Physics of Top-Heavy Objects: Easier to Tip Than Low-Mass Objects

[hotcommodity]

So I was laying in bed last night, and I was thinking about why a top-heavy object is easier to tip than an object with its center of mass lower to the ground. I couldn't come up with the main physics concept that would explain this behavior.

Take a truck banking a turn for instance. If you think of its wheels as a pivot, and consider its center of mass to be at the top of the truck, you could consider the potential for the truck to accelerate angularly about its tires (the pivot). But the further the center of mass is from the pivot, the harder it becomes to accelerate the truck about its pivot, that is, the harder it becomes to apply a torque to it as its rotational inertia increases. Am I thinking about the rotation of the object improperly, or should another concept be applied to explain this behavior?

 

[mgb_phys]

An object overbalnaces when it's centre of mass goes outside the base.
If the centre of mass is lower down you have to move it through a greater angle to move it a certain horizontal distance from the start. If it is higher up you have a smaller angle.

 

[hotcommodity]

Thanks for the reply. That makes sense, but what exactly constitutes the "base" ? Would it be the width of the object in question?

Edit: AH I think I've got it. If you consider the normal force and weight force acting on the truck, they usually act along the same line of action. Once the weight force starts acting along a different line of action, a couple will form, causing rotation. Is this sound reasoning?

 

[russ_watters]

I think you pretty much have it, but let me explain another way anyway:

The base is what is contacting with the ground. You can calculate stability easily enough by drawing a diagram. The angle between the edge of the base and the COG produces a net force either toward or away from vertical, either stabilizing or destabilizing it.