enter image description hereenter image description here

The picture is showing the swinging atwood and a hoop and pulley.

I know the lagrangian for both two, I have no problem with the kinetic energy of both but i couldn't convince myself that for the swinging atwood, the potential energy is : $$V = Mgr - mgr \cos\theta$$ and for the hoop and pulley, the potential energy is : $$V = -Mgr \cos\theta - mgr\theta$$

where $\theta$ is the angle mass $m$ makes with vertical

I'm having the sign problem here. I don't understand why for the atwood we use $+Mgr$ and the hoop we use $-mgr\theta$

When and how do we use the $+$ and $-$ sign?


In the first case we have $Mgr$ because as $r$ increases the potential energy increases for the block of mass $M$. In the second case we have $-mgR\theta$ because when $\theta$ increases the potential energy decreases for the block of mass $m$.

In general you pick the sign so that the potential energy function behaves how it should given the variables it depends on.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

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