How Long to Change an Asteroid’s Rotation Axis with a Tug Spacecraft?

[deuce123]

Homework Statement

A spherical asteroid with radius r = 123 m and mass M = 2.10×1010 kg rotates about an axis at four revolutions per day. A "tug" spaceship attaches itself to a vehicle which follows the asteroid's south pole (as defined by the axis of rotation) and fires its engine, applying a force tangentially to the asteroid's surface keeping the direction of the force in the same plane. The initial situation is shown in the figure. (Figure 1) .

If F = 265 N, how long will it take the tug to rotate the asteroid's axis of rotation through an angle of 13.0 ∘ by this method?

Homework Equations

torque= Iα

The Attempt at a Solution

I went about this problem in a wrong way at first,i found torque and the angular acceleration , then used rotational kinematics to find t. But this way to the approach was wrong, since i did not realize the rotation of the asteroid was not in coalition with the force. Then i realized that for it too move 13degrees the only real thing that would slow is the moment of inertia of the asteroid. Also initially for this case the angular velocity would be 0. This also led to a wrong answer. I am completely stumped of how to go about this.

I looked up the answer and its t=71.5 hrs. Someone please help me with how to approach to actually get that answer. thank you,

 

[TSny]

Think about the relation between torque and rate of change of angular momentum. Keep in mind that both torque and angular momentum are vectors, so you'll need to consider their directions as well as magnitudes.

It might also help to review the concept of precession of a gyroscope.