Motion in a high or low pressure system
What is this?
A puck is attached to a device that
delivers a radial force, either inward or
outward, but independent of the length of
the device. The force is analogous to that
experienced by a parcel of air in a low or high
pressure system, with concentric rings of isobars,
equally spaced. Here the time scale has been made
dimensionless using the Coriolis parameter. The
length scale is the initial radial position of the
puck. There is no friction.
The components of the equation of motion
for the puck are:
dU/dτ= sX/R + V
dV/dτ= sY/R  U
where
R=sqrt(X^{2}+Y^{2})
and s is the strength of the radial force,
negative is inward and positive is outward.
Can you write the above equations in polar
coordinates?
The initial conditions are X=1, Y=0, U=0 and V=V_{0}.
For certain combinations of s and V_{0}, the subsequent
motion will be circular.

What is the largest value of s that allows for circular
motion? With what value of V_{0}?

What value(s) of V_{0} allows for circular motion (with radius=1)
with s=0?

What value(s) of V_{0} allows for circular motion with s=1?
 Can you find the above answers using analytic mathematics, and
not just by experimenting with the physlet?
 What is the significance of the graph at the top of page? If you are
entering values of V_{0} and s within the domain and range of the
graph (probably a good idea), you should see a blue marker indicating your
choices.