Angular speed and revolutions question.

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SUMMARY

The discussion centers on solving a physics problem related to angular speed and revolutions, specifically focusing on question 22. The participant initially attempted to solve the problem by setting the derivative of theta with respect to time (dtheta/dt) to zero, which proved ineffective. The solution requires setting up a definite integral with appropriate limits to determine the time at which the wheel comes to rest, indicating a need for a more structured approach to the problem.

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I've attached the problem as an image. I solved 20 and 21 very easily. For 22, my obvious instinct was to set dtheta/dt to 0, but that's an unsolvable equation. I'm obviously missing something key in solving 22. What is it?
 

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obviously, your obvious instinct is not pointing you to the right direction...

Try to set up a definite integral with appropiate limit... (what is time t equal to when the wheel coming to rest?)
 

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