Angular speed and revolutions question.

[shanest]

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?

 

[chanvincent]

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?)