Moment of Inertia for bsc first yaer

1. SUBMITTED BY
SURBHI TRIPATHI
BSC1st YEAR
PRESENTATION ON MOMENT OF INERTIA
SUBMITTED TO
DR.SHARAD KUMAR

5. Parallel axis theorem:
Consider the moment of
inertia Ix of an area A
with respect to an axis
AA’. Denote by y the
distance from an element
of area dA to AA’.
2
xI y dA 

6. Consider an axis BB’ parallel
to AA’ through the centroid C
of the area, known as the
centroidal axis. The equation
of the moment inertia
becomes
 
22
x
2 2
2
I y dA y d dA
y dA y dA d dA
  
   
 
  

7. The first integral is the moment
of inertia about the centroid.
0
0
y A y dA y
y dA
    
 


2
xI y dA 
The second component is the first moment area about the
centroid

8. Modify the equation obtained
with the parallel axis theorem.
2
x 2I y dA y dA   
2
2
x
d dA
I d A

 
 

9. RADIUS OF GYRATION
Radius of gyration is the root mean square distance
Of particles from axis formula . Therefore, the radius of the
gyration Of a body about a given axis may also be defined
As the root mean square distance of the various particles of
the body from the axis of the rotation .It is denoted by Rg.

10. ROTATIONAL ENERGY
Rotational energy or angular kinetic energy is kinetic energy
due to the rotation of an object and is the part of its total kinetic
energy . The instantaneous power of an angular accelerating body
is the torque times the angular velocity.

12. THANK YOU