# Tag Info

11

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 ...

6

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 ...

3

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 ...

3

The statement is really about the transformation between inertial co-ordinates and co-ordinates fixed to the body. This is expressed by: $$D_t = d_t + \omega(t)\times\tag{1}$$ where $D_t$ is the "total" derivative, i.e. the time derivative in the inertial frame, $d_t$ is the time derivative in the frame fixed to the body. Since there there are no torques ...

3

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 ...

3

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 ...

2

I don't have that text, but I can find the table of contents on the internet. Somewhere in that text (most likely chapter 5 on non-inertial reference systems), there should be a derivation that for any vector quantity $\boldsymbol q$, the time derivative of that vector in an inertial frame and a rotating frame that share the same origin are related by $$... 2 The basic physics in laymen's terms Okay, so the basic idea is: an object in motion tends to stay moving at the speed that it's moving. When we apply this to rotational dynamics we have an interesting effect: an objects speed goes linearly with the radius it is from the center it rotates around. So if something is rotating with a period T, it must go a ... 2 I doubt it is all fluid dynamics. The have to stay upright even with dead engines. If the integral of the lever below the water line is bigger than above then it should stay upright. Ballast at the bottom goes a long way as it has a long lever. Stuff like engines below deck tends to be heavy anyway. Weight is not a big deal as they are not going up ... 2 Notice that you have implicitly chosen to measure angular momentum about the axle of the platform. That means that all the forces exerted by the axle on the platform are applied through the axis for rotation, meaning the torque they exert is$$\text{force} \times \text{lever arm} = F \times 0 = 0\,.$$And there are no other forces present expect those ... 1 When our solar system formed it had a certain amount of intrinsic angular momentum. As it collapsed over time it began to spin faster like an ice skater that brings her arms in. Our planet, Earth, was formed in this cloud. It too is the product of that spinning gas cloud long gone. So the Earth retains the angular momentum of the matter that formed it. The ... 1 I think the answers are all correct, but it's worth pointing out that a lot of Earth's rotation came when it was hit by Theia. If Theia had hit the earth's other side, the Earth just might be spinning clockwise, against the spin of all the other planets. 1 I think you need to be careful here. The total power contained within a hurricane ranges from 1 \times 10^{12} to 6 \times 10^{14} Watts or 1 to 600 TW. The world energy consumption in 2008 was 20,279 TWh. There are 8760 hours/year, thus our consumption rate was ~2.31 TW (1 TW = 10^{12} W). The point being, the energy you would need to dissipate ... 1 While I'm not willing to spend the money to get access the paper, one issue jumps out at a casual reading of the abstract - turbine design. Honeste_vivere's answer mentions the possibility of destroying a farm, and the abstract includes "The reduction in wind speed due to large arrays increases the probability of survival of even present turbine designs." ... 1 Solution based on wind energy and cost aspects: Typical design range 10-20 m/s: Wind Turbines are designed to produce maximum power under somewhat above normal mean wind speeds such that overall energy output per total cost of ownership is maximised. This typically results in optimum operating velocities in the 10-20 m/s range. Wind Turbines already ... 1 Let's make this concrete by using a \text{spin-}\frac 1 2 state in the z direction, where we get to use the Pauli matrices, usually written as$$\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 = ...

1

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 ...

1

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 ...

1

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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