62. We denote the wheel with subscript 1 and the whole system with subscript 2. We take clockwise as
the negative sense for rotation (as is the usual convention). Conservation of angular momentum gives
L = I
1
ω
1
= I
2
ω
2
,where I
1
= m
1
R
2
1
. Thus
ω
2
= ω
1
I
1
I
2
= (
−57.7 rad/s)
37 N/9.8 m/s
2
(0.35 m)
2
2.1 kg
·m
2
which yields ω
2
=
−12.7 rad/s. The system therefore rotates clockwise (as seen from above) at the rate
of 12.7 rad/s.