if you stir a cup of coffee, is the velocity at the centre different from the velocity outside?
If the angular velocity is constant, yes. Linear velocity equals angular velocity times radius: v = ωr.
but is the angular velocity always constant?
No, hence the qualification of "If the angular velocity is constant".
but what affects the angular velocity?
I wouldn't know, I don't drink coffee.
Something else: why does the pitch sound different when you tap a spoon to the bottom of a cup with spinning (hot) liquid compared to when the liquid is not spinning?
You can actually hear the pitch change when you first stir it very well, start tapping until the vortex slows down.. it's my dad's favorite scientific experiment ;)
My hypothesis is that the spinning liquid rises higher up the sides, thus making more contact with the container. The more liquid a container has, the higher the pitch, right? Well, assuming that I've got the correct relationship, then I would conjecture that the glass with spinning liquid returns a higher pitch than when the liquid finally slows down. Should this turn out to be true, I would draw the tenuous conclusion that the pitch is controlled by how much length of glass (to the brim) is not in contact with the liquid.
pitch change -coffee or cocoa?
Works much better with cocoa, made with milk.
Isnt it the suspended solids (not the vortex) which make the difference to the resonance? Try stirring up and down so the liquid is moving but NOT creating a vortex.
Newsflash … important research paper …
A very similar issue was examined in the Proceedings of the Cambridge Philosophical Society, volume 65, page 365 (1967), in an experimental research paper entitled:
On note emitted from a jug while mixing instant coffee.
The authors were Farrell W.E. (whose usual field seems to be plate tectonics), Mackenzie D.P., and Parker R L.
Unfortunately, my library has no volumes before volume 77, but from memory they discovered that the note depends on the density of air molecules trapped against the coffee grains - which changes as you stir it!
Well … it was the sixties … and that sort of thing was important …
[size=-2](I know this is almost a duplicate of a post in another thread
- but I thought it was important)[/size]
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