A person pushes a roller of radius R and inertia mR2/2, with a force f applied at

Question:

A person pushes a roller of radius R and inertia mR2/2, with a force f applied at an angle of cp to the horizontal (see Figure). The roller weighs 800 N and has a diameter of 0.4 m. Assume the roller does not slip. Derive the equation of motion in terms of
(a) The rotational velocity co of the roller and
(b) The displacement x.