Problem
Set 2: Problem 5.
Problem:
A lighthouse keeper’s son enjoys sliding down the spiral staircase railing from the light to
the ground floor. His path is a spiral of constant radius,
R
. The cylindrical coordinates of his position
as measured from the top of the staircase are
r
=
R
,
θ
=
Ω
t
and
z
=
−
wt
, where
t
is time,
Ω
is his
angular rotation rate and
w
is his vertical speed. Both
Ω
and
w
are constant. Determine his velocity
and acceleration components. If his speed along the railing is
5
4
w
, what is his angularrotation rate?
Solution:
Because the stairway has cylindrical symmetry and motion occurs at constant radius
r
=
R
, we
compute the velocityvector components by differentiating as follows.
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 Spring '06
 Shiflett
 Acceleration, Velocity, Euclidean vector, Lighthouse, Rotational symmetry, DT DT DT

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