Inertia Tensor - Scalar Moment of Inertia of A Simple Pendulum

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 = is defined by the angular acceleration α of the pendulum, therefore

where r is the length of the pendulum. The quantity I = mr2 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 = 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 = mr2 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 mr2 for all of the elements of mass in the body.

Read more about this topic:  Inertia Tensor

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

    It’s an old trick now, God knows, but it works every time. At the very moment women start to expand their place in the world, scientific studies deliver compelling reasons for them to stay home.
    Mary Kay Blakely (20th century)

    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)

    Religion is the dream of the human mind. But even in dreams we do not find ourselves in emptiness or in heaven, but on earth, in the realm of reality; we only see real things in the entrancing splendor of imagination and caprice, instead of in the simple daylight of reality and necessity.
    Ludwig Feuerbach (1804–1872)

    The pendulum oscillates between these two terms: Suffering—that opens a window on the real and is the main condition of the artistic experience, and Boredom ... that must be considered as the most tolerable because the most durable of human evils.
    Samuel Beckett (1906–1989)