Grand Prix Racing - The Science of Fast Pinewood Cars

# Wheel Moment Of Inertia Worksheet

Here's how to estimate the moment of inertia for your wheels.

## Estimating Moment Of Inertia Of A Wheel

1. Identify each cylinder to model.
2. For each cylinder, measure its inner and outer radius and length in inches, entering them in the worksheet table below.
3. For each cylinder, compute its volume, Vi = 3.141592L(R2-r2), entering it in the worksheet table.
4. Add all of the cylinder volumes together and write the total, V, in the table at the end of the "Volume" column.
5. For each cylinder, compute its percent mass, %mi = Vi/V, entering it in the worksheet table. We assume the wheel is made of a material that is uniformly dense throughout its volume.
6. Add all of the percent masses together and write the total, %m, in the table at the end of the "%Mass" column as a sanity check. The total should be very close to 1.0.
7. For each cylinder, compute the value of Ii/mi = (R2+r2)/2, entering it in the worksheet table.
8. For each cylinder, multiply Ii/mi by %mi to get Ii/m, entering it in the worksheet table.
9. Add all of the Ii/m values together and write the total, I/m, in the table at the end of the "Ii/m" column.
10. Finally, the moment of inertia for the wheel, I, is the wheel total mass, m, times the value I/m calculated in the last step. I = m x I/m.
 Cylinder Radius (in) Width Volume %Mass Ii/Mi Ii/M outer inner (in) (in3) (in2) (in2) 1 ________ ________ ________ ________ ________ ________ ________ 2 ________ ________ ________ ________ ________ ________ ________ 3 ________ ________ ________ ________ ________ ________ ________ 4 ________ ________ ________ ________ ________ ________ ________ 5 ________ ________ ________ ________ ________ ________ ________ 6 ________ ________ ________ ________ ________ ________ ________ 7 ________ ________ ________ ________ ________ ________ ________ 8 ________ ________ ________ ________ ________ ________ ________ Totals v=________ %M=________ I/M=________

Weight(________ oz)/386.088 = Total Mass (_________ ozs2/in).

I/m (________) x Total Mass (________) = Total Wheel Moment of Inertia, I = (________ ozins2).

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