Aula_10-Rotacao_de_Corpos_Rigidos

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http://profanderson.net 
anderson.gaudio@ufes.br 
Prof. Anderson Coser Gaudio 
TecnoLab – Depto. Física – CCE - UFES 
r

O
y
xi
2 1    
r1

O
y
xi
r2


s r  
s
O
y
x
r2

r1
2 1
2 1
m
t t t
  
 
 
 
0
lim
t
d
t dt
 
 

 

2 1
2 1
m
t t t
     
 
0
lim
t
d
t dt
 
 

 

0 
0
d
dt


0d dt 
0 0
0
t
t
d dt


  
 0 0 0t t    
0 0t 
0 0t   
0 0xx x v t 
Movimento translacional 
(Direção fixa) 
Movimento rotacional 
(Eixo fixo) 
0v v at 
2
0 0
1
2
x x v t at  
 2 20 02v v a x x  
 0
0
2
v v
x x t

 
2
0
1
2
x x vt at  
0 t   
2
0 0
1
2
t t     
 2 20 02      
 0
0
2
t
 
 

 
2
0
1
2
t t     
1 2 2 1       
 ©2002 by John Wiley & Sons 
1 2 2 1d d d d  θ θ θ θ
x
y
z
d
r1
r2
d
dt

dθ
ω
dt

dω
α
d
dt

θ
ω
ω



v1


t
t




t
t

senab   c a b
 ©2002 by John Wiley & Sons 
x
y
z
d
r1
r2
d d = dr s
ds dr rd 
d d s θ r
d d s θ r
x
y
z

r
v
 
d d
d
dt dt
 
s
θ r
d d
d
dt dt
   
θ r
v r θ
 v ω r
 v ω r
 
d d
dt dt
 
v
ω r
d d
dt dt
   
ω r
a r ω
x
y
z

r
a
atar
   a α r ω v
t r a a a
x
y
z

r
a
atar
   a α r ω v
t r a a a
t  a α r
r  a ω v
 
22 2 21 1 1
2 2 2
i i i iK mv m r mr   
2 2 2 2 2 2
1 2 1
1 1 1
2 2 2
K mr mr mr     
   2 2 2 2 21 2 1
1 1
2 2
K m r r mr     
21
2
K I
2 2 2
1 2 iI mr mr mr   
2 2
0
lim
m
I r m r dm
 
   
 ©2004 by Pearson Education 
2I r dm 
 ©2004 by Pearson Education 
2 2
L h
h
M
I x dm x dx
L


  
3
3
L h
h
M x
I
L


  
   
  
 2 2
1
3 3
3
I M L Lh h  
M dm
L dx
  
M
dm dx
L

21
3
I ML
21
12
I ML
 2 2
1
3 3
3
I M L Lh h  
 2 2CM i i iI m x y 
   
2 2
P i i iI m x a y b     
   2 2 2 22 2P i i i i i i i iI m x y a m x b m y a b m        
2
P CMI I Md 
 ©2004 by Pearson Education 
 i i i i iU m gy m y g 
   1 1 2 2 CMU m y m y g My g   
CMU Mgy
CMU Mgy
CM
 ©2004 by Pearson Education 
CMU Mgy
CM