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How Long Can You Balance a Pencil?

Balancing a pencil or any other top heavy object on its tip is quiet precarious task

It’s easy to see why top heavy objects are unstable

They just…Wanna fall down

Any little nudge will put it off balance

with gravity happy to pull its center of mass even more off balance and the more off balance it is, the more gravity pulls until…

Physicist call this kind of tipping an Inverted pendulum, becouse it´s kind of like upside down pendulum.

And careful mathematical analysis of inverted pendulums will tell you the obvious:

They’re really unstable. In fact, these equations predict that if a perfectly balanced pencil with a perfectly sharp tip

were to get nudged off balance by just 1/10000th of the width of an atom,

it would take only three seconds to fall over.

There are indeed acrobats who can balance poles with other acrobats on top,

and robots that can balance and catch and throw upright sticks,

and people who make seemingly impossible artistic rock stacks.

But in all these cases, keeping the objects balanced either requires an active stabilization effort,

or else carefully taking advantage of the fact that the balancing point isn’t actually a point.

So the question is this: can you balance a pencil sharpened to a perfect single atom wide tip

on its tip, without active stabilization?

Well, to start, you’d better get rid of all the air bumping off the sides of the pencil,

since the kinetic energy of a typical oxygen molecule is enough to destabilize the pencil

Remember: if the pencil gets off-centered by even 1/10000th the width of an atom,

it’ll fall down in under three seconds.

And you’d better cool the pencil and table down as close to absolute 0 as you can,

since the thermal jiggling of their atoms when they’re hotter will similarly jiggle the pencil off balance.

But even then, matter at very small scales has a spread-out, wave-like nature

which means you can’t have both the pencil perfectly upright

and not moving at the same time.

And while this quantum effect is never a real life inhibitor of precarious pencil balancing,

it means you never even COULD succeed.

However, it’s still fun to see how long you can keep a pencil balanced on your fingertip.

The shorter the pencil, the harder it is.

My best time for a standard 19 cm pencil was 1,3 seconds.

Think you can beat it?

This minutephysics video was brought to you by Audible.com,

one of the leading providers of online audiobooks across all types of media

including fiction, non-fiction, and periodicals.

I’d like to recommend The Tipping Point by Malcolm Gladwell this week.

It’s a book about exponential increases in spreads, uh, trends, social trends epidemics, that sort of thing.

And, uh, it’s – the mathematic is somewhat related to the mathematics of

balancing an object on its… tip, so, anyway, The Tipping Point, by Malcolm Gladwell.
Audible.com赞助了一分钟物理 没有它们我们就做不到这些
Audible.com supports minutephysics and without them, we wouldn’t be able to do what we do, so…

Thank you to Audible, and, uh, head to audible.com/minutephysics to get your free audiobook.