# Im making a flywheel and need help with the math

1. Nov 1, 2012

### wheelslave1

First off thanks in advance for any help given here.

Hope you dont mind bullet points. Makes it easy for me.

Im building a type of flywheel that consist of:

1) A single rod 2 ft across. Axel in the middle.

2) A 2 lb weight on both ends of the arm.

3) Rod weight 1 lb.

4) There will be a constaint 20 rpms applied to the flywheel at the 1 in axel.

5) A speed change from 20 rpms to 80 rpms (engaged gearing system) will occure for 1/2 rpm.

The question is:

How many foot pounds of force is needed to make the change from 20 rpms to 80 rpms?
As a side note all force is applied to the 1 in axel.

2. Nov 1, 2012

### Simon Bridge

force is rate of change of momentum ... so it depends how fast you want to make the change.
Rotationally - this will be an applied torque:
$\tau=dL/dt = I\alpha$.

You are probably better to do this in terms of energy, and ask how much work you need.
This will mean working out the moment of inertia for your flywheel.
$W=\tau \theta$

The, from knowing how fast you want to make the change, you can work out the required torque.
If you know where the force is to be applied, you can work that out by:
$\vec{\tau}=\vec{r}\times \vec{F}$

3. Nov 2, 2012

### wheelslave1

Simon,

The change will be instant. I understand most of your answer but being self taught has me at a disadvantage. So, being that the change is a jump from 20 rpms to 80 rpms what is the answer?

4. Nov 2, 2012

### cjl

If the change is instant, the required torque is infinite, which is clearly not possible. There has to be a period of acceleration - you cannot instantaneously change the angular velocity.

5. Nov 2, 2012

### wheelslave1

Cil,

The constaint applied rpm is 20. A 4:1 gearbox changes the rpm to 80. Im just looking for the simplest answer. The project is a form of art that will be viewed by a large number of people. The handmade gears need to be able to handle the load without breaking.

The greatest amount of force will be at the time of rpm change.

6. Nov 2, 2012

### Simon Bridge

depends on your teacher :) You should never teach or learn in isolation - odd ideas can get reinforced. As long as you are talking about your ideas, and using critical inquiry, you should be fine.
The answer is that it will take an infinite amount of energy. It is impossible.
The shorter the time for the shift the more energy and the bigger the force that is needed.

You don't "apply" a speed. You apply a torque. There will be some losses (i.e. friction) in the system creating a counter-torque. When the applied torque is the same as the losses, the wheel turns at a constant speed (at a set rpm).

That is a fairly complex situation - presumably something is applying a torque to the wheel - then you want to quickly change gears. Will the something also be able to provide the additional torque and energy to produce the acceleration to the new rpm or will it just jam, or go at a slower speed?

Anyway, I think you'll need to do this in terms of "specific impulse" (you'll have to look it up): τΔt = ΔL = IΔω for the rotational case ... you'll need to look up the term and also look carefully at how the gearbox changes gears. The best bet is just to over-engineer it.

I also think you need to add some classes in Newtonian mechanics to your self-education ... newtons laws of motion, and how the apply to rotation. Then you can deal with how gears affect things.

7. Nov 2, 2012

### cjl

Wait - so you have one axle turning at 20 rpm, and a different axle turning at 80 rpm? I think we've all been assuming that you're trying to accelerate an axle from 20 to 80 rpm, which is a completely different scenario. If you just have a simple gearbox, the torque on the 20rpm shaft will be 4 times the torque on the 80rpm shaft, ignoring any losses in the system

8. Nov 3, 2012

### wheelslave1

Cil,

"Wait - so you have one axle turning at 20 rpm, and a different axle turning at 80 rpm?"

Yes and no. I`ll explain a little more in detail. There is only one axle that acts like two. The gearbox is configured to, if held in place, turn the rod at 80 rpms for 1/2 rotation. All while the axle remains at a constant 20 rpms.

