Wikipedia:Reference desk/Archives/Science/2012 January 12

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January 12

suicide rate vs gdp

Terry Gou, who chairs Hon Hai Precision which owns Foxconn, recently remarked that suicide rates climb with GDP growth. (source). Does this phenomenon have a name (if it's true)?Smallman12q (talk) 00:57, 12 January 2012 (UTC)

Here's a list of countries by suicide rate. Only 5 out of the top 20 are developed countries. Two of them are South Korea and Japan. Both of these have higher suicide rates than the number for China (but who knows how reliable Chinese statistics really is?) So, even if there is such an effect, it is weaker than cultural effects. --Itinerant1 (talk) 07:18, 12 January 2012 (UTC)

I advise massive caution for any country's reported suicide rate. Standards vary widely as to what is recorded as suicide, and in many cases are not even publicly known. HiLo48 (talk) 07:47, 12 January 2012 (UTC)

Also, DEVELOPED countries are not likely to have high GDP growth. They have high GDP, but it would be relatively stable. It is less developed countries, like China and India which experience high growth. Vespine (talk) 23:49, 12 January 2012 (UTC)

Suicide is associated with rapid societal change, which could include rapid economic development. But slower increase in GDP seems unlikely to have similar effects. Emile Durkheim in his classic Suicide (book) grouped suicides into four different types. Anomic suicides occur in conditions of anomie i.e. where there is societal change resulting in some breakdown of the traditional social order, meaning people can no longer fit into established social roles and their aspirations become detached from what society is willing or able to offer. Rapid changes in GDP would typically produce such social changes. (The WP article on the book includes some criticisms of Durkheim's ideas.) --Colapeninsula (talk) 11:48, 12 January 2012 (UTC)

Pellagra experiment article?

Do we have an article on Joseph Goldberger's famous pellagra experiment? I don't see a relevant link in either of the articles that I've just linked, and WhatLinksHere for those articles doesn't yield anything that looks promising. Nyttend (talk) 05:44, 12 January 2012 (UTC)

There is a paragraph about the experiment in the article on pellagra, but no dedicated article, I think. --Itinerant1 (talk) 08:47, 12 January 2012 (UTC)

seawater intrusion

is groundwater intruded into the fresh water column from its bootom or top part?--Savi3here (talk) 08:45, 12 January 2012 (UTC)

It comes from the bottom. Soil_salinity_control#The_soil_salinity_problem and the rest of the article should explain things for you. SmartSE (talk) 12:11, 12 January 2012 (UTC)

Angular momentum question

I am aware that if a body is moving with constant angular momentum that, depending on the body's inertia tensor, it need not have constant angular velocity; however, if a body has both constant energy and constant angular velocity, is its angular momentum necessarily constant also?--Leon (talk) 21:27, 12 January 2012 (UTC)

Yes. Angular momentum is always conserved in any system that doesn't exchange mass or energy with its surroundings. Red Act (talk) 23:43, 12 January 2012 (UTC)

But the question didn't rule out interaction with the environment. An object that's externally constrained to rotate at a constant rate around an axis that isn't a principal axis willmay(?) have constant angular velocity and kinetic energy, but nonconstant angular momentum. -- BenRG (talk) 02:02, 13 January 2012 (UTC)

Is there a proof that it will always have constant kinetic energy? I didn't realize that this was true.--Leon (talk) 09:15, 13 January 2012 (UTC)

I was thinking of an irregular object turning on a spit (at a constant rate, with no gravity), in which case the kinetic energy is constant by symmetry. The vector quantities all rotate around the spit, but the energy is a scalar. What I forgot is that the angular velocity won't be parallel to the spit except in special cases. I think you can still construct an example, but for all I know there's a theorem that the angular velocity is only parallel to the spit when the angular momentum is also. Rotational physics is hard. -- BenRG (talk) 17:29, 13 January 2012 (UTC)

I'll defer to BenRG's greater expertise, and strike out my incorrect answer above. Red Act (talk) 02:46, 13 January 2012 (UTC)

A good real-world example of BenRG's explanation is the little motorized weight inside a lot of mobile-telephones. "To first order approximation," the angular velocity and kinetic energy of the motorized portion are kept constant by the control-circuitry; but its angular momentum is not. Consequently, when powered, the rotation causes a net force to be applied to the device, "wobbling" or vibrating it. Nimur (talk) 03:11, 13 January 2012 (UTC)

