(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Humanity uses energy at the rate of about 10^13W 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 minute?

2. Relevant equations

I_Earth = (2/5)(MR^2)

M_Earth = 5.97 * 10^24 kg

R_Earth = 6.37 * 10^6 m

W = dK_rot = (1/2)(I)(w[f]^2)-(1/2)(I)(w[0]^2) = (1/2)(I)(dw_sq)

P = W/t

3. The attempt at a solution

w[0] = (1rev/1440min)(min/60s)(2pi rad/s-rev)

w[f] = (1rev/1441min)(min/60s)(2pi rad/s-rev)

dw_sq = w[f]^2 - w[0]^2 = -3.17089611*10^-7 (edit: here is my mistake... the diff is actually -7.3374904*10^-12... with this plugged in, everything works out fine)

W = (1/2)(I)(dw_sq) = (1/2)(2/5)(MR^2)(dw_sq) = (1/2)(2/5)(5.97 * 10^24)([6.37 * 10^6]^2)(7.3374904*10^-12) = 3.55492722 × 10^26

P = W/t, so t = W/P = (3.55492722 × 10^26)/(10^13) = 3.55492722 × 10^13

MasteringPhysics says I am wrong. Where's the mistake in my calculations?

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# Homework Help: Humanity uses energy at the rate (earth-rotational problem)

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