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6. DYNAMICS OF ROTATIONAL MOTION OF A RIGID
BODY

6.1 Kinetic energy of rotational motion of a rigid body.
Moment of inertia of a rigid body.

Let’s consider a rigid, body that
rotates around a fixed axis .(fig.6.1)
The total kinetic energy of the body is
the sum of the kinetic energies of all

particles in the body
2
 m 1 v  1 2  m 2 v  2
E K    ...
2 2
(6.1)
2
 m n v  n
... 
2
So
v   r  , v  r  2 ,..., v   r  (6.2)
n
1
2
n
1
Then
Figure.6.1
2
2
( m r   m r    m r 2 ) 2
E  1 1 2 2 n n

2
(6.3)
or
2 2 2 2
( m 1 r   m 2 r 2    m n r n )
1
E   . (6.4)
2

Compare this result with kinetic energy of translation motion
2
  2 2 2
E   . The sum m 1 r   m 2 r  ...  m n r looks like mass
n
2
1
2
in rotational motion. Therefore, this sum is called the moment of
inertia of the body around the axis of rotation, and is represented by

I , i.e

m 1 r 1 2  m 2 r 2 2  ...  m n r n 2   m i r i 2  I . (6.5)

z
In SI units the unit of moment of inertia is 1 kg-m The rotational

kinetic energy of a rigid body can now be written as

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