The document discusses parallel axis theorem and radius of gyration. It states that parallel axis theorem can be used to calculate the moment of inertia about any parallel axis through the centroidal axis using a formula that considers the first moment of area and distance between the two axes. Radius of gyration is defined as the root mean square distance of particles from the axis of rotation and represents the equivalent radius of a rotating body. Rotational energy is the kinetic energy due to an object's rotation and is part of its total kinetic energy, calculated as the torque times the angular velocity of a rotating body.

1. SUBMITTED BY
ADITYA VERMA
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