Water on the Carousel (June 2023 challenge question)

If the glass is full the first thing that happens is that water flows over the edge of the glass. If there is a big enough gap so that the water does not flow over the edge, then the first thing that happens depends on the coefficient of friction between the glass and the surface it's resting on, and, the centre of gravity of the glass.

Another good reply. First answer to consider if the glass has an unusual shape, which does unmentioned in the challenge.

Without more complete information about coefficient of friction, how full, etc. I would have to say that centripetal acceleration would cause the liquid to flow up the outside edge of the glass, essentially raising the CG and causing the glass to tip over. This is similar to a tanker truck that is partially full going around a corner and flipping when the CG shifts.

It all depends upon how the glass with water is anchored to the carousel. If it is stuck at oerifery in a vertical position, water in it would assume horizontal position, with most of it spilling out, if the speed is considerable .

If held between two ginger's near the top, with freedom to tilth, then the glass would be near horizontal but water in tact.

If the glass is just placed, it would fall due to centrifugal force.

So many variables. Depending on the friction between the glass & ride, it might just slip. If it does not slip, depending on how full the glass is, the water might ride up the glass & spill or, if it is a tall glass with a high CofG, it might just tip over.

Most likely, some small child will jump on the ride & knock it over.

A lot of variables here.How fast is the carousel accelerated?How much water is in the glass?How close is the glass to the edge?All of these and more factors determine the ultimate result,but the first thing to happen is the water will displace to the outer edge of the glass,and up the side, and how high it goes up the side will depend on the initial acceleration,the final velocity and the amount of water in the glass.

What - ignoring relativistic effects as negligible?

Depends on a number of things, mainly the friction between glass and merry-go-round surface, whether the glass is full, and the shape of the glass. With various combinations, it could do any of the 3 options given.

A kid takes the glass and drinks all of the water. She then says to my flabbergasted face "Thanks, mister. I was thirsty. Will you push this for me?"

Since it is specifically mentioned that it is a hot day, the first thing that happens might be that the water starts boiling - or is it not that hot? If it boils it might spill a little over the edge, capillary creeping under the glass, significantly reducing the friction.

Even if the boiling temperature is not reached, the temperature might further be of influence on the viscosity of the water and the the friction between the glass and the metal surface. It all comes down to comparing the numbers...

But what if one uses a half-filled martini glass?

I doubt any glass would slide. What engineer of a play yard carousel would design the floor of the surface with a low sliding coefficient of friction? The one pictured has a rusty diamond plate, hardly a slick surface. I doubt even a rock's glass would slide on that surface.