Re: [Phys-L] coffee

[John Denker <jsd@av8n.com>]

On 1/31/20 8:57 AM, Anthony Lapinski wrote:

> I see faculty walking past my room with their coffees every morning. Is
> there an optimal walking frequency (speed) to minimize the liquid from
> sloshing back and forth and spilling over? I imagine this depends on the
> leg length, diameter of cup, depth of cup, etc.

If done right, it doesn't depend on details of the legs or
cups or anything like that.

To a first approximation, while enroute, the idea is to
create and maintain an inertial platform.  There is no
reason why your hand has to track your foot or your knee
or your center of mass.  Hand and cup move at constant
velocity, even though your gait is a bit irregular.

Runners gain some biomechanical efficiency by swinging
their arms, but if you're just walking, you don't need
to do that.  

As a demonstration that exaggerates the principle, hold out
your hand and point to right *here* on the computer screen.
Sway your torso left and right, keeping your hand in the
same place.  It's not hard to achieve a very substantial
decoupling from torso to hand.

You can even do this with your eyes closed.  Try it.
Sway a few cycles and then open your eyes to see how
far your finger has drifted.

I can walk, chew gum, carry liquids, and do physics
calculations all at the same time.

===

To a second approximation, consider what happens when
starting, stopping, or cornering.  The idea is to keep
the g-vector -- in the accelerated frame comoving with
the cup -- pointing toward the bottom of the cup.  This
may be easier to observe when carrying a whole tray full
of cups.  When cornering, tilt the tray toward the inside
of the turn.  This is just leaning a bicycle into a turn.
When starting, raise the back of the tray a little bit.
When stopping, raise the front.

Carrying a plumb-bob in such a way that it does not
appreciably oscillate is possible, but harder, because
it is only very lightly damped.  A cup of liquid of any
reasonable size has considerable damping, which means
that small mistakes die out rather than accumulating.
Sticking a spoon in the cup increases the damping.

=== 

To a third approximation, if you want to be a smart-alec
(who, me?) you can accelerate and decelerate the tray
as you walk along. You can even do loop-de-loops, although
that takes a bit of practice.  Start by practicing with
something that has a handle, like a bucket or a handbasket,
filled with something non-fragile and non-messy, e.g. the
proverbial bag of beans.  As long as you keep the g-vector
(in the accelerated frame) pointing toward the bottom
of the basket, the payload isn't going to spill.

I have used the language of accelerated frames.  Yeah,
I know that almost all introductory physics books scream
and shout that accelerated frames do not exist, and
therefore centrifugal forces don't exist, but I refuse
to play along.  Students have plenty of experience with
real-world cars and bicycles and playground merry-go-rounds
and other situations where it is entirely conventional
and reasonable to choose an accelerated frame.  For
that matter, from the modern (post 1915) point of view,
the lab frame is an accelerated frame, accelerating
skyward at the rate of 9.8 m/s/s relative to any local
freely-falling frame.

--> The centrifugal field exists in the rotating frame
 and not otherwise.

There is no such thing as "apparent" weightlessness.
Items in the space station are really and truly
weightless /in the frame comoving with the station/.
This idea is one of the crown jewels of modern (post
1915) physics.

==================

There is some reeeeeally serious physics in this.  There
are lots of laboratory situations where you need to
create a high-quality inertial platform.  Again and again
in my physics career I've had to deal with this.

++ One of the key subsystems in the LIGO instrument is
 the exquisite vibration isolation.  It creates an
 inertial platform for the mirrors.

++ Optical tables have a huge mass, lots of internal
 damping, and sophisticated vibration-isolating supports.

++ Any low-temperature physics cryostat floats on an
 inertial platform.  That's because you can't tolerate
 vibration.  That's because the heat capacity of
 anything at those temperatures is zero cubed.

++++ etc. etc. etc.