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
.