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In this question I understand what we have to do to solve it and is equate the sum of moments with the moment of inertia. However I am not sure on how the LHS became negative as I see that the angular acceleration follows the same direction as the moment, so positive.

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So why is the LHS negative?

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If im not mistaken the angle is increasing when the door is opening. That is defined as positive angular displacement.

On the other hand if you see the moments that are acting in the door they appear to be directed towards clouding the door.

Thus the -sign in the equation.

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