Difference between revisions of "2413: Pulsar Analogy"

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(Explanation)
(Explanation: ...you /could/ tie a thread to the loose end, wrap that around the untensioned spool and out of the access hole, reattach the sideplate and then tug the end back out. Assuming the tape itself doesn't try to 'straighten' off the spool!)
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When a tape measure retracts, the part of the tape outside the tape measure is not going directly towards the tape measure's center but rather towards a hole in the side. This means the tape possesses some angular momentum relative to the tape measure. In addition, when the tape measure retracts, the part of the tape inside the tape measure rotates around a spool (which pulls the part of the tape outside the tape measure inside), so it also has angular momentum relative to the tape measure. When the tape is completely retracted, the tape can no longer rotate relative to the tape measure, so the entire tape measure rotates due to the conservation of angular momentum. While pulsars also rotate quickly due to the conservation of angular momentum, the exact mechanism is different. Pulsars are formed when stars collapse due to no longer performing enough fusion to produce enough heat and energy to cancel out gravity. This causes the star to contract, which causes its mass, on average, to be closer to its access of rotation, which causes the rotational inertia (also called the moment of inertia) to decrease. If the star's angular velocity stayed constant, this would cause the angular momentum to decrease, so the star's angular velocity must increase in order to offset the decrease in rotational inertia, i.e. the star (which is now a pulsar) spins faster.
 
When a tape measure retracts, the part of the tape outside the tape measure is not going directly towards the tape measure's center but rather towards a hole in the side. This means the tape possesses some angular momentum relative to the tape measure. In addition, when the tape measure retracts, the part of the tape inside the tape measure rotates around a spool (which pulls the part of the tape outside the tape measure inside), so it also has angular momentum relative to the tape measure. When the tape is completely retracted, the tape can no longer rotate relative to the tape measure, so the entire tape measure rotates due to the conservation of angular momentum. While pulsars also rotate quickly due to the conservation of angular momentum, the exact mechanism is different. Pulsars are formed when stars collapse due to no longer performing enough fusion to produce enough heat and energy to cancel out gravity. This causes the star to contract, which causes its mass, on average, to be closer to its access of rotation, which causes the rotational inertia (also called the moment of inertia) to decrease. If the star's angular velocity stayed constant, this would cause the angular momentum to decrease, so the star's angular velocity must increase in order to offset the decrease in rotational inertia, i.e. the star (which is now a pulsar) spins faster.
  
Letting the tape snap into the fully retracted position will shorten the measure's lifespan, however: If the rivets that hold the bracket at the end of the tape shear off, the tape will retract entirely inside the measured body, and will be useless.
+
Letting the tape snap into the fully retracted position will shorten the measure's lifespan, however: If the rivets that hold the bracket at the end of the tape shear off, the tape will retract entirely inside the measured body, and will be useless until repaired - which will entail opening up the body itself in order to re-extend the slackened tape against the spring (without anything bursting out sideways, with further reassembly issues) and somehow affix the end bracket without notably altering the measuring length.
  
 
Some tape measures have a built-in {{w|laser line level}}. Pulsars emit electromagnetic radiation out of their magnetic poles, which is similar to a laser, but unlike the laser of a tape measure, the pulsar beam is emitted through the axis of rotation (i.e. at a right angle to the "tape").  The pulsing nature of a pulsar does not come from its rotation, as in Ponytail's analogy, but rather its precession, which swings the axial beam towards and away from Earth.
 
Some tape measures have a built-in {{w|laser line level}}. Pulsars emit electromagnetic radiation out of their magnetic poles, which is similar to a laser, but unlike the laser of a tape measure, the pulsar beam is emitted through the axis of rotation (i.e. at a right angle to the "tape").  The pulsing nature of a pulsar does not come from its rotation, as in Ponytail's analogy, but rather its precession, which swings the axial beam towards and away from Earth.

