Moment of inertia

Moment of inertia


According to Newton's first law, if any body is in a state of rest, then it remains in a state of rest and if it is. If it is moving in a straight line from the same trick, then it moves in the straight line from the same trick, unless it has to be replaced with some exterior forces and it should not change in the present state. These properties of the body that they oppose their state-change are called inertia (inertia).

Similarly, when a body rotates the back of an axis, then it has its tendency to resist its state-change. This quality of the body due to which it opposes the change in the rotation of an axis: the rotation of the body - the back of the axis: the inertia - the horizontal '. It's often To display. Rotation of any particle of the body - the surface of the axis: Inertia - the mass of the particle that is incomplete and its rotation - equals the product of the square of distance from the axis.


. Assuming M is a strong body of mass. Its vertical axis passing through its point of zero is to find the inertia - the horizontal. For this, the body is made up of several small particles. If the mass of these particles is M1, M2, M3,. . . . And rotate them - away from the axis R1, R2, R3, respectively. . . . . If so, the inertia of the particles - phonera na11, nepr:. . . . . Will be.

Therefore rotation of the whole body - the balance of the axis: the inertia - horizontal (i) the inertia of all particles - will be equal to the sum of the halves

           
                

Or
Here ! (Sigma) means - the sum of all the positions. Thus, the backbone of a given axis is equal to the sum of all the particles of the particles and the sum of the products of the distance groups corresponding to their axis
.
Inertia - In the SI method of acceleration, Molecular  and C. G. S Method is '. Its immense formula is [ML]

From the above, it is clear that any body of the body of an axis depends on the inertia -
 (i) on the mass of the body,
 (i) the position of the axis relative to the body, and
(iii) on the distribution of mass in the body mass relative to the axis


When the position of the rotating axis of the body is changed, the inertia of the body changes - the horizontal. Therefore, its rotation with the inertia of a body - it is necessary to clarify the position of the axis


Rotating - Radius of Gyration:

 If any mass is considered centered on one point, its rotation - the distance per axis so that the distance of the body is multiplied by the mass of the body, rotation of the object - after the axis: . Strength - When the torque is received, this distance is rotating - the body of the body relative to the axis is called 'rotation - radius'

If a body of the mass of the mass is rotated by a rotating axis then the inertia is i

  

Where the rotation radius relative to the rotation axis of k body is
 

Therefore, the rotation of a body is called the rotating radius relative to the rotation axis of the body, the square root of the motion of the inertia and the
mass of the mass of the rotating axis.