What Is Torque?

Torque is the rotational equivalent of force — it describes how much a force acting at a distance from a pivot point will cause rotation. In dance, torque appears anytime the body’s center of gravity (COG) shifts away from the center of support (COS) — usually the standing foot.

The Basic Equation for Torque

Torque (τ) is defined as:

τ = r × F

Where:

  • τ is torque (in Newton-meters)
  • r is the lever arm — the distance vector from the pivot point (e.g., the COS) to the point of force application (COG)
  • F is the force vector (usually gravity: F = m × g)
  • × is the vector cross product

Scalar Version (Top-Down Dance Context)

In simplified top-down analysis, we reduce the formula to:

τ = |r| × |F| × sin(θ)

If we assume gravity acts vertically and use only horizontal offset from COS to COG:

τ = (x_cog - x_cos) × (m × g)

Where:

  • x_cog - x_cos is the horizontal distance between the center of gravity and the center of support
  • m × g is the dancer's body weight

This torque attempts to rotate the dancer around the foot. The larger the offset, the greater the tipping force.

Why Opposing Torque Matters

  • If the COG is not directly above the COS, torque is generated.
  • That torque must be countered by muscular effort, foot rotation, or body repositioning.
  • A dancer is stable when torque from the upper body (COG 2) is opposed by torque from the standing leg (COG 1).

This torque equilibrium is why dancers can shape and extend dramatically without falling — the torques cancel or rebalance.

How DanceBot Uses This

DanceBot calculates:

  • Segment-based COG
  • Vector from COS to COG
  • Resulting torque magnitude

It visualizes:

  • Safe balance: COG inside COS → torque minimal
  • Risk zone: COG near tipping edge → torque rising
  • Loss of control: COG outside COS → torque unopposed

Why This Matters in Ballroom

This explains:

  • Why certain shapes “hold” despite being off-center
  • Why some extensions feel secure and others feel like you're tipping
  • How balance is maintained even during rotation

It underpins:

  • Poise and shaping
  • Connection (managing shared torque with a partner)
  • Footwork transitions and suspension moments

Torque is the invisible architecture behind all visible balance.