Consider a very gentle slope and a fairly inelastic ball. Why is it that there are some circumstances such that:
1. The ball can sit on the slope without rolling.
2. If nudged downhill, the ball will begin to roll down the slope and pick up speed.
3. If nudged uphill, the ball will roll uphill, slow down, and then start rolling downhill and pick up speed.
During (3), mustn't the ball at some point pass through whatever zero-velocity condition is required for state (1)? At that point, why doesn't the ball stop? The only explanation I can think of is that there must be some lateral motion that doesn't get zeroed.