Suppose that Superman wants to stop Earth so it does not rot

Suppose that Superman wants to stop Earth so it does not rotate. He exerts a force on Earth F_S on E at Earth\'s equator tangent to its surface for a time interval of 1 year. What magnitude force must he exert to stop Earth\'s rotation? Indicate any assumptions you make when completing your estimate.

Solution

One year = 365.25 days

Total time = 365.25 * (24 * 60 * 60) = 3.16 * 10⁷ s

In one day, earth rotates an angle = 2 pi rad

w_f= w_i+ alpha * t

0 = (2 pi / 86,400) + ( alpha * 3.16 * 10⁷ )

alpha = 2.30 * 10^-12 rad/s²

Torque = F * r = I *

For a solid sphere, I = 2/5 m r²= 2/5 * 5.98 * 10²⁴ * (6.37 * 10⁶)² = 9.71 * 10³⁷

Torque = 9.71 * 10³⁷ * 2.30 * 10^-12= 2.23 * 10²⁶ N.m

F = (2.23 * 10²⁶) / (6.37 * 10⁶) = 3.51 * 10¹⁹ N

Force = 3.51 * 10¹⁹ N