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(I have taken angular displacement positive for counterclockwise.) First definition Angular velocity is positive when the rotation is counterclockwise and negative when it is clockwise. Second definition: Angular velocity is positive when the angular displacement is increasing and negative when the angular displacement is decreasing. Contradiction: According to second definition When angular displacement is decreasing then angular velocity is negative and from first definition angular velocity is positive. These two upper statement are confusing and i think have contradiction between them will any one expert elaborate.

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  • $\begingroup$ Ask yourself, what is bigger $-2$ or $-3$? When going from $-2$ to $-3$ is the change positive or negative? What about when going from $2$ to $3$? I think you are confusing a quantity change with a change in its magnitude. $\endgroup$ Dec 18, 2016 at 8:12

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First of all, ask to yourself

Does nature care how you are examining it ? (In Newtonian Mechanics)

The property of positive and negative only depends on your coordinate system, i.e how you are looking to the system.Similarly, the matter of some quantity is decreasing or increasing also depends on your coordinate axis.Nonetheless, they describe the $\textbf{same}$ thing.

Addition to that, think "decreasing" as increasing in the negative direction.

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The answer is simple. Lay out the angular displacements in a number line. If you are moving from left to right then the velocity is positive. Otherwise it is negative. It is a matter of convention, but the velocity sense has to be the same as the angular sense.

This is such that statements like $\theta_2 = \theta_1 + \omega \Delta t$ make sense algebraically as well as conceptually.

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