dynamics
posted by shivankar .
13. The constant angular acceleration of a pulley is 4 rad/s2 and its angular speed its 3 rad/s. Determine the radius of the pulley if the total acceleration of a print on the rim of the pulley is 3.5m/s2.

I assume that you mean a point on the rim, not a print. The radial and tangential acceleration components are perpendicular. Therefore
(3.5)^2 = (4 R)^2 + [ 3^2*R]^2
The first term on the right is the square of the tangential acceleration. The second term is the square of the centripetal acceleration.
Solve for R. 
13. The constant angular acceleration of a pulley is 4 rad/s2 and its angular speed its 3 rad/s. Determine the radius of the pulley if the total acceleration of a print on the rim of the pulley is 3.5m/s2.