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15 Wheel spinning precession<br />
x<br />
MgL<br />
L<br />
y<br />
z<br />
Mg<br />
Wheel spinning around y-axis,<br />
hanging from ceiling<br />
Weight create a torque which<br />
changes the angular<br />
momentum<br />
Torque vector<br />
representation<br />
y<br />
<br />
Important: This<br />
analysis is valid<br />
only for LARGE<br />
y<br />
H Angular momentum<br />
x<br />
z<br />
y<br />
H y I yy y<br />
p<br />
y<br />
t<br />
Angular momentum<br />
change due to the<br />
torque applied<br />
After torque applied for t<br />
z<br />
This is what wheel will<br />
look like after del T<br />
time due to<br />
precesses, notice that<br />
SPIN angular<br />
momentum changes<br />
in the direction of the<br />
torque<br />
y<br />
Time it takes<br />
for the wheel<br />
to precesses<br />
one full cycle<br />
T p 2<br />
p<br />
H<br />
z<br />
Angular momentum<br />
after<br />
t<br />
t<br />
H aftert<br />
x<br />
H I yy y t<br />
x<br />
I yy y<br />
p<br />
y<br />
H t H<br />
t<br />
<br />
But<br />
H<br />
t<br />
I yy y p , hence I yy y p hence p <br />
<br />
I yy y<br />
MgL<br />
I yy y<br />
Nasser M.<br />
Abbasi<br />
Precesses.vsd<br />
6/1/2011<br />
Therefore, precession velocity p is MgL<br />
I yy y<br />
16 References<br />
1. Structural <strong>Dynamics</strong> 5th edition. Mario Paz, William Leigh<br />
63