The statement that a property of a system does not change if the system is isolated.

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Determine path of point mass using the Hamilton's principle

I am very new in this field but I try to solve a problem by using the Hamilton's principle and afterwards I want to compare the solution by solving the same problem using conservation laws. What I ...
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1answer
36 views

Charge conservation in the complex Klein-Gordon Field

This is an extremely naive question (based on a knowledge of chapter 2 of peskin and schroeder) so apologies for any things that seem obvious. The complex scalar field, when quantized, has a conserved ...
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200 views

Confused about elasticity and collisions

I was solving the following problem and the explanation to it confused me. There are two objects with mass $m$ and $M$, respectively. The object with mass $m$ has a velocity of $\sqrt{2gl}$ and ...
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2answers
91 views

How many hours will be in a day if the radius of Earth increases by 70 m?

I am little confused about the linear momentum and angular momentum, will the linear momentum of earth change due to changing of its radius or it will stay as it was and i know that the moment of ...
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2answers
804 views

Can conservation of momentum be violated?

The law of the conservation of momentum has been established for hundred of years. Even in Quantum field theory every particle collision must be momentum-conserving if there is homogenity in space. ...
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3answers
69 views

Constants of motion in quantum mechanics

What is the meaning of a constant of motion in quantum mechanics (an observable-operator that commutes with the Hamiltonian) in contrary with classical mechanics?
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5k views

Conservation of momentum but not kinetic energy in inelastic collisions

In inelastic collisions, the kinetic energy of the system is not conserved but the momentum is. Kinetic energy is: $0.5 \times \text{mass} \times \text{velocity}^2$. Momentum is: ...
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1answer
209 views

Shooting a bullet at a system of blocks [closed]

So, I made this question up myself.... and I'm curious about the answer. It requires only secondary-school-level knowledge of physics: You have a surface (ground) with a certain coefficient of ...
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2answers
65 views

How can I find the angular and linear velocity of a 2D body that breaks into two bodies?

Afternoon. This is my first question, so do let me know if I'm doing anything wrong. Looking for help on building a 2D physics game engine with bodies that split in half: I have a two dimensional ...
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1answer
48 views

First-order EM Feynman diagram?

Is there any 1st order electromagnetic Feynman diagram? I.e. a process whose probability is just $\propto \alpha_{EM}$? If not, is there any physical reason why? We always need at least two particles ...
3
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1answer
49 views

What justifies conservation laws in non-uniform spatial/temporal fields, if Noether's theorem doesn't?

Noether's theorem is based on the assumption that the Lagrangian is independent of position/time/angle/etc. Does this mean it doesn't prove, for example, conservation of momentum in a gravitational ...
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56 views

using tetrads to glue local currents into global currents

According to John Baez it is possible to take a locally conserved tensor $\nabla_\mu\: T^{\mu\nu}(x)=0\ \ \ \ \ \mbox{(locally)}$ and convert it to a globally conserved tensor by "patching" ...
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1answer
384 views

Hamiltonian Noether's theorem in classical mechanics

How does one think about, and apply, Noether's theorem in the classical mechanical Hamiltonian formalism? From the Lagrangian perspective, Noether's theorem (in 1-D) states that the quantity ...
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1answer
143 views

How did Feynman prove that energy cannot be extracted from electric field?

In the Feynman Lectures, vol. II, chapter 4, Feynman discusses electric potential and says: If we carry a charge from point $a \to b$, $$W = -\int_{a}^{b} \mathbf{F} \cdot ds.$$ Now, in general, ...
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3answers
181 views

Confusion regarding rotational motion!

Let us assume I have a rod of some mass m, moment of inertia I, length l and center C. If I apply a force F on C for a duration of time t, it will accelerate forward. If I apply it elsewhere, the ...
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1answer
46 views

Difference between speed of light and of bullet after passing through a barrier [duplicate]

I just read that, when a ray of light traveling in vacuum at $c$ strikes a glass slab, its speed decreases and then when it re-emerges it gets back to its original speed i.e $c$. If I draw a ...
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2answers
95 views

Pass to globally conserved currents from locally conserved currents in curved spacetime

Let us begin with a Lagrangian of the form $$\mathscr L= \frac 12 \sqrt{-g}g^{\mu\nu}\partial_\mu\phi(x)\partial_\nu\phi(x)+\mathscr L_g,$$ where $$\mathscr L_g=\frac 1{16\pi k}\sqrt{-g}R.$$ ...
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1answer
47 views

Using Conservation of momentum and Energy to solve a problem [closed]

A 9kg bullet is fired horizontally into a 10 kg block of wood suspended by a rope from the ceiling. The block swings in an arc, rising 6mm above its lowest position. Find the velocity of the bullet. ...
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6answers
706 views

Is (rest) mass conserved in special relativity?

