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1

You have proved with your analysis that $v_2$ cannot be zero. $m_2$ must be moving with some non-zero velocity, either in the same direction as $m_1$, in which case $v_2$ must be smaller than $v_1$ (or $m_1$ will never catch up to $m_2$) or $m_2$ must be moving in the opposite direction to $m_1$. With the information given, there are 4 unknowns: $v_1, v_2, ...


0

The total angular momentum of the disk doesn NOT change. There is an outflow of angular momentum due to the shearing of matter rotating at different velocities. Faster inner annuli get a spin down torque from slower outer ones, so they lose angular momentum in favour of the angular of momentum of the outer annuli. I can express this better and answering ...


2

Answer posted by Lubos Motl in the comments; I reproduce most of it here. This answer was posted in order to remove this question from the "unanswered" list. Some (sketches of) answers to your questions, one by one: Physical states have to be invariant under gauge symmetries, so all of them are singlets and there are no nontrivial representations, (and 3....


1

force is change in impulse over time, so saying that impulse is lower than static friction does not make sense, in the same way that saying that some speed is larger than some acceleration, they are different things. Impulse from a moving object is transferred to the one at rest through a force, that results in an exchange in momentum. During the ...


0

You want to read the classic paper by Richard Beth, Mechanical detection and measurement of the angular momentum of Light, Physical Review 50 115 (1936). Beth used bright circularly polarized light to drive a torsion pendulum in a vacuum chamber, and was able to observe torques due to circular polarization of order $10^{-16}\rm\,N\,m$. This was with a ...


1

It is a little different in General Relativity. Let's start with Special Relativity and all the 3 forces of the Standard Model in physics. Then we will talk about gravity and the universe. In The Standard Model spacetime is Minkowski, meaning flat in all 4 dimensions. If it is that way clearly any direction and position is equivalent. That's called ...


3

All of your claims are essentially true. The angular momentum of light, in both its orbital and spin varieties, is indeed angular momentum that can be transferred to matter to make it spin and give it the garden variety of mechanical angular momentum. This is well explained in the relevant Wikipedia section, with good references for experiments that show it. ...


4

The 'rule' that "matter can not be [created or] destroyed" simply isn't true. Matter can be created and destroyed under the right circumstances, it's just that those circumstances are not met for macroscopic quantities of matter in places where humans live. This means that the conservation of matter can be taken as true in almost all of chemistry and large ...


35

To maintain lepton number as a conserved quantity. Consider, in detail, what's going on in a beta decay (well, I'm going to ignore the nuclear context). The reaction is then $$ n \longrightarrow p^+ + e^- + \nu \,,$$ where you should take the symbol $\nu$ to mean some neutrino (without prejudice about matter-type or anti-matter-type for the moment). There ...


3

Regarding total momentum conservation, the point is that in non-inertial reference frames inertial forces are present acting on every physical object. Momentum conservation is valid in the absence of external forces. However, if these forces are directed along a fixed axis, say $e_x$, or are always linear combinations of a pair of orthogonal unit vectors, ...


0

First off I would recommend a very large boot. "Size billion" comes to mind. Second I would query "in what direction are you planning to kick said ball with said billion sized boot, fine sir?" Since direction is not specified in this...ahem...matter...ahem...I find the issue at hand confounding indeed. Still...we all could use a few more hours in our day ...


0

This is similar to Can humans control rotation of the Earth? and How can you find the impact necessary to change the direction of Earth's spin? Suppose the ball is kicked against the direction in which the Earth is rotating. This increases the speed of rotation of the Earth, reducing the rotation period (ie the length of 1 day). The angular momentum ...


1

Whilst the motion you intend is not altogether clear, the motor will indeed move as you say. But the attached rigid bodies also move, such that the center of mass of the whole system is stationary (or, more precisely, its state of motion unperturbed by the system's internal motions). Work out the path of the center of mass in your system to check this ...


0

You say: the motor's velocity is always $>=0$ but this is not true. The magntude of the velocity is indeed always greater than or equal to zero, but velocity is a vector so the direction matters as well. The motor will oscillate alternately up and down as the masses rotate around it. The combined centre of mass of the motor and the two masses will ...


4

We shall consider the man to be at the middle of the box initially. If the man starts walking left, the box shifts towards right (assuming no friction) such that the centre of mass of the man box combined system remains on the tip. If the man reaches the end of the box and starts jumping, the box begins to oscillate about the centre of mass and lf cases are ...


2

The short answer to your question: Yes, they can. But in the particular example you are considering, they don't. As mentioned by Jahan, it is the gravity that gives the system (man+box) a net non-zero momentum. A rather interesting point to worry about in this scenario is 'who gives the system a net non-zero angular momentum?' Since gravity acts through the ...


1

The net force isn't zero. There is an external force, namely gravity. If you did this experiment in outer space, where there truly was no external force, you wouldn't see the box topple over.


0

To begin with, it is important to clarify the scenario. When two masses are attracted to each other, regardless of their magnitudes, the gravitational force (and hence acceleration) vector acting on each is in the direction of the other. If two masses were sitting motionless in a vacuum, they would accelerate toward each other in a straight line until such ...


3

Since $[\hat{H},\hat{H}]=0$, you also have $[\hat{H},\hat{U}(\tau)]=0$. So, if we consider Schrodinger's equation, we have (neglecting factors of $\hbar$ for simplicity) $$ i\frac{d}{dt}|\psi(t)\rangle = \hat{H}|\psi(t)\rangle $$ Multiplying both sides by $\hat{U}(\tau)$ gives $$ i\hat{U}(\tau)\frac{d}{dt}|\psi(t)\rangle = \hat{U} (\tau)\hat{H}|\psi(t)\...


21

TL;DR: every time you use momentum conservation. One way to see this is to take a close look at Newton's cradle: Image is published under GNU Free Documentation License You can start with Newton's second law: $$\mathbf{F}=m\mathbf{a}=m\frac{d\mathbf{V}}{dt}$$ By calculating the scalar product with the velocity vector on both sides of the equation we ...


13

The reason why one often thinks that all the familiar phenomena can be explained just on the basis of the second and the first law of Newton is that it is not clearly emphasized (mainly in school textbooks) that Newton's second law for a system of particles can take the form of $F_\textrm{external}=\dfrac{\mathrm d}{\mathrm dt}(p_\textrm{system})$ only when ...


0

Newton's third law emanates from the fact that the momentum of an isolated system is always conserved viz. $$\mathrm d\mathbf p_1 +\mathrm d\mathbf p_2 ~=~0 \;.$$ From this, it can be inferred that $$\int_{t_\mathrm i}^{t_\mathrm f}~ \mathbf F_{21}~\mathrm dt ~=~ - \int_{t_\mathrm i}^{t_\mathrm f}~ \mathbf F_{12}~\mathrm dt\tag 1$$ It could be that the ...


3

The corresponding symmetry group is the Lorentz group and yes we can use Noether to derive conserved quantities: Invariance under translations $\rightarrow$ momentum conservation Invariance under rotations $\rightarrow$ spin and angular momentum conservation Invariance under boost $\rightarrow$ some strange, not really useful, conserved quantity



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