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 27.0 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 4.50 ? 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

so,

initial speed of rotation of earth = u = circumference / time

= 2*pi*R / 24 m/hours .......( R= radius of earth = 6371.14 km

=( 2*3.14*6371.14*10^3)/24

=1667114.96667 m/hour

final speed of rotation of earth = u = circumference / time

= 2*pi*R / 32 m/hours .......( R= radius of earth = 6371.14 km)

=( 2*3.14*6371.14*10^3)/32

=1250336.225 m/hour

Now, Angular acceleration = torque / moment of inertia of earth

= F*R /(2*m*R^2/5)

=3*10^7*6371.14*10^3/((2*5.79*10^24*(6371.14*10^3)^2)/5)

=2.0331319e-24 m/hour^2

As rotation and acceleration are in opposite directions

so,

as v=u-at

t=(v-u)/-a = (1250336.225-1667114.96667)/-2.0331319e-24

=2.0499346e+29 hours

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