How Does a Spool's Acceleration Relate to Force and Mass?

[cryptoguy]

Homework Statement

A spool of wire mass M and radius R is unwound under a constant force F. Assuming the spool is a uniform solid cylinder that doesn't slip, show that the acceleration of center of mass is 4F/3M

Homework Equations

$$\tau$$ = I$$\alpha$$ = F*R

The Attempt at a Solution

Here's what I got, not sure if this is right.
$$\tau_{}net$$ = $$\tau$$F - $$\tau$$Ffric
I$$\alpha = F*R - Ffric*R$$
$$.5MR^2(a_{cm}/R) = F*R - Ffric*R$$

$$a_{cm} = (F-Ffric)/.5M$$

The problem is that I don't know Ffric (Friction force).

Thank you in advance for help

 

[awvvu]

Use F = ma on the spool to get another equation, this should allow you to eliminate F_fric.