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 31.0 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 4.00 107 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.) s

Explanation / Answer

If we assume that Earth is a solid sphere, then
I = (2/5)mr² = (2/5) * 5.98e24kg * (6.371e6m)² = 9.71e37 kg·m²
torque = I, but also
= F*r = 4.0e7N * 6.371e6m = 2.55e14 N·m
Since = ,
2.55e14 N·m = 9.17e37kg·m² *
= 2.78e-24 rad/s²

o = 2 rads / (24h*3600s/h) = 7.27e-5 rad/s
1 = 2 rads / (31h*3600s/h) = 5.63e-5 rad/s

1 = o - t
5.63e-5 rad/s = 7.27e-5rad/s - 2.78e-24rad/s² * t
t = 5.9e18 s

Hope this helps!

Related Questions

Navigate

• Browse (All)
• Browse Z
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.