Rotational Motion Physics - Please help on all parts!

Question

The figure shows a solid, uniform cylinder of mass 7.00kg and radius 0.450 m with a light string wrapped around it. A 3.00-N tension force is applied as shown to the string, causing the cylinder to roll without slipping across a level surface that exerts a static friction force, Fs, on the cylinder. The rotational inertia of a solid cylinder rotating about its center is MR^2/2.

a. Calculate the linear acceleration of the center of mass of the cylinder.

(I came up with Στ = T R - R Fs = 1/2 M R^2 α but could not reach the correct answer of a = .571 m/s^2. Could someone please show me the proper steps to reach this answer?)

b. Calculate the magnitude and direction of the angular acceleration of the cylinder. ( α = 1.27 rad/s^2)

c. Calculate the magnitude and direction of the friction force that is exerted on the cylinder. ( Fs = 1N)

Answer 1

a) Sum forces to find ma=3-Fs . Sum torques to find I∝=3r+Fsr. Note that ∝r=a. Solve this series of equations to find ma=6-Ia/r² thus a=4/m = .571m/s².

b) ∝ =a/r = 1.27 rad/s²

c) Fs=-3+ma= .997 N and it points opposite of Tension