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shifting one's weight



As promised, here's a simple model for shifting one's weight:

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That's a see-saw made of a board on a pivot. Note that the pivot is
constrained to stay in the center of the board. The 'X' is a significant
mass, and it is held on an arm which is capable of extending due to some
internal energy source (that could be a compressed spring overdamped by a
dashpot, for instance). The mechanism is placed so that it's center of
mass is above the pivot, so that the whole thing is in metastable
equilibrium.

Now extend the arm. Internal forces cannot move the center of mass of a
system. Therefore, if the board were on a frictionless surface, the mass
would move right and the board would move left. But the board is
constrained not to move: the pivot exerts a frictional force on the board
to the right. This external force pushes the center of mass of the (board
+ mechanism + mass) to the right, allowing gravity to then pull the board
down on the right. This is "shifting one's weight.

One feature of this model which connects to my experience, and therefore
convinces me that it's basically correct, is what happens to the board.
Note that, considering the (board + mechanism) alone, it experiences a
torque out of the page, so that it initially tips down on the *left*.
However, angular momentum of the (board + mechanism + mass) must remain
zero, so that once the extension has occured everything will tip down on
the right as described.

This initally came up in the context of what is going on in bicycle
riding. If you replace the pivot with the road, the board with a bike, and
the (mechanism + mass) with a person, then the system above applies. It
remains to be seen whether the effect is large enough to actually platy a
significant role. Unfortunately, the initial torque on the board is
important in determining how far the CoM moves. On bicycle it is
difficult to say just what the moving mass is, or with what lever arm it
acts. This makes any calculation speculative at best.

Instead, I suggest an experiment. Ride a bicycle standing on the pedals
(no seat contact) and only lightly touching the handle bars. Now move all
your weight onto one foot. This morning I found that this had a very
significant effect on the bicycle, leaning it over and tending to make it
turn.

--
--James McLean
jmclean@chem.ucsd.edu
post doc
UCSD

PS. While riding fast in a tight cicle (to check whether the front wheel
is actually turned a bit), I also found out that it is possible to break a
rear axle by skidding severely! No damage to myself, happily.