Angular Dynamics: Solving 2-Wheel Problem w/ Initial Resting Wheel

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The discussion focuses on solving a physics problem involving two wheels on a shaft, where one wheel is initially rotating and the other starts at rest. The key points include the need to apply conservation of angular momentum to find the new angular speed after coupling the two wheels. The second wheel, having twice the rotational inertia of the first, affects the overall system's inertia and angular speed. The correct equation to use is (I_A + I_B)ω_new = I_Aω_old, emphasizing the importance of understanding the initial conditions. The conversation concludes with clarification on the approach to calculating the loss of rotational kinetic energy.
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I need help starting this problem. How does that fact that the second wheel starting at rest, effect the problem.

A wheel is rotating freely with an angular speed of 800 rev/min on a shaft whose rotational inertia is negligible. A second wheel, initially at rest and twice the rotational inertia of the first, is suddenly coupled to the same shaft. We have to find (a) the angular speed of the resultant combination of the shaft and the two wheels; (b) the fraction of the original rotational kinetic energy lost in the process.
 
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angular momentum must be conserved. The 2nd wheel adds to the rotational inertia.
 
Could I say something like this...
I_A\omega_A+I_B\omega_B=(I_A+I_B)\omega
 
No, you must say:
(I_{A}+I_{B})\omega_{new}=I_{A}\omega_{old}
Think about it..
 
Thank you...my mistake. It makes sense now.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
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