162: Angular Momentum

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Angular Momentum


A moving object (like the Earth) has momentum. Momentum is the mass (size) of the object multiplied by the velocity (speed) of the moving object. So the Earth has a very high momentum because the Earth has a large mass (size) and is moving at a high velocity (speed) around the Sun. A moving object has to keep moving at the same velocity for its momentum to stay the same. The momentum of a moving object can increase, decrease, or stop via the force of another object. Force is the transfer of momentum from one object to another.

Megan attempts to slow down the Earth's momentum, and spins counter-clockwise to force her momentum onto the Earth, so that she can have more time with the one she loves.

The Earth has a massively high momentum, and the momentum that she produces is minuscule relative to the Earth's. And the few nanoseconds gained by spinning, while being with Cueball, is effectively offset by the seconds spent spinning.

Slowing down the rate of time in the universe directly slows down the velocity of life, so there would be no change in the total duration of life. And as the text implies, this isn't even possible: While not being able to reverse time, enjoy your night time. Sunrise always comes too early.

Her attempt of surmounting the seemingly impossible is grand; culturally, we value this kind of high romanticism.

Later in 442: xkcd Loves the Discovery Channel, the same kind of spinning Megan is used in the first frame to tell that xkcd loves momentum.

Technical notes: Angular momentum depends on the axis used for measuring angular momentum.


[Cueball sits sideways on a bed under an open window in the corner of a room. He is looking at Megan, who is spinning fast, indicated with two large circles indicating where her arms that a spread far out rotate, as well as two smaller circles around her knees and feet. The bed sheets are clearly messed up, as if someone has used it for activities other than sleeping. It is night and dark gray outside the window, and inside the room everything is also gray but lighter. Behind the spoken text, the background is white, but fades to the darker gray at the edges. There is also different gray shading in different parts of the room.]
Cueball: What are you doing?
Megan: Spinning counterclockwise
Megan: Each turn robs the planet of angular momentum
Megan: Slowing its spin the tiniest bit
Megan: Lengthening the night, pushing back the dawn
Megan: Giving me a little more time here
Megan: With you








Here's the formula:

L_Earth_i = L_Earth_f + L_spinner <=>




Where the variables have names in the format:


L = Angular Moment

I = Moment of Inertia

T = Period of rotation about one's axis

f = frequency

I used as values:

T_Earth_i = 86400 seconds (24 hours exactly)




Taking that a bit further, the relative decrease is:











I'm guessing she's spinning counter-clockwise as viewed from above. (I think that would be up-spin, by the right-hand-rule, if that's what you mean.) Assuming she's in the northern hemisphere, if I understand this correctly, as she pushes herself counter-clockwise, her feet exert clockwise torque on the earth, opposing the earth's counter-clockwise rotation on its axis (as viewed from above the north pole), slowing the earth's rotation slightly, thus "lengthening the night, pushing back the dawn"...by a mere 5.767×10-24 seconds (according to earlier comments) — I think that's the joke in this comic. -- Yfmcpxpj (talk) 16:24, 6 December 2019 (UTC)

I'm no physicist, but the opening paragraph of the explanation seems to be about linear momentum, p=mv, whereas I think the comic might be referring to angular momentum, L=Iω. I wonder if Megan isn't trying to slow the earth's speed around the sun, nor trying to "slow down the rate of time", but is actually trying to "lengthen the night, push back the dawn" (because their time together will end at dawn), by slowing down the earth's rotation on its own axis? -- Yfmcpxpj (talk) 16:24, 6 December 2019 (UTC)