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 = 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 = 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 = 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 pendulum, simple, moment and/or inertia:
“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)
“The real drawback to “the simple life” is that it is not simple. If you are living it, you positively can do nothing else. There is not time.”
—Katharine Fullerton Gerould (1879–1944)
“The moment a mere numerical superiority by either states or voters in this country proceeds to ignore the needs and desires of the minority, and for their own selfish purpose or advancement, hamper or oppress that minority, or debar them in any way from equal privileges and equal rights—that moment will mark the failure of our constitutional system.”
—Franklin D. Roosevelt (1882–1945)
“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)