# Tag Info

46

The astronaut can change his or her orientation in the same way that a cat does so whilst falling through the air. After the transformation, the astronaut is still and angular momentum is conserved. There is a rather beautiful way of understanding this rotation as an anholonomy i.e. a nontrivial transformation wrought by the parallel transport of the cat's ...

24

At the physics 101 level, you pretty much just have to accept this as an experimental fact. At the upper division or early grad school level, you'll be introduced to Noether's Theorem, and we can talk about the invariance of physical law under displacements in time. Really this just replaces one experimental fact (energy is conserved) with another (the ...

21

Warning: this is a long and boring derivation. If you are interested only in the result skip to the very last sentence. Noether's theorem can be formulated in many ways. For the purposes of your question we can comfortably use the special relativistic Lagrangian formulation of a scalar field. So, suppose we are given an action $$S[\phi] = \int {\mathcal ... 21 It's a very common misconception that black holes suck in matter. Outside the event horizon the gravitational field from a black hole is just like the gravitational field from normal matter with the same mass. The black hole can't suck in matter because matter will orbit it just like matter orbits a normal star. It's likely there are a lot of black holes in ... 20 For those that are cat-challenged, here's an alternative explanation and demonstration you can try at home! This demonstration was taught to me by my math lecturer. All you will need is: A swivel chair and a heavy object (e.g. a big textbook) Stand on the seat of the chair (watch your balance now) holding the heavy object. Extend your arms forward ... 13 The symmetry you are asking about is usually called a scale transformation or dilation and it, along with Poincare transformations and conformal transformations is part of the group of conformal isometries of Minkowski space. In a large class of theories one can construct an "improved" energy-momentum tensor \theta^{\mu \nu} such that the Noether current ... 13 From conservation of angular momentum we have (I+\Delta I)(\omega+\Delta \omega) = I\omega, or$$\frac{\Delta \omega}{\omega} = - \frac{\Delta I}{I+\Delta I} \simeq -\frac{\Delta I}{I}. We make the following simplifying assumptions: The earth is a sphere of uniform density of mass $M$ and radius $R$. The building is constructed on the equator by ...

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When the cosmonaut sneezed they would start moving, and rotating, in the opposite direction, but when the sneeze hit their faceplate (ugh!) this would stop the motion. The net result is that the velocity of the cosmonaut would not have changed, but their position and angle would have. According to Wikipedia a typical breath is 500cm$^3$ and a sneeze ...

10

No, it's caused by conservation of angular momentum. Reducing air resistance won't cause her (or anything else) to speed up without an external force. Like linear momentum ($m v$), angular momentum ($r \times mv$) is a conserved quantity, where $r$ is the vector from the center of rotation. For a skater holding a static pose, for each particle making up ...

10

Another way of solving such problems is to go to another reference frame, where you obviously don't have enough energy. For example you've got a $5 MeV$ photon, so you think that there is plenty of energy to make $e^-e^+$ pair. Now you make a boost along the direction of the photon momentum with $v=0.99\,c$ and you get a $0.35 MeV$ photon. That is not ...

10

Well, if we make a quick estimate of the mass of a huge building. Let's say the building has a base of $100\times100 \;\text{m}^2$ and a height of $1500 \;\text{m}$, this is already substantially bigger than the current biggest building. Then we have a volume of $1.5\times 10^7\text{m}^3$. If we make the assumption, again very rough and on the high side, ...

9

The stress energy tensor $T^{\mu\nu}$ contains all the energy/momentum components of the elctromagnetic field and the conservation of these components is expressed by $\partial_{\nu}T^{\mu \nu} = 0$ Which states that the change in time of energy/momentum is zero. If the above is non-zero then electromagnetic field energy/momentum is transferred to charged ...

9

This is a fairly subtle question! Griffiths recently published a paper on this. Hidden momentum, field momentum, and electromagnetic impulse: Electromagnetic fields carry energy, momentum, and angular momentum. The momentum density, $ϵ_{0}(E\times B)$, accounts (among other things) for the pressure of light. But even static fields can carry ...

9

It is possible to show that the total momentum of any static system is zero in an inertial frame where nothing is moving. This does not mean that the momenta associated with various components of that system are individually zero. As you point out, there can be finite electromagnetic momentum associated with static charge distributions. Even though there is ...

9

Here is a visualization: Momentum is mass times velocity, so draw it as the area of a rectangle: If we change the mass and velocity a little, we change the momentum: The total change in the momentum is the sum of green, blue, and purple rectangles. Their sizes are just length times width, so overall we have $\Delta p = m\Delta v + v\Delta m + \Delta ... 9 Not much sense. Your "center of charge" is nothing but the dipole moment divided by the net total charge. "Normalised dipole moment, if you will". If you take$q|\vec v|$instead of$q\vec v$, you get something related to current (generally current times a factor). Current is conserved at a junction. Regarding your equal-and-opposite situation, the closest ... 8 As with any other rocket, ejecting the propellant out the nozzle generates an equal and opposite thrust. The difficulty here is that the propellant is in the body of water the device flys above. If you read the FAQ at the jetlev website you will see that power and pumping is provided by a separate floating unit. The buoyancy of the boat unit supports the ... 8 Anglular momentum is conserved, so any tiny initial rotation that a the original ball of gas had becomes faster as the gas collapses down into a star and disk of planets. Planets near the sun rotate slowly for the same reason that the moon always faces the same side to the Earth - tidal braking Venus probably received a hit from a some lump of rock / ... 8 We can prove it in perturbative string theory but it's probably valid beyond it. In perturbative string theory, any (continuous) global symmetry has to be associated with a conserved charge which, because of the locality of the physics on the world sheet, implies the existence of a world sheet current$j$or$\bar jor both (left movers vs right movers) ... 8 Just conserve angular momentum. If I have two photons on a collision course, their spin can either be aligned or anti-aligned, since photons must have spins lying on the same plane as their motion by virtue of their masslessness. Then, you can either add one to one to get two, or you can subtract one from one to get zero. If you have a decay to two ... 8 Of course you can define such a quantity, but the question is: does it mean anything physically? Contrary to what has been stated in some of the answers/comments, this quantity is not comparable to a "normalized" dipole moment. A dipole is a system of two charges equal in magnitude but opposite in sign. The corresponding dipole moment, which is of great ... 7 thank you for the nice question. It directly relates to the topics of conformal field theories. I found a very nice thread in another forum where I guess your question has been answered. Nevertheless, I will try to summarize the main points here and maybe add some points. Symmetries in General Relativity In general relativities, symmetries correspond to an ... 7 Joe's answer is of course right and I gave it +1. However, let me say some slightly complementary things. Whenever the laws of physics don't depend on the orientation in space, a number known as the angular momentum is conserved. For a rotating body - including the body of a lady - the angular momentumJ\$ may be written as the product of the moment of ...

7

Well I ought to be studying for a physics exam, but I'll consider answering this to be my studying. Newton's third law states that for every action, there is an equal an opposite reaction. In this case, the jetpack is ejecting water at high velocity toward the ground. This is generating a significant force downward. The resulting opposite force pushes ...

7

In elementary particles all particles that have spin different than 0, spin, i.e. have angular momentum, so photons are spinning too, they have spin 1. There exist particles and systems with spin 0 (pions as an example), those do not spin :) . Since physics started from macroscopic studies one has to look at the equations that describe motion classically, ...

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If by "they are associated with different masses" you mean that the flavor eigenstates have different masses then you are working from a misconception. Those states are not eigenstates of the free Hamiltonian so they don't have a mass as such. (They do have a mean expectation if you could weight a bunch of them, but it does not apply to any given neutrino.) ...

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