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.