Center of Gravity as Performance Art

Before you read this blog, head over and watch this video.  Sorry, I tried to embed it, but it is a really long video.  If you’re short on patience, get the general idea, then go to 6:38 and watch to the end.

See you back in a moment.

OK, pretty cool, huh?  Nine times out of ten, when someone sends me a video and asks me the physics behind it, I have to burst their bubble and tell them there’s a trick somewhere and the video isn’t actually “real”.  (There are no actual talking animals as far as I can tell.)  This video came from @88marty88 — and it’s a great demonstration of a concept you hear talked about all the time in racing, which is center of gravity.

Center of gravity (CG) and center of mass (CM) are the same thing in a uniform gravitational field — which is usually the case here on Earth.  I’ll use them interchangeably because I can never remember which one I decided to use.  Or I may even use them simultaneously.

The CG/CM of an object is the point at which an object balances perfectly in all three dimensions.  (This cartoon illustrating the concept is NSFW.)   If you have a meterstick, the meterstick will only balance if you place your pivot at the 50-cm mark.  That is it’s center of gravity in the dimension along the meterstick.

In the still at right (which is from about 9 seconds in), the woman is balancing the feather on her forefinger.  She moves it back and forth and finds the spot where it stays balanced.  This is the CM.

It’s important for her to know where that is because the key to balancing something is that you have to support it over it’s CG.   A system is stable as long at its CG/CM is within its base of support.  Stand up and lean forward.  At some point, your CG/CM will extend past your feet and you will fall on your face.  Hopefully you are paying enough attention that you catch yourself before that happens.  If you were dancing or ice skating and your partner wanted to balance you with one hand, he/she would have to place that hand such that a line running through the support point also goes through your CG/CM.

Once the performer knows the CM/CG of the feather, she is ready to use something  else to balance the feather – in this case, a stick.  Note that the sticks are not sticks you’d find fallen from trees.  They have a  specific shape:   very thick (massive) on one end, tapering to almost nothing on the other end.  If a stick were uniform, it’s CG/CM would be halfway along its length; however, when the mass isn’t distributed uniformly, the CG/CM ends up being closer to the end with more mass.  In the case of the first stick, that’s about 2/3 of the way from the skinny end.    There’s a distinct reason for doing this.

She balances the feather at its CG.  Adding the feather to the stick changes the stick’s CG – not by much, but by the time she’s gotten to the last stick, all that weight will add up.   She doesn’t put the feather all the way at the end of the stick.  It’s about 1/4 of the way from the smaller end.

Next, she feels for the CG/CM of the stick/feather combination  (about 35-40 seconds in is a good place to see) .  When she balances stick 1 on stick 2, the place where stick 2 must support stick one is – you guessed it – the CG/CM of the feather/stick 1 combo.

I’ve tried to show the first four steps below.

You can do something similar at home in one dimension (which is much easier than what the performer does in the video.)  Get a bunch of books.  Hang one a little over the table, so it just balances.  Now put a second book on.  The second book will make the first book fall — BUT if you pull the first book back just a little, both books will be stable.  You can get quite the stack of books going if you’re careful.  I have a short attention span and my colleagues were starting to wonder what the heck I was doing, so I stopped at five.

It works as long as the cumulative center of gravity remains over the desk.  The minute I slide a book out too far, the CG extends past the desk and the whole thing tips.  

You can take some hints from the video if you want to build your own tower of books. She uses shorter sticks at the beginning.  As she adds sticks, she needs larger sticks to keep the CM/CG within the balance point.  If you used small books on bottom (your first “sticks”), you wouldn’t be able to extend as far as if you used larger books on the bottom.

Now books are big, clunky objects, and stacking them this way, you’re really only worrying about the CG along the desktop direction.   (The books aren’t suddenly going to rotate out of the picture!)

The performer in the video is balancing the CG essentially in two dimensions.  The curvature of the materials makes it easier for things to stay put.  That lowers the CG in the up-down direction and low CGs are  pretty much always good when it comes to balance.

It would be interesting to know how heavy the materials she was using are – are they like balsa wood?  Specially made for this very purpose?   If you haven’t watched the end of the video, do so before reading on.

At the very end, she removes the feather and the entire thing tumbles. If you have the largest stack of books you can make and then you nudge the bottom one a few millimeters out, your book stack will collapse two.  That’s how sensitive balance is.

Now… just because it’s basic physics doesn’t mean it’s simple.  The talented acrobats you see in shows like those by Cirque du Soleil, for example, have excellent senses of balance, flexibility and stability.  Understanding the physics doesn’t mean you can turn around and do it.

Plus… I’d probably have to give up coffee for a few days beforehand and we know that’s not going to happen…