Moment of Inertia

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Moment of Inertia
Moment of Inertia
Area moment
of Inertia
Mass moment
of Inertia
Mass Moment of Inertia
The resistance of a body to changes in angular
acceleration is described by the body’s mass moment of
inertia about the axis of rotation. By definition, the mass
moment of inertia is
I = ∫m r2 dm
Graphics and problem statements © 2004 R.C. Hibbeler.
Published by Pearson Education, Inc., Upper Saddle River, NJ.
Where r is the distance from the axis of rotation to the
differential mass element dm.
Moment of Inertia of rectangular plate about the axis
passing through Diagonal
C
B
M/2
h
M/2
A
D
b
2
I AC
2
1
bh
 M 2
2
6 b h
Moment of Inertia of rectangular plate about the axis
passing through Diagonal
y
B
C
h
x
h/2
x
A
b/2
b
y
D
Find out the moment of inertia about & identify the maximum and minimum
(i) XX
(ii) YY
(iii) AD
(iv) AB
(v) AC
Moment of Inertia of hallow sections
Relative density (Specific gravity)
Density of the body
Relative Density (Specific gravity) of a body 
Density of water
b Vb b g wt of the body in air
 rb 


 w Vb  w g
Buoyant Force
Wair
wt of the body in air wt of the body in air
 rb 


Buoyant Force
Wt lost by the body Wair  Wwater
Relative density (Specific gravity)
Density of the liquid
Relative Density (Specific gravity) of a liquid 
Density of water
 l Vb  l g Buoyant force in liquid
 rl 


 w Vb  w g Buoyant Force in water
Wair  Wliquid
Buoyant force in liquid
Wt lost by the body in liquid
 rl 


Buoyant Force in water Wt lost by the body in water Wair  Wwater
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