# A spin in a rotation

I was recently casually tosing a fork in my hand so it completed a 360 degree rotation with the handle landing back in my hand. I noticed that everytime I did this, the fork returned to my hand upside down (ie facing downwards). So it took a 720 degree rotation for it to come back in my hand the right way up. I tried this with spoons and my handphone and got a similar result. At first I thought the way in which I was tossing the fork might be causing it to rotate on a plane perpendcular to the plane of which I tossed the object. This may be the case; if not, I was hoping to understand the physical explanation of why an object spins in a perpendiclar plane to the direction of rotation, when it is tossed up. Thanks.

## Answers and Replies

The initial cause-ual conditions of motion account for the eventual effectual conditions of motion.

I do not quite understand what you are asking, a sketch or a re-explanation could help, but keep in mind the above statement. Also think about what determines the direction of spin in a sink of emptying water...

russ_watters
Mentor
It's just a matter of the way you are throwing it. Your hand is angled and you are twisting as you throw it. Put some effort into it and I'm sure you can flip it without twisting it.

Thanks Russ, I thought that might be the reason. Just a follow up question.... If I spun a wheel in space, say a bicycle wheel, would it keep spining in the initial plane that I set it in motion. I noticed, when fixing my bicycle, that when I spun the wheel and held it at the axel, I could feel it trying to twist in my hand. Why is that?

Thanks Russ, I thought that might be the reason. Just a follow up question.... If I spun a wheel in space, say a bicycle wheel, would it keep spining in the initial plane that I set it in motion.
Yes. Provided there is no net external torque the initial angulur momentum will be conserved - in both magnitude and direction.

Meir Achuz
Science Advisor
Homework Helper
Gold Member
I was recently casually tosing a fork in my hand so it completed a 360 degree rotation with the handle landing back in my hand. I noticed that everytime I did this, the fork returned to my hand upside down (ie facing downwards). So it took a 720 degree rotation for it to come back in my hand the right way up. I tried this with spoons and my handphone and got a similar result. At first I thought the way in which I was tossing the fork might be causing it to rotate on a plane perpendcular to the plane of which I tossed the object. This may be the case; if not, I was hoping to understand the physical explanation of why an object spins in a perpendiclar plane to the direction of rotation, when it is tossed up. Thanks.
This effect is explained in most intermediate level Mechanics books.
Using Euler's equations for rotation about principle axes, you can show that the axis of rotation is stable for rotation about the longest and shortest dimension, but unstable for rotation about the intermediate axis. It is demonstrated most clearly with a book. Use a string to keep it from opening. When tossed rotating about its long or shortest axis it
spins without flipping, but acts like your fork if it is spun about the intermediate axis.

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Doc Al
Mentor
Tennis Racket Theorem

This effect is often called the "Tennis Racket Theorem", derived as clem says from Euler's equations.

Thanks Doc Al, I often thought it was just my bad luck that when I dropped a piece of buttered bread it more often that not, landed face down. Now I can blame the laws of physics. I feel much better :)