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you sure about it chief? bigger wheels also have larger rotational inertia
Yeah, try riding a folding bike with small wheels, you wobble a lot more.
It's not about the magnitude of the rotational inertia (which is roughly the same or maybe a bit higher on larger wheels that are probably heavier), it's about the center of the gyroscopic effect. It's at a greater height if you have big wheels, and closer to the ground if you have small ones.
A low center of gravity is more stable than a high one.
Gyroscopic effects do exist on bikes but they are not the main source of stability - it's the fork geometry, which tends to straighten the handlebar
The rotational moment of inertia increases a lot due to the larger diameter J ~ m r^2. Even if the masses were the same, the relatively heavy tyre and the rim are further away from the wheel hub.