# Is the non-rotational form of Newton's second law still valid for rolling objects?

Say you have a rolling (non-slipping) cylinder with mass $$m$$ and radius $$R$$. The circle below is the side view. Denote the center of this circle as $$C$$. A force $$F$$ is applied. We can find the torque around $$C$$: $$\tau = I\alpha = \frac{1}{2}mR^2$$ $$\tau = F(h-R) + f_sR$$ and this gives information about the angular acceleration and also about the linear acceleration since $$\alpha R=a$$. Now, I was wondering if you could also say that $$F_\text{tot} = F - f_s = ma$$ as if it is a point of mass or a slipping object, or if this is incorrect. I initially thought it was incorrect since the forces are acting on different places and the cylinder is rotating so can't be modeled as a point of mass, but this method was used in a solution key. I don't understand why you can do this. ## 1 Answer

(M1 + M2 + M3 + .........)Acom = M1A1 + M2A2 + M3A3............. This equation is valid for any system (rigid or non rigid) by definition of centre of mass . That's why we always try to solve the problems in Com frame as it's acceleration is easy to find if all external forces are given and for torque we don't have to consider pseudo forces also because they produce no torque in frame of centre of mass.