Okay, let's assume that we have an incline which is at say, an angle $\theta$, not too big.
Now, we have a a bunch of different objects with all the same radius and the same mass. Let's say that the objects are a sphere, hoop, shell, and disk, so clearly the moment of inertias are different.
In addition, the incline is so rough i.e. $\mu$ is so big that all the objects will roll down the incline without slipping.
If the force acting on the objects if always $$\Sigma F_{net} = mg\sin\theta - mg\cos\theta\mu = ma$$ by Newton's Second Law, wouldn't the acceleration be the same in all cases?
I know there's something wrong with my reasoning, but I can't figure out what. Any help would be greatly appreciated.
EDIT
The reason my reasoning is wrong is because friction is not always $mg\cos\theta\mu$ but instead this expression is for the maximum possible value of friction, which is not what the friction in the force equation is supposed to represent. Thanks to everybody for helping me understand this :)