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I was not able to convince him that this propulsion drive cannot work due to conservation of momentum. Am I wrong about that? No, you are not wrong. It's clear that the engine cannot work because of momentum conservation. It's basically just a fixed double pendulum. Why should there be any positive momentum in any direction after one full circle? ...


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Given the persistence of this kind of thing, maybe determining the misconceptions underlying it are not so easy to determine and resolve. [Given that we're talking about physics students, I guess it's fair to them to sort this out rather than ignore as one might otherwise.] For my money, I'd ask whether within each part of the mechanism Newton's Third Law ...


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The penny is usually not balanced when you spin it - it is precessing like a gyroscope. That means that as long as it has significant angular momentum, the torque due to gravity will not be able to topple it. As friction slows the penny down, the gyroscope effect becomes weaker until it drops. If the penny were spinning on a low friction surface about a ...


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Notice that you have implicitly chosen to measure angular momentum about the axle of the platform. That means that all the forces exerted by the axle on the platform are applied through the axis for rotation, meaning the torque they exert is $$\text{force} \times \text{lever arm} = F \times 0 = 0\,.$$ And there are no other forces present expect those ...


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Solution based on wind energy and cost aspects: Typical design range 10-20 m/s: Wind Turbines are designed to produce maximum power under somewhat above normal mean wind speeds such that overall energy output per total cost of ownership is maximised. This typically results in optimum operating velocities in the 10-20 m/s range. Wind Turbines already ...


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While I'm not willing to spend the money to get access the paper, one issue jumps out at a casual reading of the abstract - turbine design. Honeste_vivere's answer mentions the possibility of destroying a farm, and the abstract includes "The reduction in wind speed due to large arrays increases the probability of survival of even present turbine designs." ...


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I think you need to be careful here. The total power contained within a hurricane ranges from $1 \times 10^{12}$ to $6 \times 10^{14}$ Watts or 1 to 600 TW. The world energy consumption in 2008 was 20,279 TWh. There are 8760 hours/year, thus our consumption rate was ~2.31 TW (1 TW = $10^{12}$ W). The point being, the energy you would need to dissipate ...


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Any one of operators Lx, Ly, or Lz can be called quantized. There exists a set of states which are eigenstates of Lz; the matrix Lz is diagonal but Ly and Lx are not. There exists a set of states which are eigenstates of Ly; the matrix Ly is diagonal but Lx and Lz are not. There exists a set of states which are eigenstates of Lx; the matrix Lx is diagonal ...


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The basic physics in laymen's terms Okay, so the basic idea is: an object in motion tends to stay moving at the speed that it's moving. When we apply this to rotational dynamics we have an interesting effect: an objects speed goes linearly with the radius it is from the center it rotates around. So if something is rotating with a period T, it must go a ...


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Some dimensions I was able to dig up (mostly from Wikipedia). Draft of the Allure of the Seas: 31 ft (10 m) Length: 1181 ft (360 m) Beam at waterline: 47 m Height: 72 m above waterline Let's just draw the section based on these simple numbers: Now if the center of gravity were in the middle of the ship (31 m above the water line), it would indeed not be ...


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I doubt it is all fluid dynamics. The have to stay upright even with dead engines. If the integral of the lever below the water line is bigger than above then it should stay upright. Ballast at the bottom goes a long way as it has a long lever. Stuff like engines below deck tends to be heavy anyway. Weight is not a big deal as they are not going up ...


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I think the answers are all correct, but it's worth pointing out that a lot of Earth's rotation came when it was hit by Theia. If Theia had hit the earth's other side, the Earth just might be spinning clockwise, against the spin of all the other planets.


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When our solar system formed it had a certain amount of intrinsic angular momentum. As it collapsed over time it began to spin faster like an ice skater that brings her arms in. Our planet, Earth, was formed in this cloud. It too is the product of that spinning gas cloud long gone. So the Earth retains the angular momentum of the matter that formed it. The ...


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If you're asking why the Earth began rotating, the question isn't particularly enlightening, but the answer is simple: Because some torque acting on the Earth (more likely its constituent particles before gravity pulled them into a single object) in the distant past caused those particles to rotate in the counter clockwise direction. Although as LDC3 ...


