Balancing Toy Experiment: Build One That Won't Fall Over

Press a lump of clay firmly into the bottom of half a plastic egg. Knock it over. It sits straight back up. Now build the same thing with the clay stuck to the inside of the top, and it falls over and stays there. Same shell, same clay, same total weight. Only the height of one blob has changed.

This balancing toy experiment is worth doing for the build, and then worth doing again for the measurement: with a tilting board and a ruler you can work out how high the centre of gravity sits inside a box you are not allowed to open.

Key Takeaways

• You will build a self-righting toy, build a deliberately bad version, then measure the centre of gravity height of three loaded boxes.
• The concept is that stability depends on where the mass sits, not how much of it there is.
• Best for ages 7 to 13. The toy suits anyone; the tilt calculation lands around 11.
• The build detail: the clay must go right to the lowest point of the shell, pressed flat.
• The payoff formula is simple. Half the base width divided by the tangent of the toppling angle gives the centre of gravity height.

What You’ll Need

Item	How much	Where to get it	If you don’t have it
Half a plastic egg or ping-pong ball	1	Craft shop, or a chocolate-egg shell	Half a plastic bottle cap, for a smaller version
Modelling clay or plasticine	1 block	Stationery shop	Blu-tack, or a coin bedded in glue
Three small boxes	1 each of matchbox, tea box, cereal box	Kitchen	Any three rigid boxes of different heights
Coins	20 identical	Pocket	Washers, taped in a flat bundle
Sticky tape	1 roll	Drawer	For fixing coin bundles inside the boxes
Flat board, 50 cm	1	Shelf or chopping board	A stiff sheet of plywood
Phone with a level or angle app	1	Pocket	A protractor and a plumb line made from thread and a nut
Ruler	1	Pencil case	A tape measure
Notebook	1	Anywhere	Three trials per box

Time: prep 5 min, building 20 min, measuring 30 min, cleanup 5 min Cost: a block of modelling clay Mess level: low

Do the Experiment

Step 1 — Build the toy that rights itself

Press clay into the inside bottom of the half shell, filling the lowest part and pushing it down hard so there are no gaps. Smooth the top of the clay flat. Set the shell down, tip it over, and let go. It should rock back upright every time, including from almost on its side.

Step 2 — Build the version that fails

Take a second shell and stick the same amount of clay to the inside of the rim instead, as high up as it will go. Set it down and tip it. It falls and stays fallen. Hold the two side by side and ask what is different, because the answer is only one number.

Step 3 — Load three boxes differently

Tape a bundle of ten coins inside the cereal box right at the bottom. Tape ten inside a second identical box right at the top. Leave a third unweighted. Measure the base width of each box and halve it; that half-width is your first number.

Step 4 — Find the toppling angle

Put a box on the board with a strip of tape along the low edge so it cannot slide. Raise one end of the board slowly until the box tips over, and read the angle with the phone app at that instant. Three trials each, taking the median.

Step 5 — Calculate the centre of gravity height

For each box, divide the half-width by the tangent of the toppling angle. That is the height of its centre of gravity above the base. You have just measured something inside a sealed box without opening it.

Step 6 — Plot the relationship

Load one box with the coin bundle at five different heights, finding the toppling angle each time. Plot load height against toppling angle. The curve should fall steadily, and your calculated centre of gravity should rise in step.

What you should see: the bottom-weighted shell rights itself from a tilt of 70 degrees or more, and the top-weighted one gives up almost immediately. For the boxes, a 20 cm tall cereal box 8 cm deep topples at around 22 degrees when empty, near 39 degrees with coins at the bottom, and near 16 degrees with coins at the top. Your calculated centre of gravity heights should come out around 10 cm, 5 cm and 14 cm respectively, which is close enough to where the mass obviously is that the method proves itself.

What’s Actually Going On

An object sitting on a flat base is stable while its centre of gravity stays over that base. Tilt it and the base of support shrinks to the edge it is pivoting on. If the centre of gravity is still inside the footprint, gravity pulls it back down and the object rocks upright. The moment the centre of gravity passes outside the pivot edge, the same gravity keeps turning it over (NASA Glenn on centre of gravity).

That gives you the geometry for free. At the instant of toppling, the line from the centre of gravity straight down passes exactly through the pivot edge. Draw that triangle and the tangent of the tilt angle is the horizontal distance from centre to edge, divided by the vertical height of the centre above the base. So half the base width divided by the tangent of the toppling angle is the centre of gravity height (The Physics Classroom on inclined planes). Nothing about mass appears anywhere in it, which is why the result does not care whether you used coins or lead.

