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
d L
 0 (6.35)
 dt
It's possible when L  const or in common case

n 
I
L
 i   i  i  const. (6.36)
 i 1
Thus we proved the law of conservation of angular
momentum:In a closed system angular momentum is constant.
This conservation law follows mathematically from continuous
directional symmetry of space (no direction in space is any different

from any other direction).
And now consider some examples of the law of conservation of
angular momentum

a b c

Figure 6.11
1) a man stands at the center of a turntable, holding his arms

extended horizontally (fig. 6.11a) and rotates with angular velocity
 so that angular momentum of a man is equal to
1

L  I 1    1 , (6.37)

where I 1 - moment of inertia of a man at first position a;

2)a man drops his hands (fig. 6.11b) , that results in diminishing
moment of inertia of a man to I so that angular momentum of a man is
2
equal to
 
L  I 2   . (6.38)
2
According to the law of conservation of angular momentum,
diminishing of moment of inertia results to increase of angular velocity

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