fisica1-youn-e-freedman-exercicios-resolvidos

9.37: a) For each mass, the square of the distance from the axis is
2 −2 2
2(0.200 m) = 8.00×
10 m , and the moment of inertia is
4(0.200 kg) (0.800×
10
−2
2
m ) = 6.40×
10
−2
kg ⋅ m
2
.
b) Each sphere is 0 .200 m from the
−2
2
axis, so the moment of inertia is 4( 0.200 kg)( 0.200 m) = 3.20 × 10 kg ⋅ m .
a) The two masses through which the axis passes do not contribute to the moment of
2
inertia. I = 2(0.2 kg) ( 0.2 2 m) = 0.032 kg ⋅ m .
2
2
9.38: (a)
I
= I
=
bar
1
12
+ I
balls
=
1
12
M
bar
2
L + 2m
balls
2
⎛ L ⎞
⎜ ⎟
⎝ 2 ⎠
2
2
2
( 4.00 kg)( 2.00 m) + 2( 0.500 kg)( 1.00 m) = 2.33 kg ⋅ m
(b)
1
3
2
I = mbarL
+
m
ball
L
2
1
=
3
2
2
2
( 4.00 kg)( 2.00 m) + ( 0.500 kg)( 2.00 m) = 7.33 kg ⋅ m
c) I = 0 because all masses are on the axis
(d)
I = m + =
=
2
2
2
bard
2mballd
M
Totald
2
( 5.00 kg)(0.500 m) = 1.25 kg ⋅
m
2
9.39: I = I + I (d = disk, r ring)
disk : m
I
d
d
ring : m
r
d r
=
= (3.00 g cm ) πr
1
Ir
= mr
( r
2
I = I + I
d
2
1
r
3
2
2
2
d
1 2
= mdrd
= 2.945 kg ⋅ m
2
3
= (2.00 g cm ) π ( r − r
+ r
2
2
= 8.52 kg ⋅ m
= 23.56 kg
2
2
2
1
) = 5.580 kg ⋅ m
) = 15.08 kg
2
( r
1
= 50.0 cm, r
2
= 70.0
cm )