Re: Physics of aerial skiing tricks

matt271829-news@xxxxxxxxxxx wrote:

Edward Green wrote:

Although it's true that a body not coupled to its environment cannot
alter its angular momentum in an inertial reference frame, there is no
condition that such a body cannot alter its orientation, provided it
can adjust its shape.

Second, airborne skiers are not uncoupled to their environment. If you
are hurtling straight ahead in the air experiencing zero torque, and
you stick out one arm to your side, you may experience a torque and so
change your angular momentum. The air is of course acquiring equal and
opposite angular momentum.

Since skiers both may change their shape and experience differential
air resistance, they may both change their orientation without altering
their angular momentum, and also in fact alter their angular momentum.

Thanks for your reply Edward. I don't fully understand your point about
the skiers changing their "shape". I don't see how changing shape can
by itself add or subtract angular momentum.

You are correct, it cannot. However, it can change the moment of
inertia of various bits of the body, and that is sufficient for a body
to reorient itself in space without changing its angular momentum. The
angular case is different from the linear case, where a body cannot
move its center of mass from A to B without having some non-zero linear
momentum in an intermediary state. In the angular case, a body can go
from an initial state to a final state which is the original shape,
reoriented, without having had any non-zero angular momentum in any
intermediate state.

I don't think this point is widely emphasized in elementary physics: I
worked it out thinking about whether or how a dropped cat could twist
around in mid air to land on its feet. I believe then can in fact do
this even over a distance of several feet, before they've picked up
enough velocity for air resistance to be a significant factor.

Maybe you are saying that
the addition of spin along the head-to-toe axis to an existing
head-over-heels spin may not change overall angular momentum, but may
merely count as a change in "shape" or "orientation"?

Well angular momentum is a vector (or pseudo vector as the cognoscenti
like to say), and so changing any of its components amounts to changing
angular momentum.

I did consider air resistance, but discounted it as I thought the
effect would be too small. Maybe I was wrong there though. The skiers
do thrust out one of their arms just prior to starting to spin along
the head-to-toe axis. Do you think that the differential force of air
resistance on the outstretched arm, acting over a fraction of a second,
would be enough to spin them round maybe three or four times before
they hit the ground? I don't know enough physics to calculate this...

I think that is exactly what is going on, but since I am also allergic
to calculations, I will merely sketch plausibility. How fast are the
skiers going when they become airborne? I'm going to guess 70 mph (110
kph). Have you ever stuck you hand out a car window at that speed? Do
you think the force on your hand would be sufficient to start you
spinning if you happened to be standing on a nearly frictionless
turntable?

.

Relevant Pages

  • Re: Physics of aerial skiing tricks
    ... up into the air, where they perform various spins and somersaults and ... WITHOUT any rotation around the long axis of their body - ... alter its angular momentum in an inertial reference frame, ... head-over-heels spin may not change overall angular momentum, ...
    (sci.physics)
  • Re: Physics of aerial skiing tricks
    ... up into the air, where they perform various spins and somersaults and ... WITHOUT any rotation around the long axis of their body - ... series of somersaults, WITH such rotation. ... alter its angular momentum in an inertial reference frame, ...
    (sci.physics)
  • Re: Physics of aerial skiing tricks
    ... alter its angular momentum in an inertial reference frame, ... The air is of course acquiring equal and ... contorting then I *don't* continue spinning. ... resistance on the outstretched arm, acting over a fraction of a second, ...
    (sci.physics)
  • Re: New Mexico Fire-Devils
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