When should the Parallel Axis Theorem be used in mechanics?

[amcavoy]

I know what the parallel axis theorem is, but I'm a little confused about when to use it. I recently had a problem where a hoop was rolling down an incline where I used the parallel axis theorem to find the translational acceleration and got it correct. However, I had a problem about a spool being pulled by a string (think of a yo-yo being pulled on the ground), and when I set up the equations I got the wrong answer using the P.A.T. For instance, I had:

$$F-F_{S}=ma$$

$$RF_{S}-rF=I_{CM}\alpha$$

Why isn't the I_CM instead I_P? I have solved the problem already and know the answer, I just can't see why the parallel axis theorem is not used. LINK: http://show.imagehosting.us/show/971155/0/nouser_971/T0_-1_971155.jpeg

Thank you for your help.

 

[Doc Al]

I just depends on what you take as your axis of rotation. If you take the center of mass, then I and torques will be about that point. (And you'll have no need for the parallel axis theorem.)

But you are certainly free to use the point of contact with the floor as your instantaneous axis of rotation. But if you do, be sure to take torques about that point as well. In this case you'll need to use the parallel axis theorem to find the rotational inertia about that point.

Done correctly, you'll get the same answer either way.