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Hi,
I would like to compute sum of work for 2 objects in rotation, look at image please. The grey disk has a rotationnal velocity of Y rd/s. Red disks turn at X rd/s in the same direction. Red disk don't turn around itself.
X > Y
At time 't' friction is on.
The Work for torque = Torque * angle of rotation ( W=T*Theta )
Theta = 1/2 * a * t² with 'a' the rotationnal acceleration
Second law of Newton : Torque = I * a , with I the inertia
Angle of rotation = 1/2 * T/I * t²
Work of torque = 1/2 * T²/I * t²
Torque to red disks is the same in value than the torque of grey disk.
Work of grey disk = 1/2 * T²/I1 * t² with I1 the inertia of grey disk
Work of red disks = -1/2 * T²/I2 * t² with I2 the inertia of red disks
It seems like that the work lost by red disks (X > Y) is not the same than work won by grey disk IF inertia I1 is different of I2. Friction produce temperature but it's possible to imagine something else where there is no friction and works will be different too. So, for me, works must be the same in value.
Maybe I can't think like that, so could you explain ? If I want to use these formulas how can I do ?
Thank you
I would like to compute sum of work for 2 objects in rotation, look at image please. The grey disk has a rotationnal velocity of Y rd/s. Red disks turn at X rd/s in the same direction. Red disk don't turn around itself.
X > Y
At time 't' friction is on.
The Work for torque = Torque * angle of rotation ( W=T*Theta )
Theta = 1/2 * a * t² with 'a' the rotationnal acceleration
Second law of Newton : Torque = I * a , with I the inertia
Angle of rotation = 1/2 * T/I * t²
Work of torque = 1/2 * T²/I * t²
Torque to red disks is the same in value than the torque of grey disk.
Work of grey disk = 1/2 * T²/I1 * t² with I1 the inertia of grey disk
Work of red disks = -1/2 * T²/I2 * t² with I2 the inertia of red disks
It seems like that the work lost by red disks (X > Y) is not the same than work won by grey disk IF inertia I1 is different of I2. Friction produce temperature but it's possible to imagine something else where there is no friction and works will be different too. So, for me, works must be the same in value.
Maybe I can't think like that, so could you explain ? If I want to use these formulas how can I do ?
Thank you