Applies to questions of primarily educational value - not only questions that arise from actual homework assignments, but any question where it is preferable to guide the asker to the answer rather than giving it away outright. Please READ THE GUIDANCE IN META before asking homework questions.

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1
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0answers
459 views

Ball rolling without slipping inside a hollow cylinder

A small ball of radius $r$ performes small oscillations within a hollow cylinder of radius $R$. What would be the angular frequency of the oscillations given that the rolling is without slipping? The ...
9
votes
3answers
200 views

Thermal equilibrium in general relativity

The Newtonian condition for thermal equilibrium for a static system is $T = \mathrm{const}$. In this homework I'm asked to show that it's curved space generalization is $T(-g_{00})^{\frac{1}{2}} = ...
5
votes
2answers
1k views

how does a sniper scope work?

How does a sniper rifle scope enables us to pinpoint the exact location even though the lens in situated 5-6 inches above the muzzle. The bullet leaves the muzzle and hits the target exactly where the ...
0
votes
0answers
26 views

Expansion of $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ [duplicate]

How can I find the expansion of the Lagragian (it it only dependent on $v^2$) $L(v^2 + 2\vec{v}\cdot\vec{\epsilon}+\epsilon^2)$ in powers of $\vec{\epsilon}$ ? (From L.Landau, E. Lifshitz, Mechanics , ...
2
votes
1answer
71 views

Finding the components of the Riemannian tensor given the components of a metric

I am looking at a manifold of dimension $n$ (And I am considering a local co-ordinates system $x_1,x_2,\ldots x_n$) and the metric defined by the components $g_{ij} = \frac{\delta_{ij}}{x_1^2}$. I'm ...
0
votes
1answer
111 views

Moment around a point in a frame

Note: Both diagrams are 2d(they might look 3d because I drew them manually.) I have a prismatic frame that looks like this: I made a section on the half of the first pillar(the red line represents the ...
2
votes
1answer
471 views

Surface charge density relation with the radius of curvature at the surface of a conductor [closed]

In a text book it was given that the surface charge density of a conductor at a particular region on its surface is inversely proportional to the radius of curvature at that region. I didn't ...
3
votes
1answer
152 views

Transmission + Reflection coefficients >1 For Potencial Barrier with Negative Complex Part Contradicts Paper

I am studying reflection and transmission coefficients for a barrier consisting of a a step potencial defined by: $$V(x):=\begin{cases}0&{\rm if}\,|x|>a/2 \\ V_0+iW_0 & {\rm ...
2
votes
1answer
267 views

Spherical harmonics

Given the following potential: $$V(\theta,\phi)=\frac{Q}{a}\left(\sin\theta \cos\phi+\frac{1}{2}\cos^2\theta\right)$$ on the surface of a sphere of radius $a$ I am trying to solve Laplace's Equation ...
0
votes
1answer
243 views

Tensor of inertia

The tensor of inertia of a solid sphere is $I_{ii}=\frac{2}{5}MR^2$ about an axis passing through its CM. Why would the tensor of inertia of each hemisphere about that axis be ...
-2
votes
2answers
239 views

Fluids and density [closed]

Is the answer C? Assume that you look at three objects that all float on water, but have different shapes and sizes. Which one has the greatest density? A.The object that has the largest fraction of ...
1
vote
0answers
58 views

Questions on 4-vector velocities and invariance [closed]

Unfortunately, I missed a few lectures on four-vectors and I am pretty confused on how to go about solving the below question. I would be extremely grateful for any responses or solutions to enlighten ...
3
votes
2answers
331 views

Commutator of $L^2$ and $X^2$, $P^2$

In our quantum mechanics script, it states that $[L^2, X^2] = 0$ and $[L^2, P^2] = 0$, therefore for the following Hamiltonan $$H = \frac{P^2}{2m} + V(X^2)$$ it is that $[H, L^2] = 0$ therefore $H$ ...
2
votes
1answer
136 views

Sign wrong in angular momentum (Quantum Mechanics)

For small angles $\theta$ the rotation along a particular axis $n$ is given by $R(n,\theta)(r)=Id+ \theta (n \times r)+ o(\epsilon)$. Now, the rotation operator in Quantum Mechanics is given by ...
-2
votes
1answer
49 views

Error conversion [closed]

$\alpha_L = \frac{1}{a}\frac{da}{dT}$ I know error in $a$, i.e., $da$ I need to find out $d\alpha$ from data of $da$. $d\alpha_L = -\frac{1}{a^2}\frac{da}{dT}da$ Is this correct? Note: ...
2
votes
1answer
182 views

