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.
 Identify each cylinder to model.
 For each cylinder, measure its inner and outer radius and length in
inches, entering them in the worksheet table below.
 For each cylinder, compute its volume, Vi = 3.141592L(R2r2),
entering it in the worksheet table.
 Add all of the cylinder volumes together and write the total, V, in
the table at the end of the "Volume" column.
 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.
 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.
 For each cylinder, compute the value of Ii/mi = (R2+r2)/2, entering
it in the worksheet table.
 For each cylinder, multiply Ii/mi by %mi to get Ii/m, entering it in
the worksheet table.
 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.
 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).
Grand Prix Racing  
The Science of Fast Pinewood Cars 
Copyright © 1997, 2004 by Michael Lastufka, All rights reserved worldwide. 