Sum of torque

I tested with frequency until 10000000 Hz and the result is the same. I tested at work with Comsol multiphysics and I obtain same result, the energy increase more and more. The difference between Algodoo and Comsol is only 10 % of results. I tested with 2D objects not point object. The energy is constant if I set friction at 0. So maybe friction act on center of gravity on small ball and center of gravity of big ball. These centers of gravity are not the same. Not same radius, so not same torque. One torque give more energy. Especially with 2d object not point, when I look at big circle, friction must slow it but a part of the object move in the direction of the friction (other part no).

Object 1 has its own trajectory, object 2 has its own trajectary. Why it's not possible to forces of friction that sometimes these two forces add energy to the system ? Like I loot the system turn, I see energy increase more in the direction of the linear velocity. There are 2 movements for each object 1 and 2: One linear movement and a rotation. When object move, it moves more in the direction of the linear velocity than in the 180° direction. Friction act with rotationnal velocity not linear, so if object move less in rotation due to the linear velocity, there is lower force so lower energy. Look at trajectory of object 1 and 2, there are not the same :



Another test with spring for add forces :



Now, maybe Comsol and Algodoo have same error because equations in the simulator are not good.

I tested with this case. Positive slope of sum of energy is more stable. The slope is bigger when spring move (rotational velocity decrease but sum of energy increase), file ste3. When spring is blocked by walls the rotational velocity increase without stop, file ste4.

Example when spring move along the big piece.



With 3 frequencies, results are differents but energy increase:



The spring move differently in these 3 frequencies and this chang the energy.


With different frequencies, result change but after 1800 Hz the slope is the same.



This interesting nobody ?

I tested with wm2d, there is a difference of energy too. The center of gravity move too. The file is here :



https://drive.google.com/#folders/0B63Jbse1IMAkaWtDTko3TTVnY0U

Even if precision is increased, the result don't be constant.

I simulated with bigger dimensions, the difference of energy is bigger even forces are in the same range than before.

This give these results:

I don't take in account the friction, but it's an energy lost because Object 2 moves relatively to Object 1. The distance is around 6 m each 9 s (a turn). With a friction at 0.5 and a force at 5 N this energy is not small. It's 6/9*F, with last system friction is at 0.3 N so the energy lost is around 0.2 W. So the sum of energy is more than I have from Algodoo (Algodoo don't take in account energy lost by friction) is bigger.



It's an asymetric forces from friction right/left, loo at image:



Object 2 has a torque and a linear acceleration. Object 1 has only a linear acceleration, not torque. The green force is always in this part of object 1. The torque for Object2 is 0.07 N at left and 0.07 N at right, the rest of forces at right is only for linear acceleration. Like Object1 and 2 don't move a lot about their center of gravity, energy from linear acceleration is small. In the contrary, torque give:

0.07 * 490 * 0.7 = 24 W

Algodoo don't trace centrifugal forces but maybe the source of the solution is here:



I increased mass for look at energy, and the power is 100 W if mass is of 50 kg. I suppress the internal mass that change nothing in the result:

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I study this new case:



It's possible to look at trajectories of the center of gravity:



Parameters and results are:




I think it's only the difference of trajectory that give energy.


For have the power: the image below showing the force : 22 N, take the radius of object2: 0.026 m and angular velocity: 18.4 rd/s this give the power of 22*0.026*18.4 = 10.5 W it's Algodoo's result (Algodoo don't compute friction).



The force is around 22 N for each part of Object2:

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image cxx3 I added an axis on Object1, this don't change the result.

P = 18.5 rd/s * 0.026 m /2 * 88 * cos(60) = 10.5 W

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F1 don't works along its trajectory, like F2 in another case but F1/F2 give a torque for all the system no ?



A possibility for forces and distance that explain the difference of torque:



Look at trajectories:







I added a gif for show where is the torque.

