Initially resting on a frictionless surface in a lab, a solid aluminum disk with a mass of 18.0 kg and radius 0.75 m is acted upon by a string wrapped around its rim. A steady horizontal force of 40.0 N is exerted on the string, which remains fixed on the rim without slipping. The string does not slip on the disk's rim. When the disk has moved a distance of 4.0 m, calculate the angular velocity of the disk (in radians per second). Use: acceleration of the center of mass = $2.22\mathrm{~m}/\mathrm{s}^2$.