0162: "Angular Momentum"

[Shoofle]

Whenever I'm with you, I feel like there is a tiny Foucault pendulum in the back of my mind, a grim reminder of the brief time I have left in the night...

[phlip]

Silly northern hemisphere and your silly backwards directions... everyone knows that you spin clockwise to slow the planet down. At least, in the real hemisphere. This is almost as mad as claiming Christmas belongs in the winter...

[n1000]

Silly northern hemisphere and your silly backwards directions... everyone knows that you spin clockwise to slow the planet down. At least, in the real hemisphere. This is almost as mad as claiming Christmas belongs in the winter...

I don't think anyone would argue that more people live in the southern hemisphere. I am fine with the North being the default!

[miss kyri]

its half cute, and half hopeless. who said a little knowledge is a dangerous thing? :p

[shobadobs]

This is incorrect? Each turn wouldn't rob the planet of angular momentum. Starting turning would rob the planet, but then the only thing that would allow additional turns to rob the planet of more angular momentum would be drag with the air (and this effect would also plateau). As long as you're turning, though, you would push back dawn... But once you stop turning, the Earth gets its angular momentum back.

[OmenPigeon]

See, I always thought of Foucault's Pendulum more as representing that one fixed point that it swings from. Sort of the opposite of a feeling of encroaching time, instead symbolizing something physically and metaphorically above and outside of time.

But maybe I just read too much Umberto Eco in high school.

[phlip]

This is incorrect? Each turn wouldn't rob the planet of angular momentum. Starting turning would rob the planet, but then the only thing that would allow additional turns to rob the planet of more angular momentum would be drag with the air (and this effect would also plateau). As long as you're turning, though, you would push back dawn... But once you stop turning, the Earth gets its angular momentum back.

Certainly, but the Earth would spin (marginally) slower while you were spinning, and dawn would be (marginally) later.

[spatulated]

that almost made me cry. I am such a sucker for mixing love and science. Also i am over 1000 miles away from my girlfriend and just about anything like this makes me miss her so much.

cute, warm, fuzzy, and a bit sad all at the same time.

well done mate.

[Tropylium]

This is incorrect? Each turn wouldn't rob the planet of angular momentum. Starting turning would rob the planet, but then the only thing that would allow additional turns to rob the planet of more angular momentum would be drag with the air (and this effect would also plateau). As long as you're turning, though, you would push back dawn... But once you stop turning, the Earth gets its angular momentum back.

Certainly, but the Earth would spin (marginally) slower while you were spinning, and dawn would be (marginally) later.

The spinning itself also takes time. You'd have to be spinning and making out simultaneously for this to be effectiv. Unless "seeing your partner spin" is in itself also considered romantic.

Or, maybe outsorce the spinning on other objects instead, but that doesn't really have the same romantic effect. Or, well, that depends... A playground merry-go-round might do the trick. Depends on how easily you get queazy.

Ultimately however, not even mad-science-scale concoctions - say, mile-long iron cylinders 300m in radius spinning at 600 RPM - would have any directly noticable effect on the length of the day (I calculated this once ), so maybe it's better to leave this as a ritual, a gesture... IMPHO a pointless, if cute, one, but I can see how others could appreciate it more.

[MightyMouse]

The good thing about having a tiny Foucault's pendulum is that you can barely tell that the earth is spinning.

Also, awww.

[phlip]

Well, in answer to the caption, lessee...

Assuming for now that there's no air resistance or anything like that... she just starts spinning at the start of the night, slowing the Earth, and then stops spinning at the end, speeding the Earth back up again. This is probably not even remotely like what would really happen, over such a long time air resistance would become substantial, but this system is a lot simpler... I don't want to think about what would happen with the atmosphere...

The moment of inertia of Earth is:
I = 8.034×10^37 kg m^2.
Now, suppose we wanted to delay dawn by a total of 1 second, over the course of a 12 hour period (say, the entire night). The period of the Earth during that time would increase from 24 hours to 24 hours 2 seconds, or a difference in angular velocity of:
Δω = 2π/86400 - 2π/86402
= 2π(86402 - 86400)/(86402 * 86400)
= 4π/(86402 * 86400)
= 1.6833×10^-9 rad/s
This gives the difference in rotational inertia as
ΔL = IΔω
= 1.352×10^29 Js

The moment of inertia of a human body is much harder to find... the best I could find is a model which gives the moment of inertia around a vertical axis as around:
I = 1.5 kg m^2
Now, with the rotational inertia calculation above:
ω = L / I
= 9.016×10^28 rad/s
or 1.434×10^28 rotations per second.

