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dA  M d   . (6.25)
When both sides of equation. (6.25) are divided by the time interval dt
during which the displacement occurs, we obtain

dA d
 M . (6.26)
dt dt

But dA is the rate of doing work, or the power N,and d is the
dt dt
angular velocity .,hence

N  M   . (6.27)

That is, the instantaneous power developed by exerting moment

of force equals the product of this moment multiplied by the
instantaneous angular velocity This is the analog of N  F v  for
linear motion.

6.4 Main Law of Dynamic of Rotational Motion .

Now we’ll consider more generally the dynamics of rotational

motion of a rigid body around a fixed axis, that is, the relation
between the forces acting on a rotating body and its motion. Such
relation is obtained most simply from the work-energy theorem .

Work done by moment of force must be equal to the change of

kinetic energy I  2 of rotational motion of rigid body Thus
2
 I  2 
M  d  d   . (6.28)
 2 
 

   2  d
Taking into account that d      d , and   , therefore
 2  dt
 
d
M   (6.29)
dt
d 
Аs   (angular acceleration ),then
dt
M     . (6.30)
This is the main law of dynamic of rotational motion . It is the

rotational analogue of F = ma, because this law is often named as
Newton's law for rotational motion

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