Please don't defer to my greater expertise since I don't have any. See above if you don't believe me. :-) I don't think I believe Dragons flight's answer either since the tensor of inertia isn't constant (it rotates around the axis). I'd like to think about this more but I don't have time... -- BenRG (talk) 17:29, 13 January 2012 (UTC)

If you keep the axis of rotation fixed, the moment of inertia constant, the angular velocity constant, and the total energy constant, then I don't see how one can reach any conclusion other than that the angular momentum is constant. Basic angular momentum equal Iω. If you posit that the axis of rotation is not necessarily fixed, then you can get forces on the axis that create Nimur's vibrator. However, for a fixed axis, I don't see any way to have both a constant angular velocity and energy without also implying a constant moment of inertia and constant angular momentum. So I guess the answer may depend on the kind of system that you are willing to consider. Dragons flight (talk) 11:09, 13 January 2012 (UTC)

Constant angular momentum does not imply constant angular velocity: the angular momentum need not even share an axis with the angular velocity. But I'm curious if constant angular velocity implies constant energy, and if it doesn't, does the combination of constant angular velocity and constant energy imply constant angular momentum. Thanks.--Leon (talk) 13:01, 13 January 2012 (UTC)

If you have a fixed axis, then the assumption that both angular velocity, ω, is constant and rotational kinetic energy is constant, 0.5 Iω², would seem to imply that the magnitude of the moment of inertia about that axis, I, must also be constant, which is sufficient to conclude that angular momentum measured about the same axis, Iω, is also constant. Yes, you can have a constant angular momentum without a constant angular velocity, but only if you allow either the moment of inertia or the axis of rotation to change. (As occurs, for example, in orbital mechanics where the moment of inertia relative to the center of the mass of the system will vary with distance.) However, the assumption of constant angular velocity and constant energy taken together seem sufficient to preclude such variations. You additionally asked if constant angular velocity implies constant energy. In general, no, assuming you allow the moment of inertia (or axis of rotation) to vary. However, if you have a fixed axis and a fixed moment of inertia about that axis, then constant angular velocity is equivalent to constant energy. Dragons flight (talk) 18:11, 13 January 2012 (UTC)

The more I think about my vibrator, the more I don't like it. (Insert vibrator-joke if you must). The axis of rotation isn't constant, because the whole device is wobbling. That means the axis of rotation for the little motor is also changing! So, it might be the case that the angular momentum is "non-constant" in the pathological coordinate system that is constrained to the axis of the motor spindle. But that's an unreasonable coordinate system!

If the whole device were firmly clamped down, such that it could not wobble or vibrate, then the motor would spin, and there would be a time-varying contact force against the clamps.

I'm also thinking that my assumption about constant kinetic energy is less well-grounded than I earlier believed. The control-circuit probably drives constant current, thus constant input power, but motors with mechanical load have variable efficiencies: so constant input power need not translate in to constant output kinetic energy. The time-varying rate of thermal heating may be so huge that the kinetic energy fluctuates, per-rotation.

Anyway, I think I'd have to actually work out the Lagrangian here before I'm really satisfied with the answer I gave above. Nimur (talk) 18:24, 13 January 2012 (UTC)

No. As a counterexample, suppose a rigid object is constrained to rotate at a constant angular speed of 1 radian per second around the z axis. As per the definition of angular velocity in the 3-D case, the object, and every particle within the object, has a constant angular velocity vector of ${\vec {\omega }}=(0,0,1)$. Suppose also that the mass of the rigid object is negligible, except for a point mass of mass $m=1$, which at the initial time $t_{0}$ is at ${\vec {r}}_{0}=(1,0,1)$.

The initial velocity of the point mass is ${\vec {v}}_{0}=(0,1,0)$, the initial momentum of the point mass is ${\vec {p}}_{0}=(0,1,0)$, and the initial kinetic energy of the object is $E_{0}={\tfrac {1}{2}}m{v_{0}}^{2}={\tfrac {1}{2}}$. From the definition of angular momentum, the initial angular momentum vector is ${\vec {L}}_{0}={\vec {r}}_{0}\times {\vec {p}}_{0}=(1,0,1)\times (0,1,0)=(-1,0,1)$.

