Moment of Inertia

An example of rotational motion and moment of inertia.

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Teachable Topics

• Moment of Inertia
• rotational motion
• torque

Theory

Moment of inertia is a physical quantity defined by how the mass of an object is distributed around its axis of rotation.  The axis can be through the object's centre of mass but it is not required that it be so.

The actual definition is:

I = ∑mr²

where I is the moment of inertia, m is the mass, and r is the distance between the mass and the axis of rotation.  You must sum up the contribution of each individual element of mass to get the total I.  

In plainer terms, what this leads to physically is that the inertia involved in rotation motion is not dependent just upon how much mass there is but where it is.  The further out from the centre the mass is, the harder it is to rotate.  You can see this while watching figure skaters, who can speed themselves up or slow down their spinning by moving their arms in or out.  You can see an example of that here:

Procedure

1. Build the moment of inertia demonstrator and connect it to a table clamp.
2. Tie a string and wind it around the spindle multiple times.  Lead the string over another pully and suspend a mass.
3. Release the mass and allow it to fall freely.  The falling mass applies a constant torque to the demo and it will spin up at an angular acceleration that is dependent on its moment of inertia.
4. Change the MoI of the device by changing the position of the masses on the spokes.

Safety

1. Please ensure that there is plenty of free space around the device while it is spinning.
2. Make sure the falling mass will not hit anything important (like you or someone else!).