A \(2.0-\mathrm{kg}\) solid cylinder of radius \(0.45 \mathrm{~m}\) rolls without slipping down a ramp inclined at an angle of \(60^{\circ}\) to the vertical. Calculate 

(a) the acceleration of the cylinder's center of mass,

(b) the cylinder's rotational acceleration, and

(c) the time interval required for it to travel \(35 \mathrm{~m}\) down the incline if it starts from rest.

(d) What is the rotational velocity of the cylinder at the end of the time interval found in part (c) ?