# Why are there some inconsistencies with the underlying principle of center of gravity and rotational inertia?

COG: The lower the center of gravity, the more stable and object is. Rotational Inertia: The farther the concentration of mass from the defined axis of rotation, the more resistance the object has to movement.

I'm quite confused between these two statements.

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Those aren't really arguments, just statements of fact. Neither are they the definitions of CoG and MoI. What about them is confusing to you? – Colin K Jul 7 '12 at 15:07

The difference is in how you are halting rotation once it starts.

In a car, a low center of gravity means in effect that you have several "arms" extending outwards (the tires) to push against a solid surface every time the car tries to turn over, say in a sharp curve. The more horizontal those arms and the farther they extend outwards, the more stable your vehicle will be. That argues for making your center of gravity lower. There's another twist to it that I'll get into below.

For rotational inertial, think of those long poles that people who walk tightropes usually carry. The farther out those poles extend mass (sometimes they have heavy balls on the ends for example), the greater the rotational inertia, and the more opportunity the walker will have to correct his balance by pushing against that inertia. So in that case, the rotational inertia directly contributes to her ability to remain stable. So there is an example of how, in the absence of a solid surface to push on, rotational inertia can be directly used to keep from tipping over.

The twist I mentioned for vehicles is this: They too can benefit from the rotational inertia strategy, but usually don't bother! The reason is it produces funny-looking vehicles that most folks would not want to be seen driving.

Take two big Harley-Davidson motorcycles, each with the wheel separation of and exactly half the mass each of that same small car. Also, adjust their centers of gravity to be the same in height and front-to-back position as for the small car. Now weld them together using lightweight bars, so that their wheels are the same distance apart left-to-right as in the small car. (I suggest getting permission from the Harley owners first; they can be so picky about such things...)

You now have two vehicles with about the same mass, the same wheel patterns, and the same centers of gravity. The only difference is that in one case most of the mass is located close to the center of gravity (the small car) whereas the in the other case most of the mass is located near either set of wheels (the dual Harley).

In terms of physics, this means that despite have identical masses, wheel positions, and even centers of gravity, the two vehicles are not identical because the dual Harley will have much higher rotational inertial.

So if you put them into an extreme race course designed to test flip-over stability, which vehicle do you think will win?

Yep: The dual Harley, for the same reason that a tight-rope walker is more stable with a pole than without one.

So, bottom line: Both having long "push arms" against a solid surface and having higher rotational inertial can help stabilize a ground vehicle. It's just that the pushing option is so much easier and gives such better-looking vehicles that no one bothers with the additional edge given by concentrating most of the mass over the wheels.

Addendum: The Dual Harley is not any better at roll resistance!

I made an error! The Dual Harley will not do any better on curves than the same-mass vehicle! I'm flagging myself instead of editing out the error, though, since it's kind of an interesting error.

I would have been fine if I had suggested this: Take your vehicle and add two long poles with weights on their ends sticking out both sides (passers beware!). That would have kept the vehicle more stable in the same way as for the tightrope walker. It also would have made turns harder, though, since the same added rotational inertia would resist left-right turns just as well as rolls!

Now in the case of the Dual Harley, there's nothing wrong with my assertion distributing mass towards the wheels gives higher overall rotational inertia -- it does. But there's a more subtle error in why it doesn't provide any additional roll resistance. Anyone see it? I'll leave it open as a problem for someone else for now, and answer it if no one else does.

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