# Where does the torque come from?

• B
Here's the question that I mentioned in my introduction:

If anyone can give me the answer, please keep it very simple - I was never any good at physics or higher math.

It's very easy and only requires a claw-hammer to do. Very low tech.

Hold the hammer at the end of the handle with the claw pointing to the right. Now flip it into the air having it do only one 360 degree turn. Catch it and notice where the claw is now. It's pointing to the left. Flip it once more and the claw points to the right. Why? Why does it twist when tossed? I'm not giving it any kind of twist when I toss it.

That's my question, and it's been bothering me for years.

Dale

Related Other Physics Topics News on Phys.org
Astronuc
Staff Emeritus
Hold the hammer at the end of the handle with the claw pointing to the right. Now flip it into the air having it do only one 360 degree turn. Catch it and notice where the claw is now. It's pointing to the left. Flip it once more and the claw points to the right. Why? Why does it twist when tossed? I'm not giving it any kind of twist when I toss it.
The center of mass in the head of the hammer is located some small distance from the axis of the handle, so when the handle is flipped in a vertical arc with the handle sideways, there will be a slight torque on the head with respect to the axis of the handle.

The center of mass in the head of the hammer is located some small distance from the axis of the handle, so when the handle is flipped in a vertical arc with the handle sideways, there will be a slight torque on the head with respect to the axis of the handle.

Thanks for the reply, but it seems to me that I've tried it using a 'T' shaped piece of wood (or something similar) and had the same result. The center of gravity would then be in the center of the cross piece at the end of the longer section.

CWatters
Homework Helper
Gold Member
The human body is not an ideal machine.

True, but I don't think that's the reason.

I just tried this with two separate objects: a back scratcher, and a 12" length of 1 x 2 wood. In both cases, they flipped from one side to the other, like the claw hammer in the original example.

In other words, it seems the hammer does it because anything will do it. People should try this and see what result they get.

A.T.
Hold the hammer at the end of the handle with the claw pointing to the right. Now flip it into the air having it do only one 360 degree turn. Catch it and notice where the claw is now. It's pointing to the left. Flip it once more and the claw points to the right. Why? Why does it twist when tossed? I'm not giving it any kind of twist when I toss it.
https://en.wikipedia.org/wiki/Tennis_racket_theorem

hutchphd, zoobyshoe and Dale
I guess that's the answer, then. Thanks for your help. Wikipedia seem to have all the answers to almost anything provided you know where to look.

Euler's therom is far beyond me, though.

Best,
Paul N.

A.T.
You're welcome.

Euler's therom is far beyond me, though.
The plots based on conservation laws in the videos above are nice, but still quite abstract. Terry Tao offers an more concrete explanation based on the movement of rigidly connected point masses, which might be the basis for a more intuitive visualization:

http://mathoverflow.net/a/82020

Please read my new member introduction, then you'll understand why the explanation is, unfortunately, beyond me.

If anyone wants to know where to find the cracks on a 'Tilt-A-Whirl' carnival ride, I can tell them. I spent 23 years as a Safety & Health inspector for the NYS Dept. of Labor and know how to inspect rides, ski lifts, elevators and a lot of other things. That stuff I understand; physics, no.

CWatters
Homework Helper
Gold Member
The human body is not an ideal machine.
If it was then the axis of rotation would be exactly the same as the object's second principal axis and the effect would not occur.

CWatters
Homework Helper
Gold Member
Please read my new member introduction, then you'll understand why the explanation is, unfortunately, beyond me.
Best (plain English) explanation I can manage is that...

You will have seen that a spinning gyroscope is stable and doesn't fall over. However not all spinning objects are stable. Some are unstable and very small errors in the way you spin the object become exaggerated.

Last edited:
A.T.
You will have seen that a spinning gyroscope is stable and doesn't fall over. However not all spinning objects are stable.
In the case of the gyroscope there is a qualitative explanation based on linear dynamics of point masses:

I wonder if there is something similar for the intermediate axis theorem.

Dr. Courtney
Gold Member
The Tennis Racket Theorem is the right answer.

etotheipi and mpresic3
Spinning objects with three unique moments of inertia are unstable about their intermediate axis. Try spinning a cell phone about all three axes (separately), about the axes with max and min moments, the rotation is stable, but about the intermediate axis the rotation is unstable. It's true that if you were top spin it perfectly about the intermediate principle axis, it would be stable, but this is the same kind of stability as balancing a ball on top of another ball.

The second video posted by A.T. shows a very nice illustration of the torque free rotation of objects with three unique moments of inertia.

But if you are truly asking "why?" I don't know. I studied the topic for over a year and was not able to figure it out. There are lots of solutions; you can evaluate Euler's equations numerically easily and see the instability, you could probably evaluate them analytically too and see the solution. Poinsot created something called the Poinsot construction that is also a really nice qualitative description of the motion (involving polhods and herpolhodes...).

It was a machinist who first showed me the hammer instability; I think the only satisfying answer to me would be to explain the behavior from the point of view of shrinking me down to a very small size (aka ant man) and riding on the hammer and asking myself, what forces do I feel?

If you would like, I can provide references to the sources I read on torque free rotation.

Chris

A.T.
Yeah, I linked that already. It's an explanation using angular dynamics quantities, just like the standard angular momentum vector explanation of a gyro. What I haven't found is a good explanation based on point masses, similar to the satellite analogy in the gyro video above.

Yeah, I linked that already. It's an explanation using angular dynamics quantities, just like the standard angular momentum vector explanation of a gyro. What I haven't found is a good explanation based on point masses, similar to the satellite analogy in the gyro video above.
Have you ever heard of D'Alembert's principle? I was thinking it might be a useful technique to try to understand the rotation about the intermediate axis, but I just have not have had time to do it.

Chris

tensor0910
Gold Member
Did anyone catch that The title of the post "Where does Torque come from?" was posted a "moment" ago?

from what i have read, the torque comes from the centrifugal force acting on the T tip if the tip is displaced from center... this force gets bigger as the displacement from aligned gets larger... until you have a huge momentum that carries the tip all the way to the opposite direction... but i always wonder why it can stay at the extreme for more than a bounce... like, to me, the thing should bounce from side to side, with the instability growing each and every flip/bounce... or maybe if there is drag, then it should decay to one of the other states [ min Momentum or max Momentum??]..and just wondering, if the flip force hits 0 at the apex?

any thoughts

There is no torque. When you write out Euler's equations in this case (force-free), your source terms to the three non-linear coupled differential equations = 0.

etotheipi
It's amazing that the question would seem to have an easy answer, and yet, one professor recently posted (and he attributed Ed Purcell (a prominent physicist who may have said it )), rigid body dynamics, is one of the most difficult subjects for undergraduates in physics to understand. (Not quantum mechanics, not relativity ) This is particularly true of the Tennis Racket Theorem.

A complete treatment of the problem requires Jacobi Elliptic, and Theta functions.

I congratulate the poster for the curiosity over the years of this unusual phenomena. Most observers would overlook it or regard it as unimportant. I understand when putting satellites in orbit, spin rates around an intermediate axis are a real concern.

etotheipi
A.T.
Here is a recent, longer explanation based on energy and angular momentum:

etotheipi
Isn't this the intermediate axis theorem? If so there's a good intuitive explanation here...

A.T.