The round-bottomed toy works slightly differently, and the difference is worth knowing. It has no flat base at all; it touches at a single point. For a shell whose bottom is a sphere of radius R, the criterion is whether the loaded toy’s centre of gravity sits below the centre of that sphere. If it does, tipping the toy actually raises the centre of gravity, so gravity has to be fought to keep it over, and it falls back as soon as you let go. If the centre of gravity is above the sphere’s centre, tipping lowers it and the toy keeps going. Clay at the bottom puts the centre of gravity low. Clay at the rim puts it high. The two shells are the two sides of one inequality (HyperPhysics on centre of mass).

One honest caveat for the maths: a plastic egg half is not a true hemisphere, it is closer to half an ellipsoid, so the radius changes as it rocks. The toy still works and the reasoning still holds, but if you want the clean version use half a ping-pong ball.

This ratio of half-width to centre of gravity height has a name in vehicle engineering: the static stability factor. For a car it is half the track width divided by the centre of gravity height, and it is the rough threshold in units of gravity at which the vehicle will roll rather than slide. A low wide sports car has a high factor, a tall van has a low one, and loading a roof rack lowers it further, which is why those two sentences describe the same physics as your cereal box. The same reasoning applies to a crane’s outriggers, a ladder’s feet, and a toddler’s first attempts at standing (NASA Glenn on generalized centre of gravity).

How to Explain It to Your Kid

Ages 5–8: Heavy at the bottom means it stands up

Give them the two shells and let them discover which one keeps standing. Then let them feel the clay inside each. Say the heavy part wants to be at the bottom, so if you put the heavy part at the bottom the toy helps you, and if you put it at the top the toy fights you. Then let them knock the good one over twenty times.

Ages 9–12: There is a tipping angle and you can find it

Introduce the tilting board and the idea that every object has an angle at which it gives up. Have them rank the three boxes by guess before measuring, then measure. Then show the formula as a recipe: half the width, divided by the tangent of the angle, equals the height of the heavy spot. Doing that on a sealed box feels like a trick, which is a good thing.

Ages 13+: Derive it, then use it on something sealed

Set up the toppling condition properly as a torque balance about the pivot edge and derive the tangent relation. Then apply it to something you genuinely do not know, like an unopened tin or a loaded backpack, and compare your answer with an estimate from where you think the mass is. Finish with the static stability factor and work out why a roof load is disproportionately bad.

The question to ask: “If we filled a tall thin bottle a quarter full of water, would its centre of gravity be higher or lower than when it was full?” (Lower. The glass is spread up the whole height but the water is all near the bottom, so a partly filled bottle can be more stable than either an empty or a full one. There is a fill level that minimises it, and finding it is the first item in Take It Further.)

Why Teaching This Early Pays Off

The useful idea here is that you can measure something hidden by measuring how a system behaves. A sealed box will not tell you where its mass is, but it will tell you the angle at which it falls over, and one line of geometry converts one into the other. That is the move behind an enormous amount of real measurement, from weighing planets to scanning luggage, and it is available to an eleven-year-old with a chopping board.

It is also directly practical in a way most physics for children is not. Anchoring a bookcase, loading a roof rack, stacking a dishwasher, choosing a stable travel mug and deciding whether a wobbly stepladder is safe are all the same calculation. A child who has measured a toppling angle will look at a tall narrow thing differently for the rest of their life.

Run it prediction-first. The ranking in Step 4, written down before the board is lifted, is doing the pedagogical work; this is the Predict–Observe–Explain pattern set out by White and Gunstone, and the prediction has to come before the result to count (White & Gunstone, Probing Understanding, 1992). The National Research Council’s framework places using mathematics and constructing explanations among the practices school science is meant to develop, and this activity is both at once (NRC, 2012).

One afternoon will not make an engineer, and claiming otherwise would be silly. If it lands, our companion piece on balancing two forks on a toothpick and our guide to the simple machines in your house go well next.

Before You Start: What Parents Should Know

Best age	7 to 13. Under 7, build the toy and skip the board and the arithmetic
Supervision	Light. An adult should set up the tilting board so it cannot slip off its support
Real hazards	A loaded box falling on fingers or toes, small parts such as coins and clay near toddlers, and a board sliding off a book stack
Don’t	Don’t use glass or anything breakable as a test object, and don’t use heavy weights. Coins are enough, and a tin of beans toppling off a board at 40 degrees is a genuinely sore foot

Keep the test weights light and the board low. All the physics is visible with 20 coins and a 50 cm board at knee height; nothing improves by making it bigger. Modelling clay is non-toxic but not food, and coins near a child under three are a choking risk, so count them away at the end.

