A marble in the bottom of a bowl is an example of stable equilibrium. Image credit: “Stable Equilibrium” by Urutseg, via Wikimedia Commons

^[1]

As your arm hangs from your shoulder, it is in stable equilibrium. If your arm is lifted to the side and then let go it will fall back down to the hanging position. The hanging arm is a stable position because the center of gravity of the arm is located below the base of support, in this case the shoulder. When displaced (lifted a bit) the force of gravity acting  on your arm will cause a torque that rotates your arm back down to the hanging position. In such cases, when an object is displaced from the equilibrium position and the resulting net forces (or torques they cause) move the object back toward the equilibrium position then these forces are called restoring forces. The sloth takes advantage of stable equilibrium to save energy that humans spend on staying upright. If the sloth is displaced in any direction, the force of gravity automatically acts as a restoring force and returns the slot to its equilibrium position.

A two-toed sloth hangs from its feet in a stable equilibrium position. Image Credit: Two Toed Sloth by Cliff via Wikimedia Commons

^[2]

Unstable Equilibrium

When a system in equilibrium is displaced and the resulting net force pushes the object even further away from the equilibrium position then it must have been in an unstable equilibrium. Technically, real systems cannot spend time at unstable equilibrium point because the tiniest vibration will cause them to move out of equilibrium not to mention that you could never place them perfectly into position in the first place. Trying to balance a marble on a hill is a good example:

An example of unstable equilibrium is a marble placed on a hill. Image Credit: “Unstable Equilibrium” by Urutseg, via Wikimedia Commons.

^[3]

Metastable Equilibrium

Some structures that are in stable equilibriumand can be displaced relatively far before they are no longer in equilibrium. Other structures structures that only require a small displacement to move out of equilibrium (like toddlers). We often call these systems stable and unstable, but this can be misleading because any standing structure is somewhat stable and a truly unstable structure would not stand still for any time. These structures that are in a stable region, but could be pushed passed a tipping point are known to be in a metastable equilibrium.

The marble is in meta-stable equilibrium as long as it doesn’t move outside the dip in the center. The peak at edge of the dip is analogous to the tipping point for a structure; beyond this point the marble will not move back toward the equilibrium position. Image credit: “Meta-stable Equilibrium” by Urutseg via Wikimedia Commons

^[4]

Keeping your balance requires that you stay with the the stable region of a metastable equilibrium.  For example, we expect that most people would say the person balancing on their head in the following image is unstable, but that wouldn’t be quite accurate. Actually, the person is actively adjusting the shape of their body to shift their center of gravityto remain within the stable region of a metastable equilibrium, though it is a narrow one.

A person in a barely-stable equilibrium. Image Credit: Usien via Wikimedia Commons.

^[5]

Exercises

An interactive or media element has been excluded from this version of the text. You can view it online here:
https://openoregon.pressbooks.pub/bodyphysics/?p=1174

---

1. "Stable Equilibrium" by Urutseg, Wikimedia Commons is in the Public Domain, CC0↵
   
2. Two Toed Sloth (Choloepus didactylus) By Cliff   [CC BY 2.0 (https://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons↵
   
3. "Unstable Equilibrium" by Urutseg, Wikimedia Commons is in the Public Domain, CC0↵
   
4. "Meta-stable Equilibrium" by Urutseg, Wikimedia Commons is in the Public Domain, CC0↵
   
5. By Usien [CC BY-SA 3.0 (https://creativecommons.org/licenses/by-sa/3.0)], from Wikimedia Commons ↵