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## Main Question or Discussion Point

Hi,

I would like to study these two cases:

1/ I turn counterclockwise the ring at w2, this need the energy [tex]\frac{1}{2}mr^2w_2^2[/tex] with m the mass of the ring

2/ I turn the ring with arm clockwise at w1, this need the energy [tex]\frac{1}{2}md^2w_1^2[/tex] with d the length of the arm

3/ I eject small part of ring when point are like green points, I eject all part of the ring, I recover kinetic energy [tex]\frac{1}{4}m((d+r)w_1-rw_2 ) ^2+\frac{1}{4}m((d-r)w_1+rw_2)^2[/tex]

http://imagizer.imageshack.us/v2/800x600q90/673/ZITrPH.png [Broken]

1/ I turn clockwise the ring at w2, this need the energy [tex]\frac{1}{2}mr^2w_2^2[/tex]

2/ I turn the ring with arm clockwise at w1, this need the energy [tex]\frac{1}{2}md^2w_1^2[/tex]

3/ I eject small part of ring when point are like green points, I eject all part of the ring, I recover kinetic energy [tex]\frac{1}{4}m((d+r)w_1+rw_2)^2+\frac{1}{4}m((d-r)w_1-rw_2)^2[/tex]

http://imagizer.imageshack.us/v2/800x600q90/912/lrRetE.png [Broken]

The energy needed for turn the ring around itself and with the arm is the same in case A and case B. In the contrary, the energy recover in case A seems not be the same than in case B.

Kinetic energy of the ring is:

[tex]E_k=\frac{1}{2}mr^2\omega_2^2+\frac{1}{2}md^2\omega_1^2[/tex]

With:

d: the length of the arm

r: radius of ring

m: mass of ring

w1: rotationnal velocity of the arm

w2: rotationnal velocity of the ring around itself

The ring is ejecting more and more when points are like that:

http://imagizer.imageshack.us/v2/800x600q90/909/Jfn8ou.png [Broken]

So, the expression of kinetic energy is false or there a force I forgot ?

I would like to study these two cases:

**Case A**1/ I turn counterclockwise the ring at w2, this need the energy [tex]\frac{1}{2}mr^2w_2^2[/tex] with m the mass of the ring

2/ I turn the ring with arm clockwise at w1, this need the energy [tex]\frac{1}{2}md^2w_1^2[/tex] with d the length of the arm

3/ I eject small part of ring when point are like green points, I eject all part of the ring, I recover kinetic energy [tex]\frac{1}{4}m((d+r)w_1-rw_2 ) ^2+\frac{1}{4}m((d-r)w_1+rw_2)^2[/tex]

http://imagizer.imageshack.us/v2/800x600q90/673/ZITrPH.png [Broken]

**Case B**1/ I turn clockwise the ring at w2, this need the energy [tex]\frac{1}{2}mr^2w_2^2[/tex]

2/ I turn the ring with arm clockwise at w1, this need the energy [tex]\frac{1}{2}md^2w_1^2[/tex]

3/ I eject small part of ring when point are like green points, I eject all part of the ring, I recover kinetic energy [tex]\frac{1}{4}m((d+r)w_1+rw_2)^2+\frac{1}{4}m((d-r)w_1-rw_2)^2[/tex]

http://imagizer.imageshack.us/v2/800x600q90/912/lrRetE.png [Broken]

The energy needed for turn the ring around itself and with the arm is the same in case A and case B. In the contrary, the energy recover in case A seems not be the same than in case B.

Kinetic energy of the ring is:

[tex]E_k=\frac{1}{2}mr^2\omega_2^2+\frac{1}{2}md^2\omega_1^2[/tex]

With:

d: the length of the arm

r: radius of ring

m: mass of ring

w1: rotationnal velocity of the arm

w2: rotationnal velocity of the ring around itself

The ring is ejecting more and more when points are like that:

http://imagizer.imageshack.us/v2/800x600q90/909/Jfn8ou.png [Broken]

So, the expression of kinetic energy is false or there a force I forgot ?

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