Science Buddies: "Ask an Expert"

For my experiment, I need to find the efficiency of a Stirling engine. To do this, I need the engine's moment of inertia. Since the propeller isn't a uniform rod, I can't use the formula that I = 1/12 *M * L^2. How would I then find the moment of inertia?

Also, when inputting the mass to find the moment of inertia, do I input just the mass of the propeller or the total mass of the crankshaft mechanism? (In the engine, the piston is attached to a crankshaft that spins a propeller.)

I should mention that I am a freshman. I've heard that calculating moment of inertia involves Calculus, and I don't know calculus.

Here's a picture of the engine I'm using for reference:


Thank you in advance.

The reason this is described as requiring calculus is that ultimately you have to sum all the point elements of a system at their various radii, which is most easily done for a regular shape using calculus.

However, you may better be able to *measure* the moment of inertia. I've never tried doing this, but the measurement method is commonly called a trifilar pendulum. If you google for that you find a number of descriptions of how to use one to measure this. You can do something similar, based on the basic equation relating moment of inertia to torque and angular acceleration, but doing this accurately is tricky, hence the specialized tool.

Do you know where I can get a trifilar pendulum?
I couldn't find any for sale.

Hi stuffandthings,

I would try asking around at colleges and universities that are near you. Another option would be to just use the moment of inertia equation for a uniform rod. It won't be exactly correct, but it may be sufficient depending on the sensitivity of your other measurements.

Thanks again.

My science fair is over (I know my status says Feb. 10, but that was my school science fair. The regional science fair was this Wednesday).

I was using a uniform rod before I even asked this question, and I went with that.