how to understand moment of inertia..?

Question

hi..all iam unable to understand the physical meaning of moment of inertia .can anybody plz help me..give clear idea..how it is derived and clear definition (not interms of mass multiplied by distance^2)....thansk to all in advance..

Answer 1

The moment of inertia is the resistance to change in rotational motion analogous to the mass for linear motion. If you think about the definition of energy = 1/2mv^2, using w is angular velocity we want to define I so that 1/2 Iw^2 is also the energy. But v=rw so mv^2=mr^2w^2 so if we define a variable I=mr^2, then we have the desired result, the energy of an object rotating at a angular velocity w will be 1/2 Iw^2. You can do calculations with out using I but it is more tedious

Answer 2

Say you are driving down the road and you hit the break and you feel your body move forward towards the wheel. As we all know it is actualy a backwards force and your body is just trying to stay in the same position. Basicaly the moment of inertia corresponds to newtons law "A object at rest will stay at rest or a object in motion will stay in motion unless a outside force interfere`s" The moment of intertia is when the outside force interferes and the body in question wants to stay in its original place.