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I don't feel so confident in the sign convention on this example, wouldn't a clockwise angular velocity mean negative sign not positive? Why is my answer and the books answer positive, and it seems like it should be negative to insinuate clockwise direction?

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    $\begingroup$ I think you're right. There are multiple uses of non-standard signs in the given solution. Using the non-standard sign convention can still lead to the correct solution, so I wouldn't grade this as "wrong" in student work, but it is sloppy and potentially confusing for published material. $\endgroup$
    – Marc Shelikoff
    Jul 15, 2023 at 10:56

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It's a convention though. But while dealing with magnitudes we can ignore it and consider any one direction of rotation as positive and other as negative. If the magnitude is negative then, then system in rotating opposite to chosen direction and vice versa.

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