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Collecting terms and neglecting terms in
2
ω
′
:
cos
sin
0
gg
xx
tyy
t
ll
ωω
′′
++
+
±±
=
sin
cos
0
x
xt
y
y t
+−
+
=
5.21
24
sin
T
λ
=
hours
24
73.7
sin19
T
==
D
hours
5.22
Choose a coordinate system with the origin at the center of the wheel, the
x
′
and
axes pointing toward fixed points on the rim of the wheel, and the
axis
pointing toward the center of curvature of the track.
Take the initial position of
the
y
′
z
′
x
′
axis to be horizontal in the
V
−
D
G
direction, so the initial position of the
y
′
axis is vertical.
The bicycle wheel is rotating with angular velocity
V
about its axis, so …
b
D
ˆ
l
V
k
b
′
=
D
G
A unit vector in the vertical direction is:
ˆˆ
ˆ
sin
cos
Vt
ni
j
bb
=+
DD
At the instant a point on the rim of the wheel reaches its highest point:
ˆ
sin
cos
rb
nb
i
j
′
+
G
Since the coordinate system is moving with the wheel, every point on the rim is
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
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