**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

### Famous quotes containing the words pendulum, simple, moment and/or inertia:

“During the first World War women in the United States had a chance to try their capacities in wider fields of executive leadership in industry. Must we always wait for war to give us opportunity? And must the *pendulum* always swing back in the busy world of work and workers during times of peace?”

—Mary Barnett Gilson (1877–?)

“No author, without a trial, can conceive of the difficulty of writing a romance about a country where there is no shadow, no antiquity, no mystery, no picturesque and gloomy wrong, nor anything but a commonplace prosperity, in broad and *simple* daylight, as is happily the case with my dear native land.”

—Nathaniel Hawthorne (1804–1864)

“Fashion, by which what is really fantastic becomes for a *moment* the universal.”

—Oscar Wilde (1854–1900)

“What is wrong with priests and popes is that instead of being apostles and saints, they are nothing but empirics who say “I know” instead of “I am learning,” and pray for credulity and *inertia* as wise men pray for scepticism and activity.”

—George Bernard Shaw (1856–1950)