Calculating Angular Velocity and Energy Loss in a System of Two Rotating Discs

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To find the combined angular velocity (w) of two rotating discs, the conservation of angular momentum is applied, where the initial angular momentum I1w0 equals the final angular momentum (I1 + I2)w. The equation I1w0 = (I1 + I2)w is confirmed as correct for this scenario. To calculate the mechanical energy loss during the process, the formula used is 1/2I1w0^2 - 1/2(I1 + I2)w^2. The discussion confirms that both discs rotate about the same axis, which is essential for these calculations. Understanding these principles allows for accurate determination of angular velocity and energy loss in the system.
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a disc with moment of inertia I1 turns around its axis which passes through its centre with an angular velocity of w0. we attach to it another disc with moment of inertia I2 (at first it doesn't spin), as a result of friction between the discs they achieve a combined angular velocity of w.
i need to find the combined angular velocity, w?
how much mechanical velocity was lost in the process.

basically i think i need to use here conversion of angular momentum, i.e the a.m before is I1w0, my problem is what the angular momentum after we add the second disc, i think it's I2w+I1w am i correct here?
if so then I1w0=(I1+I2)w.
and to calculate the loss of energy we have:
1/2I1w0^2-1/2(I1+I2)w^2, right?
 
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Assuming they rotate about the same axis, yes you are correct.
 
yes they rotate about the same axis.
 
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