This document explores Assertion #2:
Sway is used to control and dampen the effects of the Force of Inertia.
Our goal is to examine this assertion rigorously and explore the physical principles behind sway in swing dances (Waltz, Foxtrot, Quickstep).
Inertia is the resistance of a mass to changes in motion.
This includes:
While inertial forces are not “real” in Newtonian physics (they’re pseudo-forces), they describe the effects of motion on mass within a rotating or accelerating frame.
In ballroom dance, inertial effects appear during:
| Situation | Description | Apparent Force Direction | Dancer's Reaction |
|---|---|---|---|
| Linear Acceleration | Sudden changes in velocity | Opposite direction of change | Engage core and maintain poise |
| Turning (Angular Acceleration) | Body rotates during figure | Outward from turn center (centrifugal) | Apply sway inward to stabilize |
| Rise and Fall | Vertical body elevation | Up/down momentum affects stability | Adjust through ankle/knee/hip |
| Free Leg Swing | Limb mass adds lateral torque | Torque around spine/hip | Adjust spine or ribcage (sway) to compensate |
Sway is a mechanical response to inertia. It:
To prove the assertion, we must demonstrate:
We can simulate this using a simple physical model:
We will continue building on this to formalize sway's role as a stability mechanism in Swing dances.
“Sway is the elegant solution of the human body to a Newtonian inconvenience.” – The Great Philosopher Nandhra
In figures like the Forward and Backward Locks in Quickstep, sway is used to manage linear inertia. As the dancer rises and then "falls" forward, potential energy (PE) is converted to kinetic energy (KE), generating high-speed travel.
Though there is minimal turn, sway appears subtly to:
This form of sway is often subconscious and highly trained, but biomechanically critical to fluid, balanced movement in high-velocity figures.
“We need math to prove why we are right, not just say what someone else was told years ago by someone they can’t remember.” – The Great Philosopher Nandhra
What We're Proving: Sway is a biomechanical response to inertial forces — necessary to preserve balance during motion involving:
Rise/Fall
Acceleration (linear or angular)
Rotational inertia
To do this, we’ll show:
That inertial force shifts the effective CoG outside the BOS (base of support)
That without sway, this leads to instability
That adding a sway angle repositions the CoG back over the foot
That the sway angle correlates with inertial force magnitude (i.e., speed, mass, and angular change)
“We need math to prove why we are right, not just say what someone else was told years ago by someone they can’t remember.”
— The Great Philosopher Nandhra
To mathematically prove that:
Sway is a biomechanical necessity used to counteract inertial forces during turn and/or rise in ballroom dance.
Let:
When the dancer is turning at velocity \(v\), the apparent inertial force felt outward (from the rotating frame) is:
\[ F_c = \frac{mv^2}{r}\]
This acts laterally on the CoM, creating a torque:
\[ \tau_{\text{inertia}} = F_c \cdot h = \frac{mv^2}{r} \cdot h\]
Sway shifts the upper body’s center of mass sideways by:
\[ x = h \cdot \sin(\theta)\]
This shift creates a restoring torque:
\[ \tau_{\text{sway}} = m_b \cdot g \cdot x = m_b \cdot g \cdot h \cdot \sin(\theta)\]
For the dancer to maintain equilibrium:
\[ \tau_{\text{inertia}} = \tau_{\text{sway}}\]
\[ \frac{mv^2}{r} \cdot h = m_b \cdot g \cdot h \cdot \sin(\theta)\]
Cancel \(h\):
\[ \frac{mv^2}{r} = m_b \cdot g \cdot \sin(\theta)\]
Solve for \(\theta\):
\[ \sin(\theta) = \frac{mv^2}{r \cdot m_b \cdot g}\]
\[ \boxed{\theta = \sin^{-1} \left( \frac{mv^2}{r \cdot m_b \cdot g} \right)}\]
This equation proves that sway is not optional — it’s dictated by physics when movement and elevation are involved.
Sway is a biomechanical response to rotational and linear inertial forces.
Its magnitude can be derived from physical first principles.
It is not just styling — it is torque control.