63. We use L = Iω and K =

1
2

Iω

2

and observe that the speed of points on the rim (corresponding to the

speed of points on the belt) of wheels A and B must be the same (so ω

A

R

A

= ω

B

r

B

).

(a) If L

A

= L

B

(call it L) then the ratio of rotational inertias is

I

A

I

B

=

L/ω

A

L/ω

B

=

ω

A

ω

B

=

R

A

R

B

=

1

3

.

(b) If we have K

A

= K

B

(call it K) then the ratio of rotational inertias becomes

I

A

I

B

=

2K/ω

2

A

2K/ω

2

B

=

ω

B

ω

A



2

=

R

A

R

B



2

=

1

9

.