The above calculation give the static friction force Fr=(1/3)m*g*sin?.
And maximum firction force is proportion to normal force Fr[sub]max[/sub]= ? N
So ?*m*g*cos? ? (1/3)m*g*sin?
It means that ??(1/3)tan?
If the angle is increased or ? is not large enough, then the condition for rolling without slipping is not satisified.
It will loss energy due to sliding friction.
So it will be easier to satisfy the condition if static friction coefficient between surface and the rolling object is [b]larger[/b] (instead of [u]smaller[/u]).
P.S. static friction coefficient is a property between two objects.