A solid cylinder of mass $M$ and radius $R$ rolls without slipping on a horizontal surface. A horizontal force $F$ is applied at the top. Find the acceleration of the center of mass.

Torque about contact point:

$$F \cdot 2R = I_{contact} \cdot \alpha$$

where $I_{contact} = \dfrac{3}{2}MR^2$ (parallel axis theorem) and $a = R\alpha$:

$$2FR = \frac{3}{2}MR^2 \cdot \frac{a}{R} \Rightarrow a = \frac{4F}{3M}$$

$$a = \frac{4F}{3M}$$