Moment of inertia - parallel and perpendicular axis theorem are the important topics in class 11 physics. This topic is coming under the chapter system of particles and rotational motion. Let us study the moment of inertia and what is its significance. Then we will study the perpendicular axis theorem and parallel axis theorem. So let us start.
We all know In linear motion, when mass increases the inertia will also increase. That is, It is difficult to stop an elephant than a small child. Similarly, the moment of inertia is analogous to mass. But the moment of inertia is defined in rotational motion.
We all know In linear motion, when mass increases the inertia will also increase. That is, It is difficult to stop an elephant than a small child. Similarly, the moment of inertia is analogous to mass. But the moment of inertia is defined in rotational motion.
We can derive the equation for moment of inertia from the kinetic energy equation. Consider a rotating body of mass M. So kinetic energy of i th particle is given by
we know linear velocity is related to angular velocity by the equation
substituting this to the above kinetic energy equation gives
suppose consider the system is rotating with a constant angular velocity. Then the total kinetic energy can be represented as
The extra term coming in the equation defines the moment of inertia. In space of mass in the kinetic energy equation of rectilinear motion, here
comes and that defines the Moment of inertia. So the moment of inertia I is given by
Where
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