Problem
Set 9: Problem 5.
Problem:
A thin disk of mass
m
and radius
R
spins at constant angular velocity
ω
about an axis that
passes through its center, Point O. The axis is supported by a housing, which is attached to a horizontal
rod that rotates at constant angular velocity
Ω
as shown. Determine the couple,
M
, that represents the
dynamic reaction at support plate A.
Solution:
To solve, we work in a coordinate system rotating about the
x
axis with
Ω
=
Ω
i
.
In this
reference frame, the disk rotates about the
z
axis with
ω
=
ω
k
, and the angular momentum about the
disk’s center, Point O, is
H
O
= [
I
]
ω
where the disk’s inertia tensor is
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 Spring '06
 Shiflett
 Angular Momentum, Mass, Rigid Body, Polar coordinate system, constant angular velocity

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