And that's assuming she's standing on the north pole... if she's standing elsewhere on the planet, you get confusing stuff in three dimensions... but I'm pretty sure she'd have to spin even faster just to get that one extra second.

Going the other way, assuming she spins about once per second:
ω = 2π rad/s
L = 4.189 Js
Δω = 5.214×10^-38
which comes to a difference in period of about 1.112×10^-48 seconds.

Now, you'll notice that the speed in the first part would mean most of her body is travelling significantly faster than the speed of light, and that the time in the second is less than the Planck time. But since I couldn't be bothered getting into relativity or quantum theory, that'll do for me.

Sorry for the downer.

[The Udjat]

...And then the hardcore scientists diligently killed romance wherever it lurked.

[Lemi4]

The spinning itself also takes time. You'd have to be spinning and making out simultaneously for this to be effectiv. Unless "seeing your partner spin" is in itself also considered romantic.

How 'bout spinning with your partner? (in a dance... all night long...)

[xkcd]

This is incorrect? Each turn wouldn't rob the planet of angular momentum. Starting turning would rob the planet, but then the only thing that would allow additional turns to rob the planet of more angular momentum would be drag with the air (and this effect would also plateau). As long as you're turning, though, you would push back dawn... But once you stop turning, the Earth gets its angular momentum back.

You're right that she only causes a change in angular momentum when she spins up. But I hold that you can read it another way -- if you integrate the angular momentum over time, there's an amount that the Earth would have with her spin and without her spin, and each turn she makes subtracts more angular momentum*time, which I guess has the unit of angular impulse? It's a unit mismatch, but maybe unit mismatches can be chalked up to poetic license -- sort of like mixed metaphors ("take arms against a sea of troubles" -- you're allowed to break the rules in art sometimes when it's pretty. But I prefer to have the science in harmony with the art, yes.)

Alternately, and this is more how I thought of it while writing, you could think that she's spinning and stopping each turn, or just think that each time she comes around she has to make the decision to do another spin, so each turn 'steals' momentum all over again. It doesn't say she robs it of MORE angular momentum, just that each turn steals some. So, not an aggregate delta-momentum per turn, but each turn is a theft of what should be the planet's.

[livingexception]

Not to mention that the girl's spinning creates angular momentum tangential to the Earth's axis of rotation. So really, it would cause an even smaller increase in the length of the night, because her spinning isn't slowing down the Earth on it's main axis of rotation.

Now, if she were in a hampster wheel, that might help.

[Grincement]

Being female (sorry to be sexist) I found it really sweet...

However I feel this could only work if you were spinning with your partner OR you get other people to spin for you so you don't have to worry...surely that has the same effect?

[Marrow]

If she throws up then it wasn't meant to be.

[Binary.Tobis]

And that's assuming she's standing on the north pole... if she's standing elsewhere on the planet, you get confusing stuff in three dimensions...

*phew* Ok I was worried that I was silly. Wouldn't she be turning the axis of the earth as well? That would be disasterous and cause storms and riots and general disharmony.

That was insanely cute though. It would be a lot more effective if they spent their time running west together.


...



Also the moon would fly into space.


[Edit:] Crap, ok west if they wanted to spend more time during the night. East if they wanted to slow the rotation.

[rockintom99]

Man, this one was great. But that really goes without saying, no?

[littleblackheart]

...it accentuates the utter impossibility of extending the time you have with someone versus the desire to do so...

[James]

I think the real question here is, "given that she is spinning counter clockwise, is it reasonable to assume that she is a prayer weasel?"

[mkwan]

If she *ran* around in circles she'd also benefit from relativistic time dilation (her partner wouldn't though)

[Marrow]

Anyway you put it, at least she is getting some excercize, who needs sleep anyway.

[RealGrouchy]

(skips over most of the posts)

I live in the Western hemisphere. Should I be doing somersaults?

- RG>

[Teaspoon]

If she *ran* around in circles she'd also benefit from relativistic time dilation (her partner wouldn't though)

Doesn't that mean her personal time moves slower than the rest of the world? By extension, doesn't that mean the rest of the world appears to move faster from her perspective? Which would mean it shortens the amount of time she perceives the night as lasting.

So maybe if they made themselves move slower than the rest of the world their time would pass faster than the world's standard time and they'd perceive a longer time before morning arrived. Of course, if they were detaching their movement from the world they could just move to stay on the opposite side of the planet to the sun and have an unending night regardless of relativistic time shenanigans.

[Pau!]

Let me just saw: Awwwwwwwwwwwwww

I cannot even describe how happy this comic made me. I'm saving that forever.


...I'm such a romantic sap/nerd

[Tropylium]

If she *ran* around in circles she'd also benefit from relativistic time dilation (her partner wouldn't though)

Doesn't that mean her personal time moves slower than the rest of the world? By extension, doesn't that mean the rest of the world appears to move faster from her perspective?

