$(60pts)A50-kg$ wheel with a diameter of $1\mathrm{.}5$ m has a moment of $75N-m$ applied at its center, causing it to roll along a surface with ${}_s=0\mathrm{.}35$ and ${}_k=0\mathrm{.}29.$

a$.$ Determine the acceleration of the center of gravity G $,$ as well as the angular velocity and the displacement of G after $20$ seconds. Assume the wheel starts from rest.

b$.$ What is the maximum moment M that can be applied to the wheel without causing clin?