If a cylinder is rolling down an inclined plane with inclination $\theta=30^\circ$ (with coefficient of static friction between cylinder and the plane $\mu_s=0.8$) without slipping and it has mass $12kg$ and radius $0.5 m$ then the frictional force $f$ required is to be calculated . If you calculate it (I have done the calculations too but I don't have time to write all that and that's not of much importance to the question) it comes out to be $f = (mg\sin\theta)/3 = 20N$ . (Take $g = 10m/s^2$)
Here's a hideous FBD :
So shouldn't the friction be equal to $60N$ ? I mean isn't that what happens when the maximum static friction is greater than that applied force, which it itself adjusts to the applied force and cancels it. I am sure this is what happens with the non-round objects.
I know if friction would be equal to $60N$ then the cylinder would stop translational motion and it won't roll but start slipping instead as the torque provided by the frictional force will provide more angular acceleration than the required value for rolling and then ultimately this will lead to a very complicated motion.
So why would the friction adjust itself to $20N$? Just because this is the exact force required to make the cylinder roll?
But the friction doesn't calculate how much it should adjust to make something roll . Why would the friction care if something is rolling or not? And if it does then how does it "know" how much to adjust? It can be $60N$ (that would mean no rolling though). So is the question flawed or am I missing something?