If I take the system like this:



All the system turn at w rd/s, w is constant, can't change (another system recover torque for let w constant). I apply force F1 and F2 from blue object to red object, the red object turn around its center of gravity, I lost energy for turn red object but I have potential energy in red object (1/2Iw²). But blue object has receive a torque in the same time, this torque is recover from external system (not drawn), torque is equal at d2F2p-d1F1p, F1p and F2p are projections. The sum of energy is greater like Algodoo shows.

with :



w1=-w2

if a stator of a motor is fixed to disk1 and the rotor is fixed to disk2 (at axis "y"), when the motor apply its torque on disk2 it apply torque on disk1, the motor need energy to apply torque to disk2 but why it need energy to apply torque to disk1 ? stator and rotor rotate at the same rotational velocity around axis "x".

Maybe I can use this last technic with this example. The idea is to accelerate an inertial mass with a motor. All energy consume by motor is in mass in rotation. The motor accelerate only rear bottom green pole from magenta pole ant front top green pole from another magenta pole, the rotor has always Fr/-Fr and turn around its axis of rotation and the stator has Fs/-Fs and turn around axis X. Radius r2 > r1 so the torque on stator is not the same. Magenta pole is fixed to stator. For the stator it's not more difficult to repuls green pole even it rotates in the contrary direction because the rotor rotates perpendiculary to axis X.








Angular velocity around axis X can be fixed at 10 rd/s for example if external system recover energy in the same time. With a unique rolling element in the center of rotor all forces cancel themselves in the center except 2Fr and 2Fs. Fr increase angular velocity of rotor and Fs give torque for external system.

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With a slope for the motor:

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In this follow image, the motor moves perpendiculary to your screen:




Fr/-Fr => rotates the rotor energy from motor goes to kinetics energy of rotor

Fs/-Fs => rotates the stator around X axis, this give extra energy

Magenta pole are fixed to the stator.

I will cite when I have the solution, sure. Nobody reply, but even I don't find, sometimes I would like to understand where the solution don't works. In all last examples with Algodoo I don't find the error of the software, when 2 objects turn free, this is logical each object apply a torque to another due to friction, the software can't be wrong at this level. The work of a torque is torque by angle of rotation, angle of rotation depends of moment of inertia, if moment of inertia are differents, why work of torques must be the same ? I found example where in one direction the torque destroy energy in another direction it can create. I tested now with Multibody of Comsol for look at the sum of energy, like I'm teacher I can have a trial. But if someone can explain what's happen in physics with maths it's better.

If I take this example, energy increase more than 5%, it's logical there is a problem with sum of energy, no ? The frequency change the delay of mouvement of spring, so the slope of energy change too but the top value of energy don't change really with frequency. Without friction sum of energy is fixed. Someone could help me, or at least Humanity, or your children, to demonstrate it with maths ?










With the basic case of 2 objects (without axis), it's possible to see the angular velocity of Object1 is not the same than Object2, if a torque exist due to the friction I could say the work of this torque can be not equal at 0.



With this example energy increase of 13 % per second, it's not possible it's an error from frequency:



With frequency at 2400 Hz, the result is exactly the same :

I done a mistake, sorry

With one ball with 2 contacts, right and left. The ball is allow to turn around itself without friction. Like inertia of ball I1 is different of global system I2 (that turn too), the sum of energy must be not constant. And this is like Algodoo software is showing from last tests, the sum of energy of the system increase due to the difference of inertia. A positive torque on a system can add energy, in the contrary the negative torque will decrease energy but :

1/ The angle of rotation change with inertia and t², second law of Newton
2/ Work of torque is torque by angle of rotation

Work of T1 is K/I1 and work of T2 is -K/I2 how they can be equal in value ?

If inertia are not the same, angle too for the same time, so like torques are the same (one positive and one negative), the work is not the same I think, no ?

with 2 free objects in rotation, the unique question is:

- a torque can be exist from one object to another ?

if yes, the sum of energy is not constant.

Another example on image with 3 objects and gears for give torque, energy don't goes to temperature (friction is at 0) but goes to rotationnal velocity of red disks. They increase their velocity. Here 4 disks will turn at different velocity and the sum of energy is not constant. Each disk receive a torque and this allow to have different velocities.

http://www.youtube.com/watch?v=GwN8YoHPKH8

With 2 objects in rotation with friction like Algodoo simulation:



Friction create forces F1/F2 and reaction -F1/-F2.