Revision as of 07:14, 19 January 2021

Pulsar Analogy
The #2 cause of astronomer hand injuries is trying to do vector math when the second axis points off to the right.
Title text: The #2 cause of astronomer hand injuries is trying to do vector math when the second axis points off to the right.

Explanation

Ambox notice.png This explanation may be incomplete or incorrect: Created by an INJURED ASTRONOMER. Please mention here why this explanation isn't complete. Do NOT delete this tag too soon.
If you can address this issue, please edit the page! Thanks.
Pulsars are dead stellar cores that produce fast-spinning beams of radiation. Ponytail, an astronomer in this comic, explains a pulsar's fast rotation with an analogy about a tape measure retracting. This analogy could be seen as useless or misleading, considering that the tape measure starts to rotate because the retracting tape is not moving only in a radial (in/out) direction. As a star collapses into a pulsar, its natural rotation rate is greatly amplified by its shrinking moment of inertia.

While the analogy is misleading, so is the idea of a laser measure being "exactly" like the emissions of a pulsar, which, although both pulse (and for the same reason), are produced in entirely different ways and are simply helping the mind hold the concept.

When a tape measure retracts, the part of the tape outside the tape measure is not going directly towards the tape measure's center but rather towards a hole in the side. This means the tape possesses some angular momentum relative to the tape measure. In addition, when the tape measure retracts, the part of the tape inside the tape measure rotates around a spool (which pulls the part of the tape outside the tape measure inside), so it also has angular momentum relative to the tape measure. When the tape is completely retracted, the tape can no longer rotate relative to the tape measure, so the entire tape measure rotates due to the conservation of angular momentum. While pulsars also rotate quickly due to the conservation of angular momentum, the exact mechanism is different. Pulsars are formed when stars collapse due to no longer performing enough fusion to produce enough heat and energy to cancel out gravity. This causes the star to contract, which causes its mass, on average, to be closer to its access of rotation, which causes the rotational inertia (also called the moment of inertia) to decrease. If the star's angular velocity stayed constant, this would cause the angular momentum to decrease, so the star's angular velocity must increase in order to offset the decrease in rotational inertia, i.e. the star (which is now a pulsar) spins faster.

Letting the tape snap into the fully retracted position will shorten the measure's lifespan, however: If the rivets that hold the bracket at the end of the tape shear off, the tape will retract entirely inside the measured body, and will be useless until repaired - which will entail opening up the body itself in order to re-extend the slackened tape against the spring (without anything bursting out sideways, with further reassembly issues) and somehow affix the end bracket without notably altering the measuring length.

Some tape measures have a built-in laser line level. Pulsars emit electromagnetic radiation out of their magnetic poles, which is similar to a laser, but unlike the laser of a tape measure, the pulsar beam is emitted through the axis of rotation (i.e. at a right angle to the "tape"). The pulsing nature of a pulsar does not come from its rotation, as in Ponytail's analogy, but rather its precession, which swings the axial beam towards and away from Earth.

The title text mentions the right-hand rule in three-dimensional space. In a typical 3D coordinate system the Y-axis will point counterclockwise to the X-axis when looking down from the positive Z-axis. In a left-handed coordinate system, the Y-axis instead points clockwise. Attempting to use the right hand here to calculate a cross product will require a 90° backward bend of the middle finger, which hurts.[citation needed]

Transcript

[Cueball and Ponytail are standing next to each other.]
Cueball: Why do pulsars spin so fast?
Ponytail: Hmm, let me think of an analogy...
[A tape measure is retracting above Ponytail's head. To the right of her head, a tape measure is spinning rapidly.]
Retracting tape measure: zzzzzzzzzzzzzzz
Spinning tape measure: SNAP
Ponytail: You know how when you retract a tape measure and let go, it leaves it spinning?
Ponytail: It's like that.
Cueball (off-panel): Oh, I see.
[A tape measure with a laser instead of a measuring tape is spinning slowly.]
Cueball (off-panel): And if the tape measure is the kind with a laser level, that's the beam of radiation?
Ponytail (off-panel): Exactly!
[Cueball and Ponytail are walking next to each other in silhouette.]
Ponytail: And when the tape whips around and smacks your hand, that's the neutron degeneracy shockwave.
Cueball: Sounds painful!
Ponytail: Top cause of astronomer hand injuries.


