Sum of torque

[EOW]

And this idea with the balls and springs to create a pressure like a fluid under gravity. There is a torque on the red center. Use a law in 1/d^2 for the attraction. For example at 1 meter the pressure is 1 and at 2 meters the pressure is 4 not 2. Better with d^3 and don't start at p=0 at the top of the half disk => the disk in at 6 meter at proof for example.

[EOW]

With the device and with gravity.  :

https://www.youtube.com/watch?v=Pjc4dIf1aWI&feature=youtu.be

I place at the top of the orange disk a small mass [tex]m[/tex] after the device is launched. With an angle of 60°. This mass will move down of [tex] 2R.sin(60°)[/tex] so the energy lost is [tex] 2R.sin(60°)mg[/tex]. With [tex]g[/tex] the gravity. The disk is turning in the arm reference at [tex] -0.5w[/tex] and the arm turns at [tex]w[/tex]. The mean torque on the red arm is [tex] \frac{2}{\pi}Rmg.sin(60°)[/tex] so the erergy is a the torque by the angle of the arm, if the disk rotates of [tex]\pi[/tex] the arm rotates of [tex]2\pi[/tex] so the energy won is [tex]\frac{2}{\pi}Rmg.sin(60°).2.\pi[/tex] it's twice than the energy lost by the mass when it moves down.

[EOW]

There is gravity. A small mass 'm' is put at the point 'A' at top of the disk with the linear velocity V+wRcos(a) with 'w' the angular velocity of the arm, 'a' is the angle from the vertical, 'R' is the radius of the disk.  The mass 'm' is ejected at the point 'B' with the linear velocity V+wRcos(a). 'V' depends of the length of the arm. The mass will move down and lost an energy, the arm accelerates and will win an energy. In the image or in the video, the angle 'a' is at 60°.

The mass 'm' lost the energy 2mgRsin(a), with 'g' the gravity.

The mean torque on the arm is 2/pi*mg*cos(a). Like a=60°, when the disk turn of pi (from the top to the bottom, the disk must turn of pi), the arm turns of 2pi. So the energy win by the arm is 2pi*2/pi*mgR*cos(a)=2mgR

There is a difference of energy of 2mgR(1-sin(a)). And at start the disk don't turn around itself, when the mass 'm' is at the point 'B' the disk turns a little.

[EOW]

I changed the direction of the gravity like that the mass don't lost any energy. The arm receives a torque when it rotates. Gravity is always like I drawn even the arm rotates.

Or I can use 2 springs if F1>F2, the goal is to have F1+F2 (in vector) like the slope of the disk. F1=1.73N and F2=1N for example when a=60°. The arm receives a negative torque that cancel the energy 2RFsin(a). One spring win the energy RF another spring win 1.73*1.73RF+RF=3RF

[EOW]

If I use a spring, the arm will receive a negative torque but the spring will receive a positive torque. But if I turn the arm with 180° not 360° the point A turns around the center C of little less than 180°, it's maybe something like 175° in the example. The difference of the energy come from the fact the arm turns of 180° but not the point A, so the spring will receive a difference.