Blue object turn at w2 rd/s and has an inertia of I2.
Blue disk has a red axis of rotation (if it's possible to compute without axis it's better I think).
Yellow object turn at w1 rd/s and has an interia of I1 (around its center of gravity).
Yellow disk is free to move, no axis of rotation.
Yellow disk has a mass M.

Torques works like this:

-F1/F2 : increase energy of blue disk with 1/2*I2*w2²
F1/-F2: change energy like 1/2*M*(w2*d)²+1/2*I1*(w2-w1)²

w2 increase
w1 increase too

but the sum of energy change like:

E = 1/2*I2*w2² + 1/2*M*(w2*d)²+1/2*I1*(w2-w1)² + energy from friction = Eb+Ey1+Ey2+Fr

I1 = Mr² with r the radius of yellow disk, r can be 1/10 od d so Md² >> I1, the only way to lost energy is the third parameter (w2-w1)² but with I1 << Md² the energy lost is loer the energy won. And there is the 1/2*I2*w2² and friction that together energy.

Something's logical, imagine 2 cases:

1/ energy of yellow disk move up, energy of blue disk move down. Ey+Eb+friction = sum of energy

2/ energy of blue disk move up, energy of yellow disk move down. Ey+Eb+friction = sum of energy

friction is the same in two case; This could say Ey=Eb but it's not possible due to the difference of inertia. Yellow disk can change its velocity with w1 but with w2 too, not grey disk, there is an asymetric here.

How it's possible to have a constant ? Someone can help me to start the resolution of this problem ?

Forces and torque can be like that:



Blue disk can turn at w1 around red axis, yellow disk can turn at w2 around itself and at w1 around red axis, with w2<w1. Torque from friction F1/F2 on blue disk do nothing due to forces that pass throught axis. Torque F3/F4 on yellow disk add energy and friction too. The sum of energy is not constant. (Need a spring for have a contact yellow_disk/black_wall, not drawn).



I think this can works with a free red axis, not fixed to Earth, it's important.

If I come back to Algodoo's problem:




1/ The system has an axis of rotation noted Axis1. Like that the energy won by the system is 0, like Algodoo shows (a small error from Algodoo).

2/ Now, cancel the Axis1, the system is free to move in space, it can rotate around its center of gravity noted Axis2, like Algodoo compute. Look at torque T1 and T2. At case 1/ no torque T1 and torque T2 is multiply by d2. Here, T1 exist and increase rotationnal velocity of blue disk. And T2 is lower because d1<d2. So with the same force on yellow disk, it's possible to have more energy if I compare with case 1/

Maybe it's possible to compute this energy ?

Previously I posted on Boards.ie, I asked to physicsforum and french forum. Physicsforum don't want to ear about overunity ideas (or even simulation test), like french forum (in fact it's worst in french forum !), I asked in the same time at stackechange but nobody reply about Algodoo software (I think nobody know it). I had post about main problem with Algodoo and don't have any reply. The only physics forum where I can post is here, and thanks to it ! Algodoo is not a professional software but it is fine enough for compute correctly sum of energy. I tested a lot of cases and I'm sure there is a problem, because even I increase steps or another parameters the sum of energy is not constant. I'm trying to understand where is the logic about the difference of energy from Algodoo and I think this is the fact the system is free to move in space (no axis) like last image shows. One disk turn around itself and win energy. I would like to test with another software but I don't have one. I think the best is to calculate the sum of energy but I don't know how to start the resolution of the problem with no axis, it's very difficult to me. Thanks for your reply ZorbaTehZ, it is so rare

http://physics.stackexchange.com/questions/113145/sum-of-energy-in-a-free-rotation-with-algodoo-sofware

If I take a system like Algodoo simulate I need to take in account the movement of yellow disk to the center. So, friction give a torque on yellow disk F4/-F4 and a force which goes to the center of gravity F3-F4. Blue disk have the same torque in the contrary direction and a force -F3+F4. It's possible to imagine black walls and spring whitout mass. And spring can have the exact value for cancel centrifugal force on yellow disk. Torque F4/-F4 on blue disk works like 2R(F3-F4)w1t but torque of yellow disk works like a part of 2R(F3-F4)w2t because yellow disk move in the same time. Friction is 2FR(w1-w2)-2Fd with d the distance move by disks.