Question

what is the physical significance of moment of inertia ?

Answer 1

⭕️Moment of inertia of a point mass with respect to an axis of rotation is the product of the mass and the square of the distance from the axis!!!!!!!!!!!!!!!!

⭕️Moment of inertia

⇒ I = mr²

⭕️Moment of inertia [MOI] is the rotational of mass in linear motion.

⭕️[MOI] of a rotating body offers the resistance to the rotational motion.

⭕️In this the moment of inertia in rotational motion play the same role as mass in linear motion.

⭕️Example :-

⭕️A person tends to fall in the direction in which a fast moving bus is directed!!!!!!!!!!!!!

⭕️In linear motion:-

⇒ f = ma

⇒ torque= I × Angular acceleration

⇒ I is the moment of inertia....



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Answer 2

Newton’s first law of motion says a body must continue in its state of rest or of uniform motion unless it is compelled by some
external agency called force.

->The inability of a material body to change its state of rest or of uniform motion by itself is called inertia. 

->Inertia is the fundamental property of the matter. 

->For a given force, the greater the mass, the higher will be the opposition for motion, or larger the inertia.

-> In rotational motion also, a body, which is free to rotate about a given axis, opposes any change desired to be produced in its state. 

->The measure of opposition will depend on the mass of the body and the distribution of mass about the axis of rotation. 

->The coefficient of inertia in rotational motion is called the moment of inertia of the body about the given axis.

->The moment of inertia of a body about any axis is equal to the sum of its moment of inertia about a parallel axis through its centre of gravity and the product of the mass of the body and the square of the distance between the two axes.

->The radius of gyration can be defined as the perpendicular distance between the axis of rotation and the point where the whole weight of the body is to be concentrated.
 Also from the equation (2) K2 = I/M (or) K = √I/M

->Moment of Inertia of a body is equal to twice the kinetic energy of a rotating body whose angular velocity is one radian per second.
The unit for moment of inertia is kg m2 and the dimensional formula is ML2.
(Refer to the image above)