Pencils.com has a challenge for you! Grab a pencil, sharpen the tip to a perfect point, and try to balance it on a surface – your finger, a table, your morning bagel (if you need help achieving a perfect tip, check out this book by David Rees for some tips). In fact, give it a few tries right now, then come back and leave a comment with your best time. Chances are, the number isn’t very high.
Don’t worry! It’s not you – it’s physics. This experiment was inspired by this Minute Physics video aptly titled “How Long Can You Balance a Pencil?” Invariably, the answer is “not very long.”
Top heavy items – like pencils – are very difficult to balance because the slightest acting on them moves their center of gravity off-balance, and the farther off-balance their center of gravity is, the more gravity pulls it off balance until it falls. Physicists refer to this phenomenon as an inverted pendulum, due to its resemblance to an upside-down pendulum. Mathematical analysis of inverted pendulums predicts that if a pencil was perfectly balanced on a perfectly-sharpened tip (meaning a tip 1 atom wide), it would only need to be nudged off balance by one ten-thousandth the width of an atom for it to fall over, and it would only take three seconds for it to fall completely.
So far, balancing a pencil on its tip sounds pretty difficult, but not impossible. However, there are still more factors to consider. First, the kinetic energy of oxygen molecules is enough to destabilize a pencil by the extremely small margin required (one ten-thousandth the width of an atom, if you recall), so you’d have better luck attempting this balancing act in a vacuum. Second, your vacuum must be cooled down to absolute zero, because the warmer an object is the more its atoms move, and the movement of the atoms that comprise the pencil and the surface will be enough to throw it off balance.