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As shown in the figure, yo-yo is rolling on an inclined plane, and the tension and static friction are pararrel to the inclined plane. To calculate tension $T$, I wrote down 3 equations.

  1. $Mg\sin{\theta}-T-f_s=Ma$

  2. $\tau_{net}=Tr+f_sR=I\alpha$

  3. $a=R\alpha$

However, I got confused because the acceleration $a$ is negative, but the angular acceleration $\alpha$ is positive. I've been thinking about this problem for hours, but I can't think of a way to solve it.

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I believe your $a$ should not be negative, but positive.

Your equation 1 is not set up according to the coordinate axis that is drawn. That axis (the x-axis) is drawn up the incline, whereas the equation is set up according to an axis-direction down the incline.

This is no problem. All terms have a flipped sign, and so everything within this equation still matches.

But then you mention in the text that you want to input a negative $a$. That will not work with the equation set up with a downwards axis-direction. This is the same direction as the acceleration $a$ points, so $a$ must be positive when inserted.

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