Sunday night I was thinking about what to write for Monday morning and settled on the moment of inertia of the tires on a vehicle. If I may say so, it’s a pretty good illustration for an interesting topic. Friction was a possible hitch for my proposed experiment, but I figured that cars were specifically designed to minimize friction, and both cars and tires are pretty heavy. Surely friction can be ignored safely. I wrote up the post in about half an hour and went to bed feeling pleased with myself.
Well. I know from experience that physics Ph.D. holders are not infallible even when talking about their areas of expertise. I’m not a Ph.D, and cars aren’t my area of expertise. The readers of ScienceBlogs are brilliant and widely skilled, and they set to work on correcting me immediately.
Let me give you a few numbers, and I’ll skip writing the equations since we went over them in the last post. A Ford F150 sitting on an incline of 10 degrees will experience a forward gravitational force of about 3400 newtons. The combined mass of all the tires – even assuming they are thin shells in terms of moments of inertia – only adds an additional effective mass of less than 1% of the truck’s total mass. Thus the 3400 newtons is only going to need another 34 newtons or so added to produce the same acceleration that would be produced if there were no rotational inertia in the tires at all.
How does this compare to the force of friction? While you have to take Wikipedia with a grain of salt, the rolling resistance article says 300 newtons is typical for a 1000kg car. My example Ford F150 is twice that heavy, so the friction should be correspondingly greater. Either way it’s a lot more than the 34 newtons worth of effective mass added by the tires.
That will teach me not to run the numbers first. Thank you all for keeping me honest!