The conservation of angular momentum.
Momentum itself is intuitive: an object in motion will stay in motion. If a mass is moving in a straight line, it takes some force to slow it down OR change it’s direction.
If you spin something, that mass is still moving. It’s just going around in circles instead of forward. Falling over would be changing the “direction” of the motion, so the momentum resists this change.
There’s also an interesting thing where the reaction force acts at 90 degrees to the applied force, which can cause the object to rotate around instead of just tipping in the direction you push. There’s a bunch great demos of “gyroscopic procession” on youtube, if you look.
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