# Pendulum Potential energy equation

by cres222
Tags: energy, equation, pendulum, potential
 P: 4 hello every one i have this pendulum: i need to stabilize the pendulum in the inverted position , i need to know the potential energy for the pendulum , i read several articles in each one i have a different equation : $V=mgl_{p}cos\alpha$ $V=-mgl_{p}cos\alpha$ $V=mgl_{p}(1-cos\alpha)$ $V=mgl_{p}(cos\alpha-1)$ Now i'am really confused which equation is the correct one? Please help me
 Mentor P: 40,905 What are you taking as your reference level? (Where PE = 0.) The pivot? The gravitational PE is given by mgΔy, where Δy is measured from your chosen reference level. Using that you should be able to pick the correct formula.
 P: 4 $P.E=0$ at the vertical position ($\alpha=0$ from the vertical line in the picture above), now which formula should i use : $P.E=mgl_{p}(1-cos\alpha)$ or $P.E=mgl_{p}(cos\alpha-1)$
Mentor
P: 40,905

## Pendulum Potential energy equation

 Quote by cres222 $P.E=0$ at the vertical position ($\alpha=0$ from the vertical line in the picture above), now which formula should i use : $P.E=mgl_{p}(1-cos\alpha)$ or $P.E=mgl_{p}(cos\alpha-1)$
Using the vertical position as your reference, Δy will be negative for any nonzero angle. The second of those is the one you want.
 P: 4 so: $\Delta y=$(center of mass level-reference level) not the other way around , am i correct?
Mentor
P: 40,905
 Quote by cres222 so: $\Delta y=$(center of mass level-reference level) not the other way around , am i correct?
Δy is measured from the PE = 0 reference point. Another way to write the PE is mgy, where y is the vertical position of the center of mass and y = 0 is the PE = 0 point.

Since you are choosing the reference level to be where the pendulum is vertical (the angle is zero) and thus the mass is at its highest point, all values for y and thus PE for non-zero angles will be negative since they are below that point.
 P: 4 Now i understand , thank you very much for you kindly help,I'm very appreciative

 Related Discussions Introductory Physics Homework 2 Introductory Physics Homework 4 General Physics 13 Introductory Physics Homework 10 Introductory Physics Homework 13