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The total angular momentum of a closed shell is zero because for fixed $l$, we have the possible states labeled by eigenvalues of $L_i$ as $m_{l,i} = l,\dots,0,\dots,-l$ in integer steps. The sum over all $m_l$ inside a shell is always zero, so total angular momentum of a shell is zero. This is just the generalization of the argument with "up/down" for ...


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If my understanding is correct, an electron is an elementary particle which means that it is just a point in space, ... The electron spin is a special case of the general concept of angular momentum, which is a physical quantity generated by rotations. This is completely analogous to energy being generated by time translations and momentum by spatial ...


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We don't know if the electron is an infinitely small object. It may have size and if it does maybe that will make you feel better about the fact that it creates a magnetic field due to its intrinsic spin.


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As the comment above says, the word "spin" should not be taken literally, as in the spin of a beachball. The word spin came about as an attempt to physically understand the differing energy levels an electron can have, due to the magnetic field associated with it. The idea behind it goes back to when the electron was discovered experimentally to have a ...


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An electron does not spin! Its intrinsic angular momentum (the so called spin), should not be confused with the point-like electron rotating in configuration space (then the gyromagnetic factor would be one which is in a way related to charge spinning in configuration space. Actually the gyromagnetic factor of the electron spin is approximately 2.) A black ...


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anyway, how likely is it the ice ages could be explained by the earth 'realigning' so that polar regions would migrate over the surface of the earth? How about zero? The geological evidence of the Ice Ages clearly says that, between the ice episodes, the ice did not move. It's just that the polar caps shrank. For instance, the extent of the last ice ...


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The polar ice will melt, due to increase of temperature in earth's surface, by global warming. The rate of cooling of earth's inner heat will be slow, resulting more molten lava in the lower mantle, will be changed into liquid. The heavier mass of the liquid will go down, resulting decrease of angular momentum. Conclusion-Increase of angular momentum of ...


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While there is an origin for the position operator $\vec r$, and therefore the angular momentum $\vec L = \vec r \times \vec p$ has an origin, it is a little glib to say that there is an angular momentum operator. What you can is three operators $\hat L_x,$ $\hat L_y,$ and $\hat L_z$ whose forms are a inspired by the forms of the three components of the ...


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This is formally equivalent to the fact, that a magnetic field does not change the magnitude of a velocity. The answer is, because the torque is perpendicular to the angular momentum (as you point out, cast in math $\vec L \cdot \vec \tau = 0$). Then it is a one liner: $$\partial_t \left|\vec L\right| = \frac{2 \vec L \cdot \dot{\vec L}}{2 \sqrt{\vec L \cdot ...


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Let's calculate $[L_x L_y, L_z]$. I'm going to use the property $[AB,C]=A[B,C]+[A,C]B$. If you apply the property to our case, you obtain $L_x[L_y,L_z]+[L_x,L_z]L_y$. Now you can substitute the value of the commutators and find the correct answer. Note that the quantum commutation relations are pretty similar to vector product in cartesian coordinates. For ...


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As Dirk Bruere has pointed out, the mass of the earth's oceans is 1400/5 times the mass of the earth's atmosphere. If 1% of that mass is converted to vapor (and not immediately precipitated out), this implies a mass of water vapor 1400/500 times the mass of the atmosphere, or 2.8 times greater. Ignoring the slight change in gravitational attraction of the ...


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Earth's atmosphere = 5 x 10^18 kg Earth's oceans = 1.4 x 10^21 kg So if 1% of the water became atmosphere the pressure would likely increase by about a factor of 3 or so. Probably not survivable given the temperature this would require


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Let's make this concrete by using a $\text{spin-}\frac 1 2$ state in the $z$ direction, where we get to use the Pauli matrices, usually written as$$\sigma_x = \left[\begin{array}{cc}0&1\\1&0\end{array}\right]; ~~~\sigma_y = \left[\begin{array}{cc}0&-i\\i&0\end{array}\right]; ~~~\sigma_z = ...


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Gas temperatures rise with compression and fall with decompression. The outer layers of the vortex the is compressing the gas (heat) due to centrifugal force. The center of the vortex has a low pressure comparitavely. (Cool).



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