Understanding Forces and Motion in a Translating and Rotating Ring

[gator286]

1)Problem statement
A translating and rotating ring of mass 1 kg, angular speed of 500 rpm, and translational speed of 1 m/s is placed on a horizontal surface. The coefficient of friction between the ring and the surface is 0.35.

Outside radius is 3 cm.

This is a problem from a FE review manual, thanks guys.

2)Attempt at a solution.
ΣFx=ma
ΣFy=0 therefore N=mg
From summation of forces in the x direction,a=g/m
ΣM=0,(µmgR)= α I
I=3MR^2
α=µg /(3R)
v= v_0-at
ω= ω_0- αt
This is where I get lost.

 

[gator286]

Ok, this is a scanned solution of the problem according to the book. It's problem 13.

http://img218.imageshack.us/f/002kfv.jpg/

What I don't understand is why is angular acceleration negative, and a is positive. Shouldn't they both be negative? Also, how did they get v = romega, isn't romega the tangential component?