Why is a rolling cylinder's angular acceleration −2μg/R not μg/R?

[Tonyt88]

You have a cylinder (with radius R) rolling horizontally on a surface with kinetic friction of u(mu). I understand that the horizontal acceleration is u*g b/c:

ma = u*(mg)
a = u*g

and then you have

a = r (alpha_z)

thus I'd figure alpha_z is just u*g/R, but the book gives a solution of:

-2 u*g/R

Basically, what's the reasoning?

 

[Tonyt88]

Also, I have this problem related to this previous problem:

The cylinder is initially slipping completely, so initially omega_z = omega_o but v_x = 0. Rolling without slipping sets in when v_x = R(omega_z). Calculate the distance the cylinder rolls before slipping stops.

 

[berkeman]

Cool.

Oh yeah, could you please use the homework posting template? Thanks.