Zorch, an archenemy of Superman, decides to slow earth\'s rotation to once per 3

Question

Zorch, an archenemy of Superman, decides to slow earth's rotation to once per 32.0 h by exerting an opposing force at and parallel to the equator. Superman is not immediately concerned, because he knows Zorch can only exert a force of 3.46x10^7 N (a little greater than a Saturn V rocket's thrust). How long must Zorch push with this force to accomplish his goal? (This period gives superman time to devote to other villains.) Explicitly show how you follow the steps found in problem-solving strategy for rotational dynamics.

Explanation / Answer

The standard rotational velocity of the Earth is one rotation every 24 hrs. That is...

2pi/(24)(3600) = 7.272 X 10-5 rad/s

The rotational velocity at one rotation every 32 hrs is

2pi/(32)(3600) = 5.454 X 10-5 rad/s

Torque = Fr = I(alpha)

Radius of Earth = 6.38 X 106 m

Mass of Earth = 5.98 X 1024 kg

I for a sphere = (2/5)mr2

(3.46 X 107)(6.38 X 106) = (2/5)(5.98 X 1024)(6.38 X 106)2(alpha)

alpha = 2.267 X 10-24 rad/s2

Finally wf = wo + (alpha)t

5.454 X 10-5 = 7.272 X 10-5 + (-2.267 X 10-24)(t)

t = 8.02 X 1018 sec

That is 2.23 X 1015 hrs, or 9.28 X 1013 days or 2.54 X 1011 years or 2.54 X 108 millenia

Obviously quite a long time. The earth may not even exist at that time.

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