Difference between revisions of "Talk:162: Angular Momentum"

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(My attempt at solving the "neat physics puzzle")
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I_Earth = 8,03e+37 Kg.m^2 (http://scienceworld.wolfram.com/physics/MomentofInertiaEarth.html)
 
I_Earth = 8,03e+37 Kg.m^2 (http://scienceworld.wolfram.com/physics/MomentofInertiaEarth.html)
  
f_spinner = the frequency of the woman's spinning in complete turns per second.
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f_spinner = the frequency of the woman's spinning in complete turns per second. {{unsigned ip|2.82.142.28}}
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:Taking that a bit further, the relative decrease is:
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  (T_Earth_f - T_Earth_i)/T_Earth_i = 1 / (I_Earth/(I_spinner*T_Earth_i*f_spinner) - 1)
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      = 1 / ( 1.5 e+28 - 1) ~= 67 e-30
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:Fwiw, the absolute value is 5.767 yocto-seconds. If the ''entire'' world population would spin at that 1000 turns per second (and at favourable locations as in your assumptions), the effect will still be a measly 0.041 pico-seconds. So T_Earth_f = 86 399.999 999 999 999 958 ... But the TI-84 only has about 14 digits precision, i believe, so even that won't show up. -- [[Special:Contributions/173.245.51.210|173.245.51.210]] 22:46, 30 October 2013 (UTC)
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Is it possible for someone to write an equation that factors in latitude (and, if relevant, longitude) that we could plug our locations into and get a value from? That would be awesome. Thanks. [[Special:Contributions/108.162.250.208|108.162.250.208]] 02:48, 23 February 2014 (UTC)

Revision as of 02:48, 23 February 2014

The issue date is not given, as i don't have a clue about it. Could someone fix this? Rikthoff (talk) 19:30, 3 August 2012 (EDT)

When the page was updated to the new comic template by User:Bpothier he fixed the date. lcarsos (talk) 20:48, 28 August 2012 (UTC)

That actually is a neat physics puzzle, which has probably (i.e. certainly) been addressed somewhere on the net. I may incorporate that some day. --Quicksilver (talk) 05:58, 24 August 2013 (UTC)

I tried to calculate the change in Earth's period, assuming that she was standing in the north pole (latitude = 90º N), where her spinning would have more effect. I either did something wrong, or my TI-84 Plus is not capable of detecting the very small effect her spinning would have on the Earth's rotation. I assumed the Earth had a period of exactly 24 hours, and got the same value to the second, even if she was spinning at 1000 turns per second, which seems like a lot.

Here's the formula:

L_Earth_i = L_Earth_f + L_spinner <=>

I_Earth * (2*PI)/T_Earth_i = I_Earth * (2*PI)/T_Earth_f + I_spinner* (2*PI) * f_spinner <=>

(1/T_Earth_f) = (1/T_Earth_i) - (I_spinner/I_Earth)*f_spinner <=>

T_Earth_f = 1/((1/T_Earth_i) - (I_spinner/I_Earth)*f_spinner)


Where the variables have names in the format:

[variable name]_[object it refers to]_[situation (i or f stand for initial and final)]


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)

I_spinner = 62,04 Kg.m^2 (Found on Wolfram|Alpha, for a 62Kg adult human being)

I_Earth = 8,03e+37 Kg.m^2 (http://scienceworld.wolfram.com/physics/MomentofInertiaEarth.html)

f_spinner = the frequency of the woman's spinning in complete turns per second. 2.82.142.28 (talk) (please sign your comments with ~~~~)

Taking that a bit further, the relative decrease is:
  (T_Earth_f - T_Earth_i)/T_Earth_i = 1 / (I_Earth/(I_spinner*T_Earth_i*f_spinner) - 1)
     = 1 / ( 1.5 e+28 - 1) ~= 67 e-30
Fwiw, the absolute value is 5.767 yocto-seconds. If the entire world population would spin at that 1000 turns per second (and at favourable locations as in your assumptions), the effect will still be a measly 0.041 pico-seconds. So T_Earth_f = 86 399.999 999 999 999 958 ... But the TI-84 only has about 14 digits precision, i believe, so even that won't show up. -- 173.245.51.210 22:46, 30 October 2013 (UTC)

Is it possible for someone to write an equation that factors in latitude (and, if relevant, longitude) that we could plug our locations into and get a value from? That would be awesome. Thanks. 108.162.250.208 02:48, 23 February 2014 (UTC)