# Free energy from a yoyo?

1. Nov 8, 2005

### eosphorus

this idea came after an experiment trying to improve the rotation speed of my yoyo:

i thought that increasing the radius of the axle of the yoyo,its thickness,i would increase the rotation speed but it turn out to decrease the rotational speed caused by gravity in the yoyo

the yoyo increasing the radius of the axle decreases the rotational speed

but put it the other way around, halving the radius of the axle you double the rotational speed of it and double the time it takes to fall down the same distance, is like if time become energy

you can half the radius for ever doubling the rotational speed forever and doubling the time it takes to fall the same distance infinitly

take a 1 ton yoyo that falls down 1 meter with an axle thicknes of 1 micrometer but when is recovered it winds in an axle of 10 cm

wouldnt it end up higher than it started?

can anyone explain why the yoyo rotates fastest with the same potential energy energy by decreasing the axle thickness as my experiment showed?

2. Nov 8, 2005

### whozum

Thats not true. If its heavier youre gonna throw it a bit harder, but the speed it falls is not proportional to the size of the yoyo.

The only reason, keeping everything else the same, the yoyo would rotate faster when you decreased the axle thickness (might want to define what that is) is because it has a smaller moment of inertia.

3. Nov 8, 2005

### Staff: Mentor

No, the axle can be assumed to have an insigificant moment of inertia here. The reason is that the smaller the axle is, the more potential energy will be converted to rotational kinetic instead of linear kinetic.

4. Nov 8, 2005

### whozum

We're looking at different definitions of axle thickness then. What's yours?

5. Nov 8, 2005

### eosphorus

if you consider the yoyo like an H the thickness of the axle is the horizontal bar of the H

my point is that if you consider mass as infinitesimal you can half the thickness of the pole forever using a slight potential energy forever

then the rotation speed of the yoyo would tend to infinity

6. Nov 8, 2005

### ZapperZ

Staff Emeritus
Eh? If the mass is "infinitesimal", it's gravitational potential energy is also "infinitesimal", and its resulting rotational energy (if it rotates at all) is also "infinitesimal". So where is this "free energy"?

Zz.

7. Nov 8, 2005

### eosphorus

no the yoyo has a mass of 1 ton whats ininitesimal is the thickness of the axle
,if the H is a yoyo shape the horizontal bar of the H,the vertical bars would be weights of half tons each, consider the altitude 1 meter

8. Nov 8, 2005

### Staff: Mentor

Just what I said: that the axle will be an insignificant fraction of the moment of inertia. Making the moment of inertia significant will obviously make it have an impact here, but it is an unnecessary complication, and is small compared to other considerations. So what I'm saying is: even if the moment of inertia is held constant, the rotation will vary with the axle thickness. I'm also ignoring throwing, since it adds another unnecessary complication.

Let me explain two cases:

The first is a constant moment of inertia, constant/idealized axle thickness. "Constant/idealized axle thickness" is a reference to the fact that in a real yo-yo, the axle itself may be of constant thickness, but since the string wraps around the axle, the lever arm length varies.

If you drop the yo-yo, gravity causes it to undergo constant acceleration, both linearly and rotationally. If the lever arm could be made arbitrarily small, the maximum force on the lever arm would be the weight of the yo-yo (it would then be barely accelerating linearly), and the maximum rotational acceleration would be a function of the torque - which, unfortunately, would also now be very small. So you'd end up with a rotiational kinetic energy roughly equal to, but always below, the potential energy you started with.

A real yo-yo has a variable lever arm/axle thickness, because the string wraps around the axle and increases the effective axle diameter. And this is a good thing, because as the yo-yo nears the end of it's fall, it's linear velocity is converted to angular velocty (somewhat along the lines of what eosphorus was asking), with the goal of reducing the linear velocity to near zero before the string runs out, to absorb as much of that energy as possible. It also helps to better absorb the initial impulse of throwing the yo-yo.

9. Nov 8, 2005

### Staff: Mentor

You need to get your arms around the concept of "moment of inertia". It is the resistance to angular acceleration. Also, similar to what ZZ pointed out, as the thickness of the axle tends to zero, the torque tends to zero, and therefore the angular acceleration tends to zero. The moment of inertia is constant.

Last edited: Nov 8, 2005
10. Nov 8, 2005

### ZapperZ

Staff Emeritus
What is puzzling is the reason why you are going to this extreme. This is no different than the unphysical example you had with your old tether ball. So now you are invoking an unphysical material having such an unbelievable density that it can have an infinitesimal thickness, but weighs 1 ton? Oy vey!

Why are you having so much trouble understanding the moment of inertia concept? You DO know, don't you, that when you change the geometry of the object, that the moment of inertia changes? How about starting THERE?

Zz.

11. Nov 8, 2005

### eosphorus

what confuses me is transformation of linear momentum into rotational momentum

because if i take a 1 meter radius yoyo 1 ton weight with an axle of 1 micrometer the rotational momentum will be double in the case i take an axle of 0.5 micrometers with the same altitude

so i understand that if you try every time with an axle each time half thick than the anterior the rotational speed will double as the linear acceleration caused by gravity halfs

and there always being some arm because theres always an axle the linear speed never reaches 0, it halfs all the time, but as the linear speed halfs the rotational speed doubles and this could go on forever

i think that in the ideal case of a winding axle that halfs the radius with each turn it gets more interesting

12. Nov 8, 2005

### Staff: Mentor

What makes you think that halving the radius of the axle doubles the rotational speed?

13. Nov 8, 2005

### ZapperZ

Staff Emeritus
No where in here have you even mentioned, nor seems to have an inkling, about the concept of moment of inertia. I think most of our suspicions are correct, that for some odd reason, your lessons in mechanics (or your self study) have somehow skipped a crucial aspect in understanding rotational motion.

I strongly suggest that before you come up within anymore of these things, that you put some effort into figuring out what exactly is "moment of inertia", how is such a thing is calculated, and why it is so important in any rotational mechanics.

Zz.

14. Nov 8, 2005

### eosphorus

"What makes you think that halving the radius of the axle doubles the rotational speed?"

i tested it my self, maybe it doesnt double but it certainly increases decreasing the radius of the axle, the problem is you cand decrese the radius infinitily

if the answer of how linear acceleration caused by gravity is transformed into angular momentum as is the case in yoyos were in books i wouldnt be asking it here

15. Nov 8, 2005

### ZapperZ

Staff Emeritus
So you only saw it INCREASE and you automatically assume it doubled? Whoa! No wonder your earlier postings on the tether ball were all screwed up! You trusted your flimsy "observations"!

Oh, and where exactly did you manage to find an axial with "infinitesimal" thickness to do this "experiment"? Or was this something you estimated on your own too?

Zz.

16. Nov 8, 2005

### Danger

I think that what eosphorus (aviator?) is actually referring to is the 'gear ratio'. Of course, a certain length of string unwinding on a small diameter shaft will make it rotate faster than a large diameter one.

17. Nov 8, 2005

### Staff: Mentor

Please reread Russ's description (post #8) of a falling yoyo. Reducing the radius of the axle by half does not double the rotational speed. No matter how thin the axle becomes, the rotational energy will never exceed the initial gravitational potential energy.