Zorch, an archenemy of Superman, decides to slow Earth’s rotation to once per 28.0 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 4.00×107 N (a little greater than a Saturn V rocket’s thrust). How long must Zorch push with this force to accomplish his goal? (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.
Step 1 of 5:
Zorch tries to increase the time period of Earth’s rotation by slowing down the angular speed. He exerts an opposing parallel force at the equator for longer time. We are going to calculate the time required to slow down the Earth’s rotation by the force exerted. This is done by the methods involving equation of rotational motion.
The force exerted
The radius of Earth
The initial time period of Earth
The final time period of Earth
The mass of Earth
Step 2 of 5:
The problem involves the initial and final angular speeds of the Earth.
The initial angular speed of Earth
Similarly, the final angular speed of the Earth
Step 3 of 5:
Zorch applies force on the equator and makes the Earth rotate slowly. Hence the torque is produced by the force with the perpendicular distance equivalent to the radius of the Earth.
The net torque is
The net torque can be expressed in terms of the moment of inertia (I) of Earth about its equator and angular acceleration (ɑ) produced
Where The moment of inertia of Earth
Solving the above equations for angular acceleration
Substituting the value of I