fisica1-youn-e-freedman-exercicios-resolvidos

9.75: I approximate my body as a vertical cylinder with mass 80 kg, length 1.7 m, and
diameter 0.30 m (radius 0.15 m)
I
1
= mR
2
2
=
1
(80 kg)
2
(0.15 m)
2
= 0.9 kg ⋅ m
2
9.76: Treat the V like two thin 0.160 kg bars, each 25 cm long.
⎛ 1 2 ⎞ ⎛ 1 ⎞
Ι = 2⎜
mL ⎟ = 2⎜
⎟ (0.160 kg)(0.250 m)
⎝ 3 ⎠ ⎝ 3⎠
= 6.67 × 10
−3
kg ⋅ m
2
2
9.77: a) ω = 90 .0 rpm = 9.425 rad s
K =
1
2
Ιω
2
2K
so Ι =
2
ω
6
2(
10.
0 × 10 J)
=
= 2.
252×
10
2
( 9.
425rad s)
5
kg ⋅ m
2
m = ρV = ρπR t(
ρ = 7800 kg
3
m is the density of iron and t=0.100 m is the
thickness of the flywheel)
1 2 1 4
Ι = mR = ρπtR
2 2
R = (2I
1 4
ρπt)
= 3.68 m; diameter = 7.36 m
a
= Rω
2
b)
c
= 327m
s
2
2
2
2 2
9.78: Quantitatively, from Table (9.2), I
1 , and ⋅
A
= mR Ι = mR Ι = mR a)
2 B
C
Object A
3
has the smallest moment of inertia because, of the three objects, its mass is the most
concentrated near its axis. b) Conversely, object B’s mass is concentrated and farthest
2
from its axis. c) Because Ι = 2 mR , the sphere would replace the disk as having the
smallest moment of inertia.
sphere
5
2