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84. The angular displacements of disks A and B can be written as:
2
1
,.
2
AA
B
B
tt
θω
θ
α
==
(a) The time when
AB
θθ
=
is given by
2
2
2
1
2(9.5 rad/s)
8.6 s.
2
(2.2 rad/s )
A
B
t
ω
ωα
=
¡
=
(b) The difference in the angular displacement is
22
1
9.5
1.1 .
2
A
B
ttt
t
θθ θ ω
Δ= − = −
=
−
For their reference lines to align momentarily, we only require
2
N
θπ
Δ=
, where
N
is an
integer. The quadratic equation can be readily solve to yield
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 Spring '08
 Any
 Physics

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