Why doesn't static friction point down the incline on a ball rolling down an incline? 
In the figure above in which the sphere rolls without slipping down an incline, why is static friction directed upward? Static friction is meant to oppose impending motion so it should oppose the object's tendency to slide, and gravity would cause it to slide down in the absence of friction. Doesn't this mean that friction should point down since a downward force causes the sphere to move up?
 A: Friction opposes relative motion between the surfaces, which is not always the impending motion of the bulk object. Indeed, the ball's bottom surface would try to slide down the ramp, so friction opposes this by acting up the ramp on the ball.
A: Direction of friction depends only on the direction of slipping between the __surfaces in contact __.Without friction the sphere slips down the incline without rolling, the sphere rubs downwards and friction acts upwards.
Just look at surfaces in contact and ignore rest of the bodies.
Also the direction of motion of body is determined by net force on it's centre of mass.
For calculating the net force on com all force vectors acting on the body are translated to com(their magnititudes and directions remain same) and added. Thus if friction acts down the incline (or any force acting downwards) it will not support upward motion.
A: The easiest way to find the direction of static friction, is to first imagine how the motion would be like on a smooth surface. Find out what direction the point of contact is moving with respect to surface, and then apply static friction in the opposite direction. If there is no relative motion, then there will be no friction even on rough surface.
In this case, if the surface was smooth, the ball would slide down without rolling. So as the motion of the point of contact is downward if the surface was smooth, the friction on rough surface will act upwards.
A: The static force pointing upward doesn't mean the ball is accelerated upward. It's the force of gravity that does the job. It pulls on the ball, and if the ball doesn't slip, the static friction causes a torque, together with the force of gravity, which makes the ball roll downward.
