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 4.06*10^7 N (a little greater than a Saturn V rocket's thrust). How long must Zorch push with this force to accomplish his goal in seconds? (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 mean value of Earth Rotational Inertia is 8.023 x 10^37 kg.m^2
The equatorial radius of the earth 6378 km
So the braking Torque of Zorch = Force x radius = 3.50 x 10^7 x 6.378 x 10^6 = 2.2323 x 10^14 N.m

Torque = I ?
Angular deceleration = T / I = 2.2323 x 10^14 / 8.023 x 10^37
? = - 0.278 x 10^ -23 rad /sec^2
Initial angular vel , ?o = 1rev /24 hr = 2 ? / 24 x 3600 = 7.272 x 10^ -5 rad /s

Final angular vel, ?f = 1rev/32 hr = 2 ? / 32 x 3600 = 5.454 x 10^ -5 rad /s

Time = ?f - ?o / ?
= (5.454 x 10^ -5 - 7.272 x 10^ -5) / - 0.278 x 10^ -23
= 6.53 x10^18 sec

1Yr = 365.25 (days) x 24 (hrs) x 3600 (sec) = 3.156 x10^7 sec

Time = 6.53 x10^18 / 3.156 x10^7
= 2.07x 10^11 years
= 207 billion years

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