---
title: "Potential Energy Curves, Turning Points and Stability"
description: "A plot of potential energy against position tells the whole story of one-dimensional motion: turning points where the curve meets the total energy, and minima that are stable equilibria. The curvature"
canonical: https://lightmysky.com/learn/science/potential-energy-curves-turning-points-and-stability-mt_ZgRbrDaQzh
source: https://lightmysky.com/learn/science/potential-energy-curves-turning-points-and-stability-mt_ZgRbrDaQzh.md
retrieved: 2026-09-12
---

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# Potential Energy Curves, Turning Points and Stability

A plot of potential energy against position tells the whole story of one-dimensional motion: turning points where the curve meets the total energy, and minima that are stable equilibria. The curvature at a minimum sets how fast small oscillations run.

Subject: Science · Area: Energy · Ages 18 to 20
Page: https://lightmysky.com/learn/science/potential-energy-curves-turning-points-and-stability-mt_ZgRbrDaQzh

## Ready when they can

- Marks the turning points and the allowed region on a potential energy curve for a given total energy
- Classifies equilibria as stable or unstable from the shape of the curve
- Predicts the direction of the force at any point from the slope of the curve

## Lesson: Reading motion off an energy hill

Draw potential energy against position, then draw a flat line for the total energy E. Since E splits into motion plus stored energy, motion energy is the gap between the line and the curve. Where the curve sits above the line, motion would need negative energy, so that region is forbidden.

Where the total energy line meets the curve, the motion energy is zero and the body turns around. Those meeting points are the turning points. A ball tossed upward turns at its top height, and the same idea works for any curve.

**Example.** A valley in the curve is a stable resting place: nudge the body and it rolls back. A peak is unstable: nudge it and it rolls away and keeps going. Flat spots with zero slope are the equilibria, minima stable and maxima unstable.

**Tip.** Read the force direction straight off the slope. Force equals minus the slope of the curve, so downhill slopes push forward and uphill slopes push back. Always draw the total energy line first, since everything about allowed motion follows from it.

**Recap.** The total energy line against the potential curve shows where motion can go, turn, and rest.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [Conservative Forces and the Potential Energy Function](https://lightmysky.com/learn/science/conservative-forces-and-the-potential-energy-function-mt__053R9wrQy)

## Opens up

- [Generalised Coordinates and the Lagrangian](https://lightmysky.com/learn/science/generalised-coordinates-and-the-lagrangian-mt_9QPk1zI9jE)
- [Simple Harmonic Motion as a Second-Order Equation](https://lightmysky.com/learn/science/simple-harmonic-motion-as-a-second-order-equation-mt_HHmR-uCvwO)