Why do shopping cart wheels wobble?

Short answer: shopping-cart wheels wobble because they are casters: the wheel touches the floor behind a swivel axis so it can automatically point in the direction of travel. Under some combinations of speed, friction, looseness, wheel geometry and wear, that self-steering system becomes unstable and oscillates instead of settling straight.

A caster normally wants to follow you

The contact patch of a caster wheel trails behind the vertical steering pivot. When you push the cart in a new direction, the floor force pulls the wheel into alignment. That is why a cart can turn without a steering linkage.

But the same geometry creates a feedback loop. If the wheel swings a little to one side, the forces at the contact patch can push it back through center. With enough damping the motion quickly dies out. With too little damping, play in the bearings, an uneven tire or the wrong speed, the correction overshoots and the wheel swings the other way. The result is caster shimmy or flutter.

Why one bad wheel can shake the whole cart

Real store carts add bent forks, worn bearings, flat spots, debris and loose pivots to the physics. Those defects change friction and geometry, making one caster much easier to excite. The wheel can then transmit vibration into the frame, so a small problem at one corner feels like the entire cart is protesting.

Would a fixed wheel stop the wobble?

Usually, yes—but the cart would become much harder to steer sideways. Designers accept swiveling casters because their maneuverability is worth the possibility of shimmy. Better bearings, proper trail, tighter tolerances and damping reduce the problem.