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Discussion

I tried applying the right-hand-rule with the y-axis pointing to the right. :( I hurt my hand. Avitzur (talk) 23:22, 18 January 2021 (UTC)

Rotate your paper then do the right hand rule :)
Hand joint exercises. Gentle motions with the wrist bent backwards, and bent forwards; 3-5 circles in both directions and both postures, twice a day. 162.158.62.41 00:48, 19 January 2021 (UTC)

172.69.35.149 23:38, 18 January 2021 (UTC)

The three-finger version of the right-hand rule actually isn't too bad in that case - pointing your right index finger to the right isn't too hard. Given that the alt text said "second axis", I assume the reference is to the "curling" version of the right hand rule: if you point your four fingers toward the first axis and then bend them toward the second axis then your thumb points in the direction of the cross product, and (at least in my opinion) it's a lot more painful to try to curl towards your right. 172.68.143.70 22:33, 22 January 2021 (UTC)

The analogy doesn't seem to be inaccurate in the way currently indicated. In both cases (tape measure and pulsar), conservation of angular momentum is what produces the result. With the tape measure, a small fast-spinning thing turns into a large slow-spinning thing; the opposite happens with a pulsar. 172.69.35.150 00:05, 19 January 2021 (UTC)

Isn't a tape measure bigger, not smaller, and slow-spinning, not fast-spinning, when it is elongated? This is very confusing. Thinking of how pulling the tape out stores energy. 162.158.62.41 00:49, 19 January 2021 (UTC)
A tape measure starts off not spinning. It's the acceleration of the tape as it moves in that starts the rotation, because the motion of the tape measure is not precisely radial. Same principle, different problem. Ltmauve (talk) 02:29, 19 January 2021 (UTC)
As the tape retracts, the tape inside the case is spinning. Once it is fully retracted, the case spins. Small spinny --> large spinny.
Of course, on a frictionless surface there's some slow retrograde rotation of the case + extended tape that speeds up as the tape retracts, but the case should completely stop spinning once the tape is fully retracted in that scenario, which is opposite of the analogy being drawn. 172.69.34.12 02:43, 19 January 2021 (UTC)
On a frictionless surface, it would never stop spinning. Once the case starts to spin, there's nothing to slow it down. --172.69.63.183 17:45, 19 January 2021 (UTC)
On a frictionless surface, before the extended tape measure is released, it has no net angular momentum. After it is released, the winding tape carries angular momentum, so the case+extended tape must spin in the opposite direction for the entire tape measure system to continue to have no net angular momentum. When the tape suddenly stops, it will no longer carry any angular momentum, so the case must stop spinning entirely for the system to continue to have no net angular momentum. Because of friction, we usually don't see the retro-rotation of the case until the tape is almost completely wound up. See also dlvozza's Impact Driver comment. 172.69.35.85 21:27, 19 January 2021 (UTC)
It seems to me like the reason the full tape measure spins is somewhat similar to an Impact Driver. Shooting slow motion videos of retracting my tape measure I see a small rotation in the opposite direction of the rotation in the end (likely due to the device maintaining angular momentum as the spring inside spins up) and then a quick snap when the tape is fully retracted, followed by the tape spinning very quickly in the opposite direction. As for my comparison to an impact, this reminds me a lot of how those work, with some inner barrel spinning at a very high speed, and then mechanically imparting that energy onto the body of the driving head, causing it to turn with a high torque. Typically when you start an impact spinning you can feel a small torque opposite to how the driver end spins because of the inner barrel spinning up. In the tape measure the inner spinning barrel is the tape itself and the spring to retract it, the driver head is the outer shell of the tape measure. dlvozza (talk) 19:48, 19 January 2021 (UTC)

