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So force is a vector ,
moment of force should be a
vector as well. Therefore

moment of force as a vector is
named the torque and is
defined as vector's product
  
M  [r  F ], (6.31)

r is the vector from the point
Figure 6.10
from which torque is measured
to the point where force is
applied. Thus the main law or

equation of dynamics of rotational motion of rigid body can be
rewritten in vector form

 
M     . (6.32)

6.5 Aangular momentum. Conservation of angular momentum

Take to account that angular acceleration is the first

derivative of angular velocity with respect to time, then
fundamental dynamical principle for rotation of a rigid body can be
represented in the following form 

 d d( I )
M  I   . (6.33)
dt dt 
 d( m v)
Comparing this result with Newton's Second Law F  ,
dt
is easy to notice, that analogue of linear momentum (impulse)
 
p  m v is the product of moment of inertia I and angular velocity 
 
If product p  m v is called linear momentum or impulse then is

natural to call product I angular momentum
 
L   I  (6.34)

Therefore 
 d L
M  ( 6.34)
dt
For the closed system, where external moments of forces do not
 n 
act , i.e M  0 or  M i  0

1  i

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