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

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SUMMARY

The discussion focuses on calculating the combined angular velocity and energy loss in a system of two rotating discs with moments of inertia I1 and I2. The initial disc with angular velocity w0 transfers angular momentum to the second disc upon attachment, resulting in a combined angular velocity w. The relationship is established through the conservation of angular momentum, leading to the equation I1w0 = (I1 + I2)w. The energy loss during this process is calculated using the formula 1/2I1w0^2 - 1/2(I1 + I2)w^2.

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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?
 
Last edited:
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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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