enter image description here

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 1


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.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service and acknowledge you have read our privacy policy.

Not the answer you're looking for? Browse other questions tagged or ask your own question.