[DeepestBlue (OP)]

Hold a slipper by its toe end.  throw it into the air so it does a somersault, and catch it by the toe again.  Why does it rotate through 180 degrees at right angles to the axis of spin whilst it undergoes the 360 degrees flip

[Don_1]

I don't know, but have you ever thought of joining the England Cricket team?

[Chemistry4me]

You'll be a really good slip!

----
Maybe second slip because you lost the first one!

[DeepestBlue (OP)]

If you'd seen me play cricket you wouldn't suggest that!!  Silly mid off would be the best position...now pay attention, its a serious question...far more serious than my cricket is anyway!

I was discussing this question with a friend who is a statistics lecturer...he has a colleague who had studied a similar phenomenon in a mathematical model mathematically, and I want to see who else had explored it

[dentstudent]

My guess would be that the original forces acting on the slipper are not even, and so it is likely to spin. This also occurs with books and I know that Dave did a kitchen science on this somewhere. If you flip a book using two hands, the forces tend to be more even, and so the spin dramatically reduces or disappears completely.


All cricket related answers can be found at Wicketpedia.com

[Oortel]

Hey deepest blue since you are a cricketer there is another cricketer in the forum called Yo Mahesh playing IPL for delhi daredevils see the match you will know See his profile....
http://www.thenakedscientists.com/forum/index.php?action=profile;u=10498 [nofollow] and his profile name is Nobel prize 4 me Check out !!!!! [] []

[Chemistry4me]

If you 'newbies' want to talk cricket please do so over there: http://www.thenakedscientists.com/forum/index.php?topic=22016.0

[DeepestBlue (OP)]

Thanks Chem, much as I like Cricket, this isnt cricket.....to get you back on track take a look at this....

http://skepticsplay.blogspot.com/2008/07/home-experiment-spinning-box.html [nofollow]

[dentstudent]

Right - dragging the thread back to topic......

Here is the kitchen science experiment that I referred to earlier.

[syhprum]

I think it happens because of the manner in which you hold the slipper with the fingers beneath and the thumb above somewhat displaced of centre.
This makes it inevitable that you impart some spin.

[Don_1]

I would agree with that dentstudent & syhprum. Applying equal force throughout would be difficult with one hand. Two hands are more likely to give some stability.

[Raghavendra]

And the inclined plane which depends upon the slippery...

[DeepestBlue (OP)]

......Its not cricket and its less to do with holding the slipper wrong, more to do with it is inherently unstable along that axis, its a mathematical solution to quote the reference above.....

"Why does it do this? The reason is because the principal axes with the greatest and smallest moments of inertia are stable. That is, if you spin around these axes, the object will continue to spin in more or less the same direction, even if you didn't spin it in exactly the right way. However, the principal axis with the middle moment of inertia is unstable. If you didn't spin it in exactly the right way, or if air friction pushes the box just a little bit, it will start spinning in all sorts of weird directions.

It's sort of like carrying a handbag. It's easy to hang it over your arm, because that is a stable position. But it's difficult to balance it on your head because that is an unstable position. Stability and instability are important concepts if you want to think like a physicist.

As for why two of the principal axes are stable and the other is not, that is a difficult question with a very mathematical answer. It has to do with three equations called Euler's Equations."

(the equations are inserted here in an image in the reference)

"They are a mathematical consequence of Newton's Laws. I know many of you are looking at that and thinking, "Those equations look so ridiculously complicated!" In this case, you are absolutely right--these equations are ridiculously complicated, even after you learn about differential equations. But even if we don't solve the equations completely, we can still make qualitative predictions. If you have a cubical or spherical object, its rotation will remain constant. If you have a weirdly shaped object like your box, its rotation is stable around the principal axes of smallest and largest moments of inertia, but unstable around the third principal axis."

[Don_1]

Perhaps its just me, but I don't think you can apply Newton's laws to tossing a slipper in the air. I'm sure any competent juggler would be able to throw the slipper up and make it do exactly what they want it to do simply by holding and throwing it in a particular way, just as they can with a skittle, sword, axe and all the other things they perform with, regular or irregular shaped.

[lyner]

Hold a slipper by its toe end.  throw it into the air so it does a somersault, and catch it by the toe again.  Why does it rotate through 180 degrees at right angles to the axis of spin whilst it undergoes the 360 degrees flip

I don't think your '360 degrees of flip' is a meaningful statement. It goes up and then comes down, following a parabolic path.
I think that the reason it comes out right, most of the time is to do with the fact that the lever (your arm) rotates at a rate which sends the slipper to a certain height (i.e. a certain time for trajectory) and that the slipper will be rotating at more or less the same rate once you have let it go. I think the average length of arm gets it near enough to half a revolution by the time it lands and a certain amount of learned skill gets the fine adjustment. It is easy to make it rotate too much, by 'flicking' the wrist.
The axis of rotation will be the same as the axis of rotation of your arm around the shoulder / elbow when throwing.

Knife throwing works in a similar way - if you choose the distance appropriately.

[lyner]

Perhaps its just me, but I don't think you can apply Newton's laws to tossing a slipper in the air. I'm sure any competent juggler would be able to throw the slipper up and make it do exactly what they want it to do simply by holding and throwing it in a particular way, just as they can with a skittle, sword, axe and all the other things they perform with, regular or irregular shaped.

They only apply when there's an R in the month?

[lightarrow]

Hold a slipper by its toe end.  throw it into the air so it does a somersault, and catch it by the toe again.  Why does it rotate through 180 degrees at right angles to the axis of spin whilst it undergoes the 360 degrees flip

I'm not totally sure to have understood what you mean, but if I have, it has to do with the instability of the intermediate inertia axis. Try it with a book: if you throw it up rotating around the axis of the minimum or the axis of the maximum inertia moment, the book doesn't flip; if you make it rotate around the axis of the intermediate inertia moment, it flips before falling down.

[yor_on]

I read your link DB, it was quite interesting. Yours?

[DeepestBlue (OP)]

Lightarrow...exactly right.  Yes it works with a book, the slipper has basically the same properties, except you cant wear a book on your foot

Yor-un Im afraid its not my Arcticle...Architects like us aren't let loose on Euler's equations, we just are trained to ask awkward questions and do stupid things with slippers.  I found it after I posted the question, but I still find the range of (relevant) answers fascinating.

[lyner]

The way you naturally lob a slipper, Indian club or knife will naturally give it rotation about its stable axis of rotation. (The same thing applies to our bodies doing Gymnastics, high diving etc.) We (someone please) could do the actual sums for the ballistics and the transit time and then relate that to the rate of rotation at launch and the amount you could expect the object to rotate in that transit time. I seriously suspect that there is a slight coincidence here and that humans used that (and learned the skill) in many aspects of life as a hunter.
It is quite possible for a Klutz to get it completely wrong and drop the object or do a belly flop!