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 moment, inertia, simple and/or pendulum:
“Punk to me was a form of free speech. It was a moment when suddenly all kinds of strange voices that no reasonable person could ever have expected to hear in public were being heard all over the place.”
—Greil Marcus (b. 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)
“If when a businessman speaks of minority employment, or air pollution, or poverty, he speaks in the language of a certified public accountant analyzing a corporate balance sheet, who is to know that he understands the human problems behind the statistical ones? If the businessman would stop talking like a computer printout or a page from the corporate annual report, other people would stop thinking he had a cash register for a heart. It is as simple as that—but that isn’t simple.”
—Louis B. Lundborg (1906–1981)
“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–?)