# Moment of Inertia

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I know how to calc it but, what is it? what is the moment of inertia?!? can anyone explain me? please give me a complete explanation:)!! thanks...

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What mass is for translation is the moment of inertia for rotation.

For instance the movement energy for translation is
E = m*v²/2

And the rotation energy is
E = I*omega²/2

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thank you but... for what I use the moment of inertia?what are its utilities?

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You use it the same things for in rotations than you use mass in translation.

For instance imagine a cylinder rolling down a hill. How fast would it be after some time t ? Therefore you need to know the rotation and translation energy and set it equal to the potential energy. To calculate the rotation energy see above, that's where the inertia drops in.

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And for a classic experiment to demonstrate the effect of the 2nd moment, get two phone books (or anything heavy) and sit on a spinning chair. Spin around with the phone books held close to you, then quickly stretch them out and notice the decrease in the angular velocity.

The 2nd moment describes how the distribution of an objects mass affects the objects rotation: when the mass of an object is near the center of mass it is easier (less energy) to rotate than when the mass is spread out.

-Josh

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