IIT JEE , AIEEE Forum - Physics , Mechanics

sharkfishy

what is meant by moment of inertia?

vyomanil

its very simple isme zyada deep jane ki jaroorat nahi hai
lenear motion mein jise hum force kehte hai..circular motion mein use moment of inertia kehte hain..
kyonki circular motion mein jo force lagate hain circular motion mein uska total part na lag k,,, kuchch hi part lagta hai (as u can calculate frm vectors) isiliye usse force na kah ke moment of inertia kahte hai............

djdylan2000

What mass is for linear motion, Moment of Inertia is for rotational motion

drama_queen

Moment of inertia, also called mass moment of inertia or the angular mass, (SI units kg m2, ), is the rotational analog of mass.

That is, it is the inertia of a rigid rotating body with respect to its rotation

vyomanil is rite ....

. For example, consider two discs (A and B) of the same mass. Disc A has a larger radius than disc B. Assuming that there is uniform thickness and mass distribution, it requires more effort to accelerate disc A (change its angular velocity) because its mass is distributed further from its axis of rotation: mass that is further out from that axis must, for a given angular velocity, move more quickly than mass closer in. In this case, disc A has a larger moment of inertia than disc B.

destinationIIT09

rotational analogous of mass

snail

Just like mass, moment of inertia also cannot be defined precisely. It is a fundamental quantity in rotation.

You know mass is felt as a resistance when force is applied. This inertial resistance decides how much the body should get accelerated. So mass can be understood only with the help of force. We say that something is heavy only based on the force it excerts when lifted.

Similarly in rotational dynamics, when torque is applied w.r. to an axis mass will offer resistance. This resistive torque is proportional to the product of mass and square of the distance. So moment of inertia of a body is nothing but sum of all individual particle mass multiplied by their respective distance squares.

I =

m_{i *}r_i²

More specifically this is called mass moment of inertia. In statics there is another variation of this called area moment of inertia.

krishna.gopal

First of all vyomanil's answer is not correct. Torque is analogus to force in rotation and not moment of inertia. That ways snail's answer is perfect. Moment of inertia is analogus to mass. The inertia to rotaional motion of a body depends on its moment of inertia.

tarun_bits

Moment of inertia is the rotational analogue of mass.......like you have mass as the measure of inertia ..you have moment of inertia in rotational motion....

if you calculate the kinetic energy of a rotating body you will get as...

$K=\frac{1}{2} \Sigma m{r}^{2} {\omega}^{2}$

so here m{r}^{2} becomes I ...called as moment of inertia

Orgist

Here,

$I=m{r}^{2}$

I=moment of inertia

m=mass of the body

r=radius of the circular path on which the body is revolving.

karthik2007

Moment of inertia is the resistance shown by a body to rotation

snail

moment of inertia can also be interpreted this way. Suppose a small point body of mass m is rotating around an axis at a distance of r with an angular velocity ' w'. Then the instantaneous linear velocity of the mass is rw.
Its kinetic energy is 1/2mv^2 = 1/2 m (rw)^2

= 1/2 m r^2 w^2

So for getting K.E directly in terms of w new term moment of inertia is introduced as mr^2. Integration of this is MI of the larger bodies.

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