Gravity, Weight and Center of Gravity

Stability questions look like judgment calls and are not. There is one geometric test, and once you know it every question of this kind is the same question.

Mass and weight

Mass is how much matter there is, measured in kilograms or slugs, and it does not change with location.

Weight is the force of gravity on that mass, measured in pounds or newtons, and it does change - on the Moon a body weighs about one sixth of its Earth weight while its mass is identical.

The units are the giveaway. Pounds and newtons are forces; kilograms are mass.

Weight = mass x gravitational acceleration, and on Earth that acceleration is about 32 feet per second per second, or 9.8 meters per second per second.

All objects fall at the same rate regardless of mass, ignoring air resistance, because a heavier object has proportionally more gravitational force and proportionally more inertia.

Center of gravity

The center of gravity is the point where an object's weight acts as though it were concentrated.

It does not have to be inside the object. The center of gravity of a ring, a horseshoe or a boomerang is in the empty space at its middle, which is a question.

For a uniform object it is at the geometric center. For anything loaded unevenly it shifts toward the heavy end.

Where a load is placed moves the whole assembly's center of gravity, which is why loading is asked about for vehicles and aircraft.

Stability and tipping

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The rule: drop a vertical line from the center of gravity. If it lands inside the base, the object stands. If it lands outside, it falls.

That is stability in one sentence, and the figure's third panel is the moment it happens.

Two things make an object more stable:

A lower center of gravity. The object must be tilted further before the line escapes the base.

A wider base. There is more base for the line to stay inside.

So low and wide is stable; high and narrow is not. A sports car and a loaded truck differ in exactly these two respects, and so do a stepladder open and a stepladder leaning.

Tilting an object raises its center of gravity, which is why a stable object resists being tipped: the push has to do work lifting the weight before anything falls over. The more it has to be raised, the more stable the object is, which is a more exact way of saying the same thing.

Loading

Adding weight low increases stability. Adding it high decreases stability.

Adding weight off to one side moves the center of gravity that way, which shortens the distance the line has to travel to leave the base on that side.

So a load should be low and centered. A question about how to load a truck, a trailer or a boat wants that answer, and the reason is the geometry rather than convention.

Center of gravity and center of buoyancy together decide a ship's stability, which is why cargo is stowed low and why an empty ship carries ballast.

The forklift

The forklift is the test's favorite center-of-gravity machine. Its heavy rear counterweight keeps the combined center of gravity over the wheelbase when a load sits out on the forks. Raising the load raises the center of gravity, so stability drops - which is why a forklift travels with its load carried low.

What you can skip

Across the 44 questions on this topic in our bank:

• Pendulums never appear on this topic.
• Metric gravity. The 9.8 figure never appears; 32 feet per second squared comes up four times.
• Slugs do not appear here; they belong to the force lesson.

Where people lose points

Confusing mass and weight, or giving weight in kilograms.

Thinking the center of gravity must be inside the object. A ring's is not.

Thinking a heavier object is automatically more stable. Where the weight sits decides it.

Saying a taller object is more stable because it is bigger.

Forgetting that the base's width matters as much as the height of the center of gravity.

Thinking heavier objects fall faster. They do not, absent air resistance.

Work one in under a minute

Two identical cabinets are to be loaded with the same total weight. One is loaded with the heavy items on the top shelf, the other with them on the bottom. Which is more likely to tip, and why?

The one loaded high.

Putting the mass on the top shelf raises the whole cabinet's center of gravity, so a smaller tilt is enough to carry the vertical line past the edge of the base.

The weight is the same in both - what changed is where it sits, and that is what stability depends on.

Where this leads

The tipping rule is the same moment balance as the torque lesson, and stability is what the structures lesson is about at the scale of a frame.