# Unwounding spool of wire

1. Feb 2, 2008

### cryptoguy

1. The problem statement, all variables and given/known data
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 doesnt slip, show that the acceleration of center of mass is 4F/3M

2. Relevant equations
$$\tau$$ = I$$\alpha$$ = F*R

3. 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

2. Feb 2, 2008

### awvvu

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