Nope. Special Relativity 101: while two mooving objects both perceive the other's time having slowed down, when meeting again, the one that has accelerated more comes out younger. It's you that starts & stops running, so you do get teeny bits of extra time this way.

So this would have been a better method to attempt. In theory at least.

[Teaspoon]

If the one with the highest acceleration comes out younger, doesn't that mean the night ends sooner from their perspective?

Assume the night will end in 6 hours from the perspective of the Earth, given that the Earth's movement controls the day/night switchover. If the person does the acceleration, they come out younger than the Earth, which means thatless than 6 hours of person-time lapse before six hours of Earth-time pass and the night ends. So the night will appear to have passed faster from the perspective of the person.

<edit>
Wait, no. You said both seem to move slower, so it works either way. The making-the-Earth-do-the-accelerating thing would make the night last slower than the other way around though.

[kira]

Nope. Special Relativity 101: while two mooving objects...

Mooooooo.

This has been my contribution to the conversation. Please continue.

[SpitValve]

ok... lots of special relativity confusion here...

1) If she was running away from Earth at a constant velocity, then
a) from Earth's point of view, she is moving away & therefore time dilates for her, so she will age less over the night
b) from her point of view, the Earth is moving away & therefore time dilates for the Earth, so the night lasts longer from her pov

And yes, these are apparently contradictory. One of the principles of Relativity is that the laws of physics are the same in every frame. In each frame they see the other moving away at contant velocity, therefore in each frame they observe the other as undergoing time dilation.

However:
2) If she's running around in circles, she's not in an inertial frame (even ignoring gravity). To be in an intertial frame you must be moving at a constant velocity. This means Special Rel doesn't totally apply - we need to use General Relativity. Now I've only done a little General Rel so far, but I think the lack of symmetry between the girl and the Earth (the girl is definitely accelerating in a circle & changing reference frames, while the Earth is [pretty much] moving at constant velocity) means that from all points of view, the girl will appear to age less, and hence the night will last longer. It's basically the twins paradox.


Which is basically what Tropylium said? meh, Spitvalve is confused...

phew. moo. continue.

[Hopeless MechE]

Ok, I'm new here but i read this comic and fell in love with it. I can't wait to show it to my girl who thinks that the shirts on "thinkgeek.com" are romantic and admires me for picking "a hard major." It's very sweet and at the same time adequately geeky. Truly a beautiful blend. It's possibly romantic perfection. (not to mention i love stick figures) Dude you rock. Can this be made into some kind of bumper sticker or t-shirt or poster or something that i can display somewhere?

[phlip]

Um, if the girl was younger at the end of the night, surely that means that the night seemed shorter for her? If the guy's 12 hours older and the girl's 11.99999... hours older, then the guy saw the night as 12 hours long while the girl saw the night as that small amount shorter...

[SpitValve]

Yes, you're right, although the reason is not that simple.

[Hopeless MechE]

Yay for frames of reference, i totally sucked at that stuff in physics. But now i don't need to care about relativity. Newtons approximations are close enough for any of the stuff i'll be working on. Half of engineering is finding ways to fudge equations to make the math easier.

[Erasmus]

2) If she's running around in circles, she's not in an inertial frame (even ignoring gravity). To be in an intertial frame you must be moving at a constant velocity. This means Special Rel doesn't totally apply - we need to use General Relativity. Now I've only done a little General Rel so far, but I think the lack of symmetry between the girl and the Earth (the girl is definitely accelerating in a circle & changing reference frames, while the Earth is [pretty much] moving at constant velocity) means that from all points of view, the girl will appear to age less, and hence the night will last longer. It's basically the twins paradox.

If everybody agrees that the girl ages less (btw, I agree that that's what everybody agrees -- she is at a higher gravitational potential than the rest of the room), then there's no paradox.

Unfortunately, while she gets to be with her beau for longer, the night takes the same amount of time from his perspective (not taking into account the Earth's loss of angular momentum, of course). If they really wanted to use GTR to get some more cuddling time, they should be locked in a (high-gravitational potential) embrace :)

[Pau!]

Man, I just got back from a long, nerdy cuddling session, and I came here, and I have to say again how much I love this comic and all the warm and fuzzy feelings it gives me inside.

[deosilmau]

Geeks.

[Zee Anything]

Geeks.

Is there anything wrong with that?

[Verysillyman]

So... uh... I didn't bother actually reading what everyone said, but that's ok.

No matter how long you can stretch the night out, it'll still be much shorter because you're in love.

[Ephphatha]

Damn you and your logic.