Now if what I believe you are saying is correct. A 4:1 ratio will be expected.
The wieghts 2lb each and a rod at 1lb would equal 20ft lbs max once the gearbox is held in place. The 20ft lbs of force will act like flash collision on the gears and drop off to less than 1ft lb.

There is a 6in gear locked in place on the 1in axle. The gearbox system runs like this: 6in gear (locked to axle) to 3in gear locked to and across from a 6in gear to a 3in gear connected to the 1in axle but not locked to it.

Last edited: Nov 3, 2012
9. Nov 3, 2012

### wheelslave1

Cil,
Am I correct in my thinking here? The motor will connect to a 40in wheel. So, can you tell how many ft lbs will be needed at 40in to run this balanced system.

10. Nov 3, 2012

### cjl

I can't envision what you're trying to describe here - could you draw a diagram or something like that?

11. Nov 4, 2012

### wheelslave1

Cil,

Thank for your help. Its rare to find someone willing to help someone in need. Would you mind going to private mail?

12. Nov 4, 2012

### Simon Bridge

... and deprive others of this assistance. I hope cjl does not agree to that!

The price of free/gratis assistance is usually public exposure.
It's probably in the rules somewhere...

13. Nov 4, 2012

### Staff: Mentor

I don't think it is in the rules, but it is clearly a matter of forum etiquette. That's kinda the whole point of a discussion forum.

However, I'm guessing we have some sort of perpetual motion scheme here...

14. Nov 4, 2012

### Simon Bridge

On that note ... interested students should visit:
http://www.lhup.edu/~dsimanek/museum/unwork.htm
... paying special attention to the "physics gallery" and the "reading room".
OP will find this will fill in the gaps evident in his self-education as well as help him talk to scientists.

15. Nov 5, 2012

### cjl

I would really prefer to keep it on the public forum, partially for the reasons already mentioned, and partially because I will be the first to admit that there are a number of posters here with far more physics knowledge than myself, and if I say something misleading, I would hate to have it go unchallenged by those people.

16. Nov 5, 2012

### Simon Bridge

Even the most learned of our colleagues can slip up sometimes ... or find themselves repeating a sloppy explanation. That feedback is part of why we do this after all.

@wheelslave1
Sometimes, someone new to science will feel embarrassed or "stupid" when they are unsure of their reasoning. Nobody likes to be wrong in public, and scientists can appear unfriendly or insensitive. We understand and we've all been there. So no judgement is implied in corrections, criticisms or feedback.

Anyone prepared to post here is treated equally with the most experienced of us.
Explain away and we'll figure it out together.

17. Nov 6, 2012

### wheelslave1

The dark blue 6in gear is locked to the axle. It runs at 20 rpms.

The light blue 3in gear connects to the dark blue gear. It runs at 40 rpms

The green 6in gear and the light blue 3in gear are locked together. Both run at 40 rpms

The green 6in gear connects to the green 3in gear. The 3in gear (free floating on the axle) runs at 80 rpms.

There is a brown rod mounted to the 3in green gear. It and its and its two weights will spin at 80 rpms.

The white rod, if held in place, starts the 80 rpm cycle. Let the white rod go and it will travel with the main wheel at 20 rpms.

My question is: How many ft lbs of force will be applied to my 3in green gear?

Think of it like this. A 40in wheel is running at 20rpms. The white rod stops causing the brown rod to suddenly spin at 80 rpms.

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18. Nov 6, 2012

### Staff: Mentor

How does the white rod work?

Why?

That looke like it would give an enormous force on all components which change their rotation frequency, probably breaking something. The force depends on the ability of the material to stretch/compress/break.

19. Nov 6, 2012

### CWatters

If I've understood correctly...

With the white lever free to rotate the whole gearbox spins round so the weights go at 20rpm. Then if you slow/stop the white lever the weights spin up to 80 rpm.

Work out how fast you want the weights to spin up.
From that you can work out the torque you need to apply to the weights.
I think the torque on the white lever will be roughly twice (or is it four times that?) that.

20. Nov 6, 2012

### CWatters

PS Those weight going at 80rpm could apply quite a lot of shear force to a finger trapped in the mechanisim.