Lorentz force equation from relativistic Lagrangian

The relativistic Lagrangian is given by $$L = - m_0 c^2 \sqrt{1 - \frac{u^2}{c^2}} + \frac{q}{c} (\vec u \cdot \vec A) - q \Phi $$ I need to derive, $\displaystyle \frac{d\vec p}{dt} = q \left( \vec E ...
1
vote
1answer
97 views

Problem understanding a step in derivation of Lorentz Transformation

I need to understand a step in the derivation of Lorentz Transformation. I cannot understand how can we equate the equations 1 and 2. I am talking about the relation between ct, x, y, z. Where ...
0
votes
0answers
57 views

Eddington-LeMaitre model

I'm trying to solve Friedmann equations for $k=1 $ & $p=0$ (matter). These are equations: $$3(\dot{R}^2 +1)/R^2 -λ =8πGε$$ $$(2R\ddot{R}+\dot{R}^2 +1)/R^2 -λ=0$$ If we use $(\dot{R}^2 +1) /R^2$ ...
3
votes
2answers
145 views

Zwiebach quick calculation 2.5

I am working through Zwiebach's a first course in string theory. It's been a while since I did any math (or physics!), and I am stuck on the following problem (quick calculation 2.5 in the book): ...
1
vote
2answers
448 views

How do I find the tension in the cable from this problem? [closed]

I am trying to find the tension of the cable but I don't know what to do.
0
votes
1answer
73 views

Capacitors in parallel and dieletric [closed]

I'm trying to solve this problem: Two capacitors of capacitance $C_1=200pF$ and $C_2=1000pF$ are connected in parallel and loaded to a potential difference of $400V$. Subsequently the space ...
0
votes
1answer
126 views

Will Buoyant Force Change If The Container is Accelerated Up or Down?

If we have a fluid which is in a container that is accelerated, say, upward by $a$. Then, what will be the buoyant force on an object with volume $V$, Density of liquid, $\rho$? I believe it will be ...
0
votes
0answers
53 views

Graph of Lorentz force in function of angle between v and B-field?

I need to draw a graph of the magnitude of the Lorentz force in function of the angle between the velocity and B. Am i right in supposing this will be a sine wave?
1
vote
0answers
90 views

How much heat needed to heat 400g of ice at 0°C to 20°C in a 200g aluminium pot? [closed]

An aluminium pot has a mass of 200g and contains 400g of ice at 0°C. How much heat would be needed to melt that ice and then raise the temperature of the resulting water to 20°C. The specific heat ...
3
votes
1answer
285 views

Homopolar motor and Lorentz force

My second grader thought making a homopolar motor for her science experiment would be fun. And, it was. Now I am trying to explain how it works and the Lorentz force. Please help me by giving me a ...
0
votes
2answers
417 views

Finding the optimal angle of a projectile motion [closed]

I am trying to solve a task in which I need to calculate the optimal angle($\alpha$) with which the projectile will land the furthest from a height ($h$), so what I basically have is the equations for ...
1
vote
2answers
129 views

Questions on redshift [closed]

What are different kinds of redshifts and are they related to each other? If yes, how? Is redshift a measure of distance or time or etc? For example when we say a supernova with a redshift of $z=0.9$ ...
-1
votes
1answer
137 views

Charge of electrons and protons

I have a question which reads: "A conductor has a charge of $9.6 * (10)^{-19}$ coulomb. The conductor will have- " The problem I face in this question is due to not knowing the exact value of ...
0
votes
1answer
90 views

Show that the electric field, $\mathbf{\vec{E}}$ cannot be generated by any static distribution of charges

Show that the electric field $$\mathbf{\vec{E}}=\begin{pmatrix}0 \\ E_0x \\ 0\end{pmatrix}$$ where $E_0$ is a constant, cannot be generated by any static distribution of charges. I understand ...
0
votes
0answers
14 views

Find the position of the final image [duplicate]

I was going through Geometrical Optics and came across the following question in my textbook: Q. An object is placed $21$ cm in front of a concave mirror of radius of curvature $20$ cm. A glass slab ...
0
votes
0answers
60 views

Internal Stresses in a Horizontal Rod

Suppose we havean uniform slender rod of dimensions : $L$( length) and $A$( cross sectional area). Now at different points on the rod we apply different forces. So, in this situation how are we ...
1
vote
1answer
119 views

Change of operator in the Hamiltonian [closed]

We are told that the particle has mass m and charge e and is moving in 2 dimensions. The position operator $\mathbf{X}=(X_{1},X_{2})$ and momentum operator $\mathbf{P}=(P_{1},P_{2})$ We are given ...
0
votes
1answer
296 views

Block on an incline moving right with an acceleration [closed]

The situation looks as follows: The incline is moving rightwards with a constant acceleration The forces on the picture are: mg - weight, N - normal force, F - inertial force (already shown), ...
0
votes
1answer
96 views

How do I correctly choose signs for a falling particle?

