# Yo-yo rolling on an inclined plane

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.

## 1 Answer

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.