I don't understand why it is said that the (rest) mass of a system is not conserved in relativity. I mean, the momentum of a system is conserved (i.e.: it remains constant in a frame of reference ...
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4answers
76 views

Sun and planets orbit each other

Do not the planets and the Sun revolve in orbits around each other and the shape of the orbit depends on where the center of gravity of the system is? The greater the mass of the Sun, the closer the ...
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3answers
2k views

Does a particle annihilate only with its antiparticle? If yes, why?

Or to put the question another way - what is the result of a proton-positron collision, or an up quark-charm antiquark collision, etc.? As far as I know, annihilation happens only between particles of ...
2
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1answer
60 views

Pair-annihilation why does it occour? [duplicate]

Why does pair annihilation occur with particles and only their matching anti-particle? E.g., electrons and positrons, but not protons and positrons? What is the difference?
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81 views

Why is $p_\phi$ conserved in a Schwarzschild orbit?

This arises from the question What is the relationship between $a$ and $m$, which I'm afraid I answered just by looking it up in Schutz's book. However Schutz (as he frequently does) glosses over ...
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1answer
360 views

Why can't Compton scattering happen in leading order of perturbation theory?

Why is the matrix element of Compton scattering in leading order of perturbation theory equal to zero? Why can this process only be described in second order of perturbation theory, i.e. with exchange ...
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1answer
52 views

Collisions between an object and a wall

Is momentum conserved when an object bounces back against a wall? The wall doesn’t move, but the object moves in the opposite direction. Assume this is an ideal, elastic collision. If, initially, the ...
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1answer
1k views

Kepler problem in time: how do two gravitationally attracted particles move?

Two particles with initial positions and velocities $r_1,v_1$ and $r_2,v_2$ are interacting by the inverse square law (with G=1), so that $$ {d^2r_1\over dt^2} = - { m_2(r_1-r_2)\over |r_1-r_2|^3} $$ ...
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41 views

Two Bodies Orbiting Around Each Other and Kepler’s Laws?

If two bodies are orbiting around a central center of gravity, how does Kepler’s first law (the one regarding the ellipse) apply?
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75 views

Comparing the orbit radius of two spherical objects [duplicate]

Assume the mass of star 2 is 4 times the mass of star 1. Compare the radius of the orbit of star 1 to that of star 2. Possible answers: R1:R2=1:4 R1:R2=1:2 R1:R2=2:1 R1:R2=4:1 R1:R2=16:1 ...
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2answers
42 views

Eulerian mass conservation on a stream line to Lagrangian mass conservation

if the density of a fluid particle is conserved on a streamline, $$\frac{d\rho}{dt}=0.$$ Why does this mean $$\frac{\partial \rho}{\partial t}+(\mathbf{v}\cdot\nabla)\rho=0$$ is true everywhere? Why ...
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1answer
47 views

Do all “normal” black holes rotate?

Can we assume that most (if not all) black holes are rotating, due to conservation of momentum? I am excluding the micro world from this question, just thinking of the range of stars on the main ...
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0answers
55 views

Noether's first and second theorems

My understanding of Noether's first theorem is as follows. Consider a set of infinitesimal transformations that leave the action invariant, that are indexed by $n$ linearly independent parameters, ...
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2answers
81 views

Can gyroscope work in zero gravity?

