Humanity uses energy at the rate of about 16 TW If we found a way to extract this energy from Earth's rotation, how long would it take before the length of the day increased by 1 second?
Work done = change in rotational kinetic energy,
W = (1/2)l(wf^2 - wi^2)
wi = 2*pi / T
wi = 2*pi / 86400 s = 7.2722*10-5 rad/s
When length of the day increased by 1 second,
wf = 2*pi / 86401 s = 7.2721*10-5 rad/s
I = (2/5)*MeRe^2 = (2/5)*5.97*1024*(6.37*106)2
I = 9.689*10^37 kg.m^2
Work done, W = (1/2) * 9.689*10^37 * ((7.2721*10-5)2 - (7.2722*10-5)2
W = 7.045*1024 J
P = W / t
t = W / P
t = 7.045*1024 / 16*1012
t = 4.403*10^11 s
t = 13965 yrs
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