Dot Physics

Moment of Inertia Demo

When I was talking about balancing a stick, I mentioned the moment of inertia. Moment of inertia is different than mass, but I like to call it the “rotational mass”. What does mass do? Things with larger mass are more difficult to change their motion (translational motion). A similar thing is true for the “rotational mass”. Things with larger rotational mass are more difficult to change rotational motion. Here is the demo.

Demo for Moment of Inertia from Rhett Allain on Vimeo.

Why do I like this demo? First, it uses ordinary things. I consider juice boxes to be pretty ordinary. Second, I like this because you can give the stick with the larger moment of inertia to the “stronger” person. This way the weaker person wins. If you want to make a super fancy version of this, hide the masses inside the tube so that the two sticks look EYE-dentical.

So, what is moment of inertia? When rotated about a fixed axis, the moment of inertia is a scalar value that depends on how the mass is distributed about the rotation axis. Technically, if you have point masses, then the moment of inertia would be:

i-1715352ac0b73305fb9dce9539587881-moment-def.jpg

This equation says – take each mass. Multiply the mass by the distance to the axis squared and add up all these terms. Let me show this calculation for the two sticks used in the demo (assuming massless sticks).

i-93d52c25ab143ec8d380785a2c26b542-moment-i-pic.jpg

For stick of length L with two masses of mass m, the moment of inertia for the stick with the masses at the end would be:

i-7b71b144676c23ce5c8a0f1237c96032-i1.jpg

And for the second stick, the masses would be much closer to the axis of rotation and thus I would be much smaller. Note that this moment of inertia calculation depends on the location of the axis of rotation. If I rotated them about the end, then I would get a different value.

A final note. I did not derive this moment of inertia expression, but rather just stated it. Maybe later I will come back and give some more info.

Comments

  1. #1 Fran
    May 25, 2009

    A lovely video, with adorable assistants! Thanks for sharing!

  2. #2 Chrissy Vadovszki
    November 22, 2011

    Nice!

  3. #3 zev
    January 19, 2012

    This is a very simple, and that’s why a brilliant explanation. It supports the intuition (the feeling) the understanding. But I asked many people one question and couldn’t get an answer, for why the mass, or the area (if speaking about a section) is multiplied by SQUARE of the distance?
    Please explain.
    Many thanks,
    Zev.

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