Two rocket boosters capable of delivering 8.50x10^10 N of thrustwill be attached

Question

Two rocket boosters capable of delivering 8.50x10^10 N of thrustwill be attached to opposite sides of the earth. they will bedirect so as to coincide with the earth's rotation.

1) calculate the torque about the center of the earth
2) calculate the rotational inertia
3) calculate the angular acceleration of the earth that will resultfrom the rocket boosters
4)if the earth takes 24 hours to complete a revolution, calculatethe initial angular speed before the rocket boosters
5) what angular speed would yield a centripial acceleration on thesurface of earth of 9.8 m/s^2 (making everything fly off thesurface)
6) how long would it take for the earths rate of totations toincrease the value in part 4 to the value in part 5

mass of earth 5.98e24kg
radius of earth 6.37e4m

Explanation / Answer

(Radius of earth is 6.37e4 km not m ) We know , torque = force*redial distance =8.50x 10^10 N *radius Also as there are two rocket boosters ,So net torwue = 2* 8.50x10^10 N * radius =2*8.50e10*6.37e7 = 1.083e19 Nm 2) Rotational inertia = 2MR2/5(Assuming earth to be asphere )                                =9.706e32 kgm2 3)So angular acceleration = torque / inertia = 1.083e19 / 9.706e32= 1.116e-14 rad/sec2 4) angular velocity = 2 / time period = 2/ (24*3600) =7.27e-5 rad/sec 5) For centripetal acceleration to be 9.8 2r =9.8 = (9.8 / 6.37e7) = 3.92e-4 rad/sec 6) Time taken = (final angular veloicty - inital angularvelocity) / angular acceleration = 3.92e-4 - 7.27e-5 /1.116e-14                       = 3.195e-4 / 1.116e-14 = 2.86e10 sec

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