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Sometimes I have a Very Full Mug of Coffee and I am trying to carry it without it spilling. I noticed that if I moved the Mug up and down when carrying it, it seemed to settle the coffee and make it less likely to spill as i moves it from point A to Point B.

Does anyone know what this may be? - Is it something to do with the up/down momentum change being must greater than the horizontal momentum change, and so the coffee stays in the Mug Better?

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    $\begingroup$ My guess is that you are really trying to prevent your body from exciting the slosh mode near its fundamental frequency. Humans are very poor feedback loops when the time scale of the phenomenon they are trying to control gets close to the limits of their reaction time (which is a fraction of a second, at best). In that case we have a tendency to make things worse while we are trying to control them. By moving your arms up and down you are probably removing (or damping) the feedback loop that your brain is trying to make to prevent the coffee from sloshing. I could be wrong. $\endgroup$ – CuriousOne May 24 '15 at 17:51
  • $\begingroup$ A study was done: engineering.ucsb.edu/~rkrechet-lab/files/publications/…. But the researchers only studied motion in the x,y plane, and didn't discover the up-and-down you ask about. $\endgroup$ – Ernie May 24 '15 at 19:13
  • $\begingroup$ It's certainly not the case that vertical momentum would affect horizontal momentum. I agree with CuriousOne that you're unconsciously tilting the cup as well as raising it up/down a bit, essentially out of phase with the slosh induced by walking. $\endgroup$ – Carl Witthoft May 25 '15 at 0:57
  • $\begingroup$ @CarlWitthoft while not directly effecting the momentum, the vertical acceleration changes the effective restorative force on the fluid which will effect the horizontal momentum. $\endgroup$ – Rick Sep 28 '15 at 14:35
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Each footstep results in an impulse through your body. Holding your mug and arm stiff against this impulse does not stop the impulse from traveling along the lever of your arm. Unlike your solid arm and mug, which have your muscles to resist this impulse, the liquid coffee sloshes.

Pay attention to the way you move your mug up and down. Very likely this will match the period of your steps. Your arm essentially becomes a shock-absorber, stretching out the moment of impulse being exerted upon the liquid coffee.

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