When It Doesn’t Work

The box slides down the board instead of tipping. Your board is too slippery, so friction gives up before stability does. Tape a thin strip of card along the low edge as a stop, or lay a sheet of paper under the box for grip. Sliding is a different measurement and will give you nonsense.

The self-righting toy wobbles but does not fully stand up. The clay is not low enough or not pressed flat. Dig it out and repack it, filling the very lowest point of the shell and leaving the clay’s upper surface level rather than domed.

Both shells behave the same. You probably used too little clay, so the shell’s own weight dominates and the position of the blob barely matters. Use a bigger lump, enough that it clearly outweighs the plastic.

Calculated heights come out above the top of the box. Either you read the angle wrong or you used the full base width instead of half of it. The formula needs the distance from the centre line to the pivot edge, which is half the depth of the box in the direction it is tipping.

The angles vary a lot between trials. Lift the board more slowly. A fast lift gives the box a push, and a box that has been nudged tips early. Ten seconds from flat to toppling is about right.

Take It Further With the Balancing Toy Experiment

Find the most stable fill level. Take a tall thin bottle and measure its toppling angle empty, then at one quarter, one half, three quarters and full. Calculate the centre of gravity height each time and plot it against fill. The lowest point is not at zero and not at full, and finding where it is makes a genuinely good investigation.

Measure the static stability factor of toy cars. For three toy vehicles, measure the track width and find the toppling angle on your board, then compute half the track divided by the centre of gravity height. Rank them, then compare your ranking with how easily each one rolls over when you push it sideways on a table. The ranking should match.

Measure something you cannot open. An unopened tin, a loaded lunchbox, a sealed packet of rice. Predict the centre of gravity height from what you know about the contents, measure it with the tilt method, and compare. This is where the technique earns its keep, because there is no other way to find out short of destroying the thing.

What to Watch For Over the Next 3 Months

• Week 4: Your kid comments on something being top-heavy, and uses it correctly rather than as a general insult.
• Month 2: They apply it to a real decision: where to put the heavy books on a shelf, or how to pack a bag so it stands up.
• Month 3: They ask about something that seems to break the rule, usually a motorbike or a unicycle. Both stay up by active steering rather than static stability, which is a good thing to learn is a separate category.

Frequently Asked Questions

Why does weight at the bottom make something stable?

Because stability is about where the centre of gravity is relative to the base, not about how heavy the object is. Low weight means the centre of gravity is low, which means you have to tilt the object much further before that centre passes outside the base and gravity starts helping it fall.

How do I measure the centre of gravity height without opening the box?

Find the angle at which it topples on a tilting board, measure half its base width, and divide the half-width by the tangent of that angle. At the moment of toppling the centre of gravity is directly above the pivot edge, which is what makes the geometry work.

Does the mass of the object matter to the toppling angle?

No, and that surprises people. Mass cancels out of the toppling condition entirely. A heavy box and a light box with their mass distributed the same way tip at the same angle. Only the shape and the distribution matter.

Why does my plastic egg toy not match the formula exactly?

Because the flat-base formula assumes a flat base, and a round-bottomed toy touches at a point with a curvature that changes as it rocks. Use the round-bottom reasoning for the toy and the tangent formula for the boxes, and use half a ping-pong ball if you want the toy to match theory closely.

Is this the same reason cars roll over?

Essentially yes. A vehicle’s rollover threshold is roughly half its track width divided by its centre of gravity height, which is the same ratio you calculated. It is also why loading a roof rack makes a tall vehicle noticeably less stable: you are raising the top number in the only ratio that matters.

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About the author

Ricky Flores is the founder of HiWave Makers and an electrical engineer with 15+ years of experience building consumer technology at Apple, Samsung, and Texas Instruments. He writes about how kids learn to build, think, and create in a tech-saturated world. Read more at hiwavemakers.com.

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Sources

1. NASA Glenn Research Center. “Center of Gravity.” Beginner’s Guide to Aeronautics. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/center-of-gravity/
2. NASA Glenn Research Center. “Generalized Center of Gravity.” Beginner’s Guide to Aeronautics. https://www1.grc.nasa.gov/beginners-guide-to-aeronautics/generalized-center-of-gravity/
3. Nave, R. “Center of Mass.” HyperPhysics, Georgia State University. http://hyperphysics.phy-astr.gsu.edu/hbase/cm.html
4. The Physics Classroom. “Inclined Planes.” https://www.physicsclassroom.com/class/vectors/Lesson-3/Inclined-Planes
5. National Research Council. (2012). A Framework for K-12 Science Education. National Academies Press. https://doi.org/10.17226/13165
6. White, R., & Gunstone, R. (1992). Probing Understanding. Falmer Press. (Source of the Predict–Observe–Explain sequence used in Step 4.)