Ignoring rotational friction I have came across a scenario (in an undergraduate examination paper question) which talks about a sphere rolling up an inclined plane).
The question explicitly said that "rotational friction can be ignored".
I interpret it as that friction is not involved in slowing the sphere down, it's just that the rotation of the sphere, for some reasons, must correspond to the ground such that there's no slipping.
However, how can this be the case in real life?  From my line of reasoning, I think that reason the sphere does not slip in real life is due to the fact that there's static friction between the sphere and the surface, such that it rotates the sphere to make sure that it doesn't slip even though it's linear velocity is changing.  In other words, friction, itself, is involved in making sure that the rotation of the sphere changes such that it doesn't slip.  Doesn't this mean that friction must be taken into account?
 A: Note that the question says rotational friction can be ignored. There is a difference between static and rotational friction.
BEHOLD! The 3 main types of friction:
1) Kinetic friction is the friction from a moving object sliding across a surface and is usually (always) less than static friction.
2) Static friction is the anti-slip friction between two non-moving surfaces. This is why wheels and tires work; static friction allows the wheel to push off the ground and not slip.
3) Rolling friction or rolling resistance is the resistance to compressing two surfaces together and then pulling them apart. This happens in rolling motion. As your ball rolls, its weight is applied entirely to the point of contact between the ball and the ground. This compresses the surfaces together at that point. As the ball rolls on, the surfaces want to lift off from each other, but between the act of deforming and reforming both surfaces (that's the biggest factor) and some small effect from chemical adhesion/cohesion between the materials of the two surfaces (this is more important when cold welding becomes an issue) it takes more energy to lift off than it does to compress in the first place. This energy loss translates into something that acts very much like friction and is one of the primary reasons that a wheel will always coast to a stop.
In conclusion, what the question is telling you to do is assume that the ball will never just coast to a stop on flat/smooth ground. Static friction isn't ignored, just rolling friction
