A \(150\text{-kg}\) merry-go-round in the shape of a uniform, solid, horizontal disk of radius \(1.50\,\text{m}\) is set in motion by wrapping a rope about the rim of the disk and pulling on the rope.

What constant force must be exerted on the rope to bring the merry-go-round from rest to an angular speed of \(0.500\,\text{rev/s}\) in \(2.00\,\text{s}\)?

Note: \( I_\text{disk} = \dfrac{1}{2}mr^2 \)