Transcript Skater on Ice Cylinder or skateboarder on reverse half-pipe

Skater on Ice Cylinder
or skateboarder on reverse half-pipe
Rhine
The Problem
=?
An ice skater with mass m is
perched on top of a
cylinder of ice (radius = r,
L doesn’t matter because
the skater will skate
orthogonally to the axis of
the cylinder).
a) If the ice skater starts
downhill with virtually no
v=?
velocity, at what central
angle, , will she leave
the cylinder? What will
her velocity be at that
point?
b) What if she has an initial
velocity of vo?
Assumptions and instincts?
What about friction? If you assume it
is zero, what can you say about
non-conservative work? (that is a
big hint!!)
=?
Note the angle between r and v
appears to be ____. Why is this
important and what type of
motion equations are related to
v=?
this?
What will the skater’s apparent weight
be at the moment she departs
from the cylinder? What force
relates to this concept?
Solution Process
i) FBD at a general point on
the circle
ii) Apply Newton’s 2nd Law
=?
v=?
What next?