10/07/2025
Biomechanics Terminology and Concepts: Rotational Equilibrium
It is often helpful to review basic physics terminology and concepts so that a better understanding of foot and lower extremity biomechanics may be obtained by the podiatry student and resident, practicing podiatrist and foot-health specialist. In this post, I want to review the very important physics concept of rotational equilibrium.
When a force acts across an axis of rotation, it creates a "rotational force" or "torque" or "moment of force" or, more simply, "moment". Within the field of biomechanics, the term being used for a rotational force is "moment" which is term I will use in the subsequent discussion.
To calculate the magnitude of moment being created across an axis of rotation, both the magnitude of applied force acting perpendicular to the axis of rotation must be known and the distance from the point of application of that force to the axis of rotation must also be known. This distance from the point of application of force to the axis of rotation is known, in biomechanics, as the "moment arm" or, in lay terms, the "lever arm" of that applied force. Then, moment (M) is equal to the perpendicular force (F) times the moment arm (L) or M= F x L.
Within our bodies, moments can create both motion and stability within our joints of the foot and lower extremity. Increasing moments will tend to cause motion in the direction of the moment. For example, an increase in ankle joint dorsiflexion moment will tend to cause ankle joint dorsiflexion motion and an increase in ankle joint plantarflexion moment will tend to cause ankle joint plantarflexion motion.
One of the most important physics and biomechanics concepts in understanding how joint motion and joint stability are produced within the human body is the concept of "rotational equilibrium". What does the concept of rotational equilibrium mean? Rotational equilibrium simply means that the moments acting in one direction across an axis of rotation are exactly counterbalanced by moments acting in the opposite direction across that axis of rotation. For example, in the case of the subtalar joint (STJ), rotational equilibrium will only occur when the STJ pronation moments are exactly equal in magnitude to the STJ supination moments.
I first applied the concept of rotational equilibrium across the STJ axis within the medical literature in my paper from 36 years ago (Kirby KA: Rotational equilibrium across the subtalar joint axis. JAPMA, 79: 1-14, 1989). Then 12 years later, I combined the concept of STJ rotational equilibrium with STJ axis spatial location to better explain the kinetics of the STJ (Kirby KA: Subtalar joint axis location and rotational equilibrium theory of foot function. JAPMA, 91:465-488, 2001).
In my drawing below, the children's playground toy of a see-saw is used to better illustrate the concept of rotational equilibrium. On the left side of the see-saw board, a weight of 200N is acting at a perpindicular distance of 2.0 m (2.0 m moment arm) from the axis of rotation of the see-saw which, in turn, produces a 400 Nm counter-clockwise moment across the see-saw axis. On the right side of the see-saw board, a weight of 100N is acting at a perpendicular distance of 4.0 m (4.0 m moment arm) from the axis of rotation of the see-saw which, in turn, produces a 400 Nm clockwise moment across the see-saw axis.
In this illustration, the see-saw is balanced, and not moving, positioned in a horizontal position. How can the see-saw board be balanced, not be rotating and be stable even though the forces acting on either side of the see-saw board across it's axis of rotation are unequal? This is because the different lengths of moment arms for each weight creates exactly equal counter-clockwise and clockwise moments. In other words, the see-saw only will only balance in a horizontal position when rotational equilibrium is established across it's axis of rotation and the counter-clockwise moments and clockwise moments are exactly equal in magnitude.
Rotational equilibrium also means that there is no net acceleration across the axis of rotation and/or there is a constant rotational velocity. Rotational velocity is more commonly known as angular velocity in physics and biomechanics. Therefore, when a joint is seen to be stable, and not moving, since it's angular velocity is equal to 0, then we know that rotational equilibrium is present in that joint.
For example, if you are standing in a stable positionon both feet, and your ankle joint is not dorsiflexing or plantarflexing, then your ankle joint's angular velocity is equal to 0. But more importantly, because we now understand the physics concept of rotational equilibrium, you will now be able to very confidently state that your ankle joint must be in rotational equilibrium and all the ankle dorsiflexion moments must exactly equal all the ankle plantarflexion moments at that instant in time.
Rotational equilibrium can also exist if the joint is rotating at a constant angular velocity. This physics fact is derived from Newton's First Law of Motion which states that an object at rest stays at rest, and an object in motion stays in motion with the same velocity, unless acted upon by a net external force. For example, if the elbow joint is flexing at a constant 5 degrees/second then it also will be said to be rotational equilibrium since no net elbow flexion angular acceleration is acting at the joint.
Rotational equilibrium in the see-saw illustration below is due to the static nature of the see-saw, meaning it is balanced in a horizontal position, with an angular velocity and angular acceleration equal to 0. We can also say that the see-saw is stable or has been stabilized due its rotational equilibrium.
If, however, additional weight is added either to the left or right side of the see-saw, then the see-saw will undergo angular acceleration in the direction of rotation of the larger applied moment. Understanding how joint motion is produced from a joint position of static rotational equilibrium (i.e. static equilibrium) will be discussed in the second part of my series on rotational equilibrium.
