Zorch, an archenemy of Superman, decides to slow the earth\'s rotation to once p

Question

Zorch, an archenemy of Superman, decides to slow the earth's rotation to once per 30.0 h by exerting an opposing force at the equator and parallel to it. Superman is not immediately concerned, because he knows Zorch can only exert a force of 5.00 107 N (comparable to a Saturn V rocket's thrust). Assume the earth's initial rotation is exactly once per 24.0 h and use energy considerations to find how long Zorch must push with this force to accomplish his goal. (This gives Superman time to devote to other villains.)

Explanation / Answer

Here ,

mass , m = 5.98 *10^24 Kg

force, F = 5 *10^7 N

let the time taken is t

Using second law of motion

change in angular momentum = torque applied * time

0.4* 5.98 *10^24 * (6.371 *10^6)^2 * (2pi/(24 * 3600) - 2pi/(30 * 3600)) = 5 *10^7 * 6.371 *10^6 * t

solving for t

t = 4.432 *10^18 s

the time taken for slowing down the earth is 4.432 *10^18 s

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