Actually usually is the opposite. Things always tend to go to the most stable state due to random impulses. But you are “semi right”. If the basket always spinned in the same direction, most probably your clothes would probably end in just one side of the washing machine. But they don’t work like this (at last the ones were I live). In he washing cycles, the machine moves counter and clockwise distributing my laundry almost evenly inside the basket. Even if I put all laundry in just one side the even distribution eventually is reached because of the alternating movements.
Even so, in machines that only go in one direction the evenly distributed state could also be probably reached if the laundry is evenly distributed enough, because that is the most stable one! You seem to be kind of fluent in physics, so I’ll propose you this restricted pseudo 3-body problem: let’s say there is a central body ~~confined in a Hooke’s potential in a center~~ in a fixed center (let’s ignore the center’s movement for now!), and let’s also say that two bodies with equal masses move around the central body in a circle with fixed radius and the same angular velocity separated by some angular position. If you do the math you will notice two stable separations: 0º and 180º. And you’ll also notice which one is more stable e.g., has the least energy and /or torque. I recommend you try! If you can’t , I’ll give you some pointers.
Washing machines, when spinning quickly enough to defy gravity, can effectively be considered flat surfaces under gravity higher than 1g. That gravity is part of the process of getting the load to spread out evenly.
The other factor is that the drum will change directions and speed to toss the contents about, to spread the load more evenly.
Really though, it’s a smaller faster version of an artificial gravity spin habitat. Even though the structure is round, it has radial gravity so things can flow ‘down’ to even out.
Addendum: Forgot to mention that spin gravity changes wildly with the distance from the center. Spin grav is strongest at the edge and fades to zero near the center. Here’s a diagram of how that works with a front loader:
* Earth Gravity: Down < 1g < Up (Down is left here)
* Spin Gravity(2g): << 2g < 1g (0g) 1g > 2g >>
* Combined Gravity: <<< 3g << 2g < (1g) | 0g | 1g >
This means in simple terms that only laundry stuck to the drum can stick to the drum at the top of the arc with spin gravity. Laundry that is closer to the center will fall during that part, sorting taller lumps out by tossing them around. The faster the drum spins, the larger the zone of laundry that can stick during the top of the arc becomes, which is why the varying spin speed helps with sorting.
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