# Asteroid/Angular Momentum Problem

## Homework Statement

A spherical asteroid with radius r = 123m and mass M = 2.10×1010 kg rotates about an axis at four revolutions per day. A "tug" spaceship attaches itself to the asteroid's south pole (as defined by the axis of rotation) and fires its engine, applying a force F tangentially to the
asteroid's surface as shown in the figure.If F = 265N, how long will it take the tug to rotate the asteroid's axis of rotation through an angle of 10.0 degrees by this method?

## The Attempt at a Solution

I solved for the angular acceleration using that net torque is equal to the moment of inertia times the angular acceleration. After that I used constant angular acceleration equations to solve for the final angular velocity and then solved for time t. However, this is not giving the right answer and I would appreciate any help. The system I considered was the asteroid itself, so the spaceship applies a external torque and I said angular momentum wasn't conserved. Thanks in advance for the help.