You don't actually need the moment of inertia tensor for this problem, but it is useful as a way of double-checking my understanding of the definitions used above. Calculating from the definition of the moment of inertia tensor, the moment of inertia tensor is initially

$\mathbf {I} _{0}={\begin{bmatrix}1&0&-1\\0&2&0\\-1&0&1\end{bmatrix}}$

It can be readily verified via a matrix multiplication that ${\vec {L}}_{0}=\mathbf {I} _{0}{\vec {\omega }}$, as required.

Similarly, at a later time $t_{1}$ such that the point mass has been rotated to ${\vec {r}}_{1}=(0,1,1)$, the velocity of the point mass becomes ${\vec {v}}_{1}=(-1,0,0)$, the momentum of the point mass is ${\vec {p}}_{1}=(-1,0,0)$, the kinetic energy of the object is still $E_{1}={\tfrac {1}{2}}$, and the angular momentum of the object has become ${\vec {L}}_{1}={\vec {r}}_{1}\times {\vec {p}}_{1}=(0,1,1)\times (-1,0,0)=(0,-1,1)$.

So the object has maintained a constant angular velocity, and constant energy, but the angular momentum has changed direction, and hence is not constant. Red Act (talk) 02:44, 14 January 2012 (UTC)

Thank you all very much! I think that's answered my question completely.--Leon (talk) 21:23, 15 January 2012 (UTC)

Exploding moon rocket = nuclear weapon?

Can an exploding moon rocket really create an explosion with the force of a nuclear weapon? Whoop whoop pull up ^{Bitching Betty | Averted crashes} 21:48, 12 January 2012 (UTC)

What is an "exploding moon rocket"? This isn't a term I'm familiar with, and Google doesn't pull up anything specific. --Mr.98 (talk) 22:50, 12 January 2012 (UTC)

What is meant be this often used remark, is that a large rocket has a similar thermal energy to a small atom bomb. However, all the fuel would not combust all at once and produce the same devastating effect that an atom bomb of the same power would produce. Still, I would not care to be standing next to one if it decided to under go a process of Rapid Unscheduled Disassembly. That's the whole reason why we sent retired folk to live in Florida.--Aspro (talk) 23:02, 12 January 2012 (UTC)

Using some very rough ballpark figures grabbed from our Saturn V and List of energy densities articles, for a moon rocket you'd be looking at some two million kilogrammes of fuel with an energy density upwards of 100 MJ/kg. That would be around 50 kilotons of TNT -- significantly more than the Little Boy. As Aspro said, the fuel most likely wouldn't explode all at once, but in terms of energy, it's roughly on the same order of magnitude as a (smallish) nuclear weapon. It's definitely far larger than any practical conventional explosive. --Link ^(t•c•m) 23:40, 12 January 2012 (UTC)

For comparison, the article List of the largest artificial non-nuclear explosions give the figure of 29 TJ for the energy of the explosion of the Russian N1, well beyond the smallest nuclear explosions ever archived -but who believes anything written in Wikipedia. --Aspro (talk) 23:45, 12 January 2012 (UTC)

Talking about nobody believing anything they read in WP. I've just noticed that the Department of Homeland Security doesn’t even mention us on it list of websites. Maybe Jimmy ought send them a letter of complaint.--Aspro (talk) 00:21, 13 January 2012 (UTC)

And of course a "moon rocket" can carry a warhead as easily as it can carry a spaceship. This is why foreign space programs (Like Russia previously, and now China) make some people nervous. APL (talk) 23:42, 12 January 2012 (UTC)

Point to note about the above comment: Nukes are so small now, that you don't need a big firework to deliver a bucket of instant sunshine into your neighbour's back yard and singe his begonias. The danger now is not from the megaton 'city busters' but from little 'sky-bursts' or a device delivered at the snails-paced speed of only 22 knots in a shipping container.--Aspro (talk) 23:58, 12 January 2012 (UTC)

true enough. I was simply trying to address a possible motivation for the question. News articles sometimes discuss that space rockets could be used "As weapons" or "as icbms" without explaining that they mean you need to add a warhead first. APL (talk) 04:25, 13 January 2012 (UTC)