Why swirling spheres shift rotation at a certain number

Swirling a ball in a cup gets it spinning in the direction of the swirl, but adding six more starts them swirling in the opposite direction.

This video explains why.

It comes down to linear momentum vs. angular momentum: "The linear momentum is being wasted, but the angular momentum, that is, the tendency to keep rotating that is the quantity that measures the there is of rotation gets transmitted." Each individual sphere continues to rotate in the direction of the swirl, but the global effect is movement opposite the swirl.

Worth watching just to hear the soothing and sonorous way Tadashi Tokieda says "cedar balls."

A Strange Change of Rotation (YouTube/Numberphile)