An object falls from a height $h$ above water through air with negligible drag. In the water, the upward buoyancy exactly balances the downward gravitation force. The only remaining force on the ...
0
votes
0answers
13 views

Is this configuration correct for this spherical capacitor? [duplicate]

This capacitance contain 4 dielectric as shown in the figure dielectric 1 in half sphere and 2,3 in for 1/4 of the sphere and the fourth one in the last 1/4 of the sphere as shown and I want to find ...
2
votes
3answers
478 views

Looking for an intuitive understanding of normal force

I understand normal force to be the perpendicular force to a surface of contact. However, I have come across a problem which has caused me to rethink this. My initial understanding of force is ...
2
votes
1answer
274 views

Variation of modified Einstein Hilbert Action

In general relativity one can derive the Einstein Field Equations by the principle of least action through variations with respect to the inverse of the metric tensor. In some modified theories of ...
4
votes
1answer
171 views

Virial theorem and variational method: an exercise (re-edited)

I have a hydrogen atom, knowing that its Hamiltonian has been modified turning the standard potential $$ V_{0}(r) = -\frac{Z}{r} $$ into $$ V(r) = -\frac{g}{r^{\frac{3}{2}}} $$ with $g$ a positive ...
2
votes
1answer
102 views

Harmonic oscillator

Let $|0\rangle,...$ be the states of the harmonic oscillator. Then a squeezed state was defined as $|\xi\rangle =S(\xi)|0\rangle $, where $S(\xi):=e^{\frac{1}{2}( \xi (a^{ \dagger ^2}-a^2))}$, where ...
2
votes
1answer
91 views

Does this commutation relation hold?

I was wondering whether it is true that $[L_x^2,x^2+y^2+z^2]=0$. I could not find it in the internet and therefore I wanted to ask here whether anybody here knows that this is true or false.
-2
votes
2answers
362 views

How much water from ice and after how much time? [closed]

I need two formulas in dealing with ice and water. First: If I have 2 x 2 x 2 (cm) ice cube, after it melts, how much water will there be ? Second: If I have 2 x 2 x 2 (cm) ice cube, after how ...
1
vote
1answer
94 views

How can I show non-Abelian CS term is a total derivative?

I want to show:$$ Tr\left (F\tilde{F} \right )=\partial_{\mu}K^{\mu }=\partial_{\mu}\left (\varepsilon _{\mu \nu \rho \sigma }Tr\left ( F_{\nu \varrho }A_{\sigma }-\frac{2}{3}A_{\nu }A_{\rho ...
1
vote
0answers
77 views

Inflation problem for exponential potential

I'm trying to solve the inflation problem for exponential potential. $$v(\phi) = v_0 \exp(-\alpha \phi)$$ (it's known as barrow or power law inflation) we have two main equations: $$H^2 = 8π G / 3 ...
0
votes
0answers
67 views

Total energy of a rotating body?

I've no problems with the first part. However, I'm struggling with the last part of the question. The first thing I did is to find the a new moment of inertia for the whole system including the ...
1
vote
1answer
157 views

Finding the Schwarzchild radius of a star of solar mass 30

I am currently trying to determine the Schwarzchild radius of a star with solar mass 30. I am calculating it both with respect to solar mass, and w.r.t kilograms, however I am getting conflicting ...
0
votes
0answers
20 views

Schwarzchild radius of a star with solar mass 30? [duplicate]

I am currently trying to determine the Schwarzchild radius of a star with solar mass 30. I am calculating it both with respect to solar mass, and w.r.t kilograms, however I am getting conflicting ...
0
votes
1answer
78 views

What is the intrinsic colour of the star? [closed]

Hey I have this question and I am wrestling with it all day and I am completely lost. The V magnitude of a star is 15.1, B-V =1.6, and absolute magnitude Mv= 1.3 The extinction in the direction of ...
-1
votes
0answers
53 views

Mechanics Newtons third law [closed]

In the system suppose that the mass of the lower cylinder is $12 kg$. The system is held at rest in the position shown, with the tape taut and then released. Find the acceleration of a) the ...
1
vote
2answers
167 views

Minimum acceleration so that mass $m$ falls freely [closed]

A block of mass $m$ rests on a frictionless wedge of angle $\theta$ as in the figure. The wedge is given an acceleration $a$. What is the minimum value of $a$ so that the mass $m$ falls freely? I ...
1
vote
1answer
95 views

What is the de Sitter temperature as of now?

It is claimed that de Sitter temperature is $$T=\frac{1}{2\pi}H,$$ where $H$ is the Hubble constant. I presume it is expressed in natural units with which I am not familiar. So what it will be in ...