Objects at rest want to stay at rest, this includes liquids.
However, in the case of a rotating glass with liquid inside, the liquid near the side of the glass will rotate with the glass when it starts. The longer you rotate it for, the liquid near the middle of the glass will start rotating, until eventually all the liquid is rotating at the same speed as the glass.
It does…kinda.
Imagine the glass as a big ball pit and the water like the balls. Since the water is a liquid, the balls aren’t glued together. If you put the ball-pit glass on a merry-go-round and spin it suddenly SUPER fast (consider how fast the side of the glass must look to the teeny tiny water molecules), the balls on the edge will move because they were touching the sides—they’re pushed by friction—but not as fast as the wall because some of that motion goes instead to rolling or jostling in a different direction (or is lost to heat). The next layer in of balls will start to move too, but only because the outermost layer pushes them, and this layer will move a little slower for the same reason—they’re not glued to the other balls so they mostly get pushed forward but also then bounce off sideways or roll away or what have you. So some more of the motion is lost.
By the time you get to the balls in the very middle, they might not move at all, or move very little.
If you keep spinning the ball pit, though, eventually enough of the motion will make it all the way through these individual ball-molecules that they all start to move. This will happen in a regular-sized glass too if you spin it long enough.
It’s due to the boundary layer and depends on the viscosity of the liquid. The liquid which is touching the glass is called the boundary layer, you can consider it as a thin tube of water molecules which the rest of the liquid in the center is pushing out and sticking to the glass.
When the glass turns, this boundary layer moves with it because of the friction between the two materials.
Inside the boundary layer picture another, smaller tube of water molecules which interface with the boundary layer. When the boundary layer turns, this tube also turns, but because there is not a lot of friction between the two, not all of the energy is imparted and so it doesn’t move as quickly as the boundary layer.
This transfer of energy repeats until it reaches the centre of the liquid, or there is not enough energy to transfer to the next layer which, if all your doing is turning the glass, there won’t be.
If the liquid had a higher viscosity, then there would be a LOT more friction, which is why when turning a jar of honey, for example, all of the honey turns with the jar as though it were a solid, even though it is a liquid.
https://youtu.be/AfCyzIbpLN4 (4:18 for a visual explanation, but in your example it’s backwards)
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