Application of moment of inertia

Application of moment of inertia

Introduction : We have studied  about moment of inertia in previous topic. it is clearly understood that moment of inertia depends on axis of rotation. In this topic we are going to find out moment of inertia of different body about different axis.

Moment of inertia of a Ring about it's center

Fig A

Consider a ring of radius R and mass M rotating about an axis passing through centre C. The axis is perpendicular to the plane of ring. Whole mass of the ring is located at a fixed distance R from axis. Thus from definition of moment of inertia

I = MR²

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Moment of inertia of a Disc  about it's center

Fig B

Consider a Disc of radius R

Fig C . ring element

A disc is collection of ring

From Fig A, consider a disc of mass M made up of number of rings. In fig C, consider a ring element which is  a part of disc whose moment of inertia about natural axis is to be calculated. Mathematically,

│<<<Moment of inertia││Parallel Axis Theorem>>>│

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