dN/dV$...
72 views

### A friend and I are trying to figure out who is doing more work benchpressing? Me? Him? Or is it the same amount? [closed]

Me and a friend have been working out for some time and have been bench pressing each week, increasing our weight. Once we started getting to heavier weight we noticed that he was able to get more ...
912 views

### Acceleration and Tangential Velocity Vector?

Find the resultant acceleration of a particle moving on a circle of radius $0.70\ m$, if its angular speed is 37 rpm and its tangential acceleration is $2.9 \frac m{s^2}$. Express the angle with ...
19 views

### Question about G-Forces and Circular Motion on a Human Centrifuge

I don't really understand what a G-force is and how it can be used to solve problems using the formula: $$T=mv^2/r$$ T is tension, m is mass (in kg), v is velocity (m/s) and r is radius of the circle....
37 views

### Space-time mathematics. Do I get this right?

Trying to understand general relativity like this, do I get this right? distance in $space \neq$ distance in $time$, if $space$ and $time$ = $2$ separate dimensions distance in $space =$ distance in ...
27 views

### Accelerate to Max velocity, then decelerate to known velocity

I have an object traveling at a known velocity (Vi). It then accelerates (known A) to a known maximum velocity (Vmax), then decelerates (-A) to another known velocity (Vf). The total distance ...
24 views

### Vector magnitude notation

Is the follow equality true? $$\left| \overrightarrow {u}\right| =u$$ I wonder, because on AP Physics formula sheets, sometimes the magnitude of a vector is clearly denoted, while other times the ...
25 views

### Instantaneous rate of change of a three-dimensional parametric

In physics, it is common to define the horizontal position $x$ and the vertical position $y$ of an object as functions of $t$ and then us the formula \dfrac {dy}{dx}=\dfrac {\dfrac {dy}{dt}}{\dfrac {...
52 views

### a question about circuits and diferential equation [closed]

Consider the DC circuit of Figure $4$. Inductance L satisfies $L = (R^2) C / 2$. Calculate: a) The differential equation for the charge $Q (t)$ contained in the capacitor; b) The solution of ...
A racing car completes $5$ rounds of circle in $2$ mins . It has uniform centripetal acceleration $\pi^2 t^{-2}$ then the radius of circle is?. I asked it on physics $SE$ but I dont know how to ask ...
$v(x)$ given $a(x)$, where $v_0 = 0$ and $x_0 = 0$ I'm clueless. This is what I thought: $dv = v, dx = x$ \$a(x) = \frac{dv}{dt} \frac{dx}{dx} = \frac{dx}{dt} \frac{dv}{dx} = v\frac{dv}{dx} = \frac{...