fisica1-youn-e-freedman-exercicios-resolvidos

vr
5.00 m s
9.33: The angular velocity of the rear wheel is ω
r
= = = 15.15 rad s.
r 0.330 m
The angular velocity of the front wheel is ω
f
= 0.600 rev s = 3.77 rad s
Points on the chain all move at the same speed, so r ωr
= rf
ωf
r = r ω ω 2.99
( ) cm
r r f r
=
9.34: The distances of the masses from the axis are L L 3L
, and , and so from Eq. ( 9 .16 ),
4 4 4
the moment of inertia is
2
2
⎛ L ⎞ ⎛ L ⎞ ⎛ 3L
⎞ 11 2
I = m⎜
⎟ + m⎜
⎟ + m⎜
⎟ = mL .
⎝ 4 ⎠ ⎝ 4 ⎠ ⎝ 4 ⎠ 16
2
9.35: The moment of inertia of the cylinder is L 2
2
L
M
12
and that of each cap is m ,
4
so the
moment of inertia of the combination is ( M m 2
+ ) .
L
12 2
9.36: Since the rod is 500 times as long as it is wide, it can be considered slender.
a) From Table ( 9 .2( a)
),
I
1 2
2
= ML
12
1
=
12
2
−3
( 0.042 kg)( 1.50 m) = 7.88×
10 kg ⋅ m .
( ),
b) From Table 9 .2( b)
I
1 2
2
= ML
3
1
=
3
2
−2
( 0.042 kg)( 1.50 m) = 3.15×
10 kg ⋅ m .
c) For this slender rod, the moment of inertia about the axis is obtained by considering it
as a solid cylinder, and from Table ( 9 .2( f )),
1 2
−3
2
−8
2
I = MR
2
1
= (0.042 kg) (1.5 × 10
2
m)
= 4.73×
10
kg ⋅ m
.