Currently the description starts off “Pulsars are dead stellar cores” and that phrase seems very bizarre to me, since all stellar objects are dead. Do astronomers routinely anthropomorphize to such a degree as to call some stars alive and others dead? I would think more literal language like “A pulsar is the very compact and highly magnetized remains of a star after a nova or supernova explosion” but if the acceptable astronomical parlance is to say “dead star” far be it for me to demand a change162.158.63.94 05:26, 19 January 2021 (UTC)

I find the "dead star" also odd. Sure, I know what is meant, but in the same way I know what is meant by the tape measure analogy. Neither is accurate. Side note: I removed the part about the measures' lifespan and how you could repair it as this gives no benefit for the explanation and is totally irrelevant. Elektrizikekswerk (talk) 10:18, 19 January 2021 (UTC)
The word "dead" can be used to refer to inactivity in an object that was never classically alive. i.e. dead volcanoes --188.114.102.60 15:55, 19 January 2021 (UTC)
Humans aren't the only things that can be alive or dead, so calling it anthropomorphization is way off mark. But besides that, stellar objects aren't all "dead", they're non-living. You have to be alive and then die to be dead, in the biological sense. But in this case, it's called a "dead stellar core" because it no longer has sustained fusion reactions which is what stars are known for, just like a battery that's used up all of its charge is called "Dead" - not because we're assigning human qualities, but because it doesn't do what it's supposed to. Same with any non-living thing that doesn't function as expected being referred to as dead. --172.69.63.183 17:41, 19 January 2021 (UTC)
Astronomers also biomorphise stars by talking about when they are "born" – the moment sustained fusion starts in the core. 172.69.35.7 21:34, 19 January 2021 (UTC)
I think stars are alive! They're not biological but they have histories and stories and communities, they just have to do with unimaginably large atomic behaviors and orbiting patterns and stuff instead of fast food and mobile phones. 108.162.219.80 20:33, 20 January 2021 (UTC)

The increased angular velocity as the star shrinks is analogous to the way an ice skater's rotational velocity changes as they draw their arms in and out, no? Barmar (talk) 23:59, 19 January 2021 (UTC)

Just in, no pulsar ever managed to do "out" ... and yes, that's the analogy usually used, because it's easier to understand and considerably more fitting. Well, at least for someone who ever saw ice skating ... -- Hkmaly (talk) 06:24, 20 January 2021 (UTC)
Though they didn't use that analogy here, as they needed one that could be extended in a really ridiculous way to make the joke. It's not supposed to be the best possible analogy, but the follow up is supposed to be much worse.--108.162.216.118 17:51, 20 January 2021 (UTC)

Currently, the explanation doesn't say anything about the last panel, and should probably emphasize the core of the joke in that the explanation starts out kind of reasonable, albeit imperfect, but then gets progressively much worse when it is elaborated on in the last 2 panels (the initial analogy is a lot more reasonable than the stuff about the laser, and the fourth panel is just nonsense.)--162.158.74.85 05:01, 20 January 2021 (UTC)

Is it possible this is a reference to the anecdote in "Surely You're Joking, Mr. Feynman", in chapter "Lucky Numbers" (page 176 in my copy), in which Feynman tells a brief story about hurting his hand with a tape measure while playing with it? Nosrednayduj (talk) 03:17, 23 January 2021 (UTC)

Currently the explanation states "As a star collapses into a pulsar over unimaginably many years, its natural rotation rate is imperceptibly and eventually greatly amplified by its shrinking moment of inertia". This is not true; pulsars are formed by supernovae over the course of minutes. 108.162.246.124 17:24, 25 March 2022 (UTC)

Fixed Jkshapiro (talk) 17:57, 25 March 2022 (UTC)