**Scalar Moment of Inertia of A Simple Pendulum**

Moment of inertia can be obtained by considering the movement of a mass at the end of a lightweight rod forming a simple pendulum, which can be studied using Newton's second law of motion. The weight of the mass is a force that accelerates it around the pivot point.

This weight also generates a torque **T** on the pendulum around the pivot point and the acceleration of the mass *a* = *rα* is defined by the angular acceleration `α` of the pendulum, therefore

where `r` is the length of the pendulum. The quantity *I* = *mr*2 is the moment of inertia of the pendulum mass around the pivot point.

In the same way, the kinetic energy of the pendulum mass is defined by its velocity *v* = *rω* using the angular velocity `ω` of the pendulum to yield

The angular momentum of the pendulum mass is given by

This shows that the quantity *I* = *mr*2 plays the same role for rotational movement, as mass does for translational movement. The moment of inertia of an arbitrarily shaped body is the sum of the values `mr`2 for all of the elements of mass in the body.

Read more about this topic: Inertia Tensor

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