Most ships have two or more gyroscopes to balance on water, man made satellites uses gyroscope for orientation as they fall around earth. All these applications seems to be associated with gravity, ...
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2answers
54 views

Conservation of angular momentum in a planetary system

Why is angular momentum conserved when a planet revolves about sun in an elliptical orbit? Why is linear momentum not conserved in this case? Please use the minimum amount of equations and try to ...
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1answer
39 views

Continuity Equation for Momentum

Momentum is a conserved quantity, which makes me wonder if we can write an equation for the local conservation of momentum in the form of a continuity equation. If we're considering a system of ...
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0answers
25 views

Expected value, Fluid Mechanics and Momentum balance

I've been doing some problems on Fluid Mechanics involving the balance of Matter and Momentum and I have a question I've been wondering about. Suppose the following: We have a (viscous and ...
3
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1answer
62 views

Physics simulator based on conservation laws?

Reading the article: http://en.wikipedia.org/wiki/Newton%27s_laws_of_motion#Relationship_to_the_conservation_laws there's a section stating that: ...
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3answers
423 views

Two dimensional elastic collisions with varying angle of incident

If in an elastic collision I know all initial values and that mass for each object remains constant throughout the collision (but different from one another) how can I determine their final velocity ...
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5answers
8k views

Is it possible to shoot bullets in space or would the recoil of the gun be too strong?

I've read a few articles that say that astronauts have already brought guns in space and that shooting bullets in space is possible. But won't the recoil of the gun be too strong? Law of ...
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4answers
174 views

Thermodynamics thought experiment

There is some ideal gas in a container moving with some velocity on a smooth surface and you suddenly stop it( say by using your hands) , will the temperature of the gas increase? It seems to me that ...
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3answers
211 views

What is actually a conservation law?

Though in his lectures, Feynman didn't define conservation law, he did use it while explaining divergence theorem: [...] heat is conserved. That is, no heat is generated inside the material and ...
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5answers
875 views

Elastic collision of point particle and rod

A 1 meter long rod on the ice with mass $m_2=1$ kg is perpendicularly hit on one end by a point particle with mass $m_1=0.1$ kg. The collision is elastic and the point particle is bounced back in ...
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0answers
62 views

Antimatter universe and Noether's theorem

I am studying Feynman's "symmetry in physical laws", where he talks about conservation laws for corresponding symmetries. (I know this is Noether's theorem, I am studying this from David Tong's ...
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0answers
25 views

Interpretation of Mass Continuity Equation in MHD [duplicate]

I'm writing up my final-year dissertation and I'm required to give, as part of the introduction, an analysis of all the equations (and their terms) of which I use. Embarrassingly, whilst of course ...
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1answer
83 views

Why is $\int_{s} \mathbf{h}\cdot \mathbf{n} da = - \dfrac{dQ}{dt}$ & not $\int_{s} \mathbf{h} \cdot\mathbf{n} da = - \dfrac{dQ}{dt} .{dt}$?

I was reading the Lectures of Feynman about surface integral where a situation in which heat is conserved has been dealt. Let there be $Q$ heat energy present inside a body. Now, if there is net heat ...
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2answers
23 views

Conservation of Sea water Vs Conservation of Matter

I have been listening to people, since my childhood, saying that amount of water in Sea always remains constant even if we draw out much from it, it never changes. They used to emphasize by saying ...
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1answer
46 views

Finding final velocity in inelastic collision [closed]

Information: In a shipping company distribution center, an open cart of mass 49.0-kg is rolling to the left at a speed of 5.40-m/s (see the figure). You can ...
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1answer
33 views

Time evolution of generalized angular momentum operator

We define this operator : $$M^{\mu\nu} = \int d^3x~(x^{\mu}T^{0\nu} - x^{\nu}T^{0\mu})$$ where $T_{\mu\nu}$ is the energy momentum tensor (see e.g. Energy momentum tensor from Noether's theorem) ...
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172 views

How does the divergence theorem justify the integral form of the continuity equation?

I vaguely understand the continuity equation (at least its integral form), but I don't really understand the differential form of the continuity equation. I'm having trouble understanding how to ...
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1answer
92 views

Continuity equation in fluid mechanics

The continuity equation in fluid mechanics states that $$ \frac{\partial\rho}{\partial t} + \nabla\cdot(ρ\mathbf u)=0 $$ Can you explain to me what is the physical meaning of each term of the ...
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1answer
40 views

What is the definition of parity conservation?

I searched quite hard, and am still confused what is the exact definition of parity conservation? For example, we have quantum system with initial state $\Phi_i$, and after decaying it comes to final ...