Moment of inertia and rotational kinetic energy prob

[pb23me]

Homework Statement

A spool of wire mass m and radius r is unwound under a constant force F. Assuming that the spool is a uniform solid cylinder that does not slip, show that the acceleration of the center of the mass is 4F/3m

Homework Equations

F+f=ma
f=ma-F
$\tau$ =I$\alpha$=Fr-fr

The Attempt at a Solution

My instructor worked this out in class and got the answer,but there was one thing that i didnt understand and hope someone can clarify this for me. When he did the force equation he put F+f=ma because friction and the force applied are in the same direction.Then when he did the net torque equation $\tau$=I$\alpha$=Fr-fr now it seems he switched the direction of friction? The problem worked out correctly this way but i don't understand why the direction of friction changed?

 

[kuruman]

That's because friction acts below the center of mass (CM) while the pulling force acts above the CM. Thus the forces point in the same direction (they add), but the torques about the CM subtract because one would tend to rotate the spool clockwise and the other counterclockwise.

 

[pb23me]

wow i never even thought of that...thank you