A living appendix translating physics equations into plain English and dance insights.
Social dancers: skim the plain English.
Serious dancers: peek into the dance analogies.
Competitors: study the equations for performance edges.
Equation:
\[ T = \dfrac{1}{2} m v^2\]
Plain English:
The energy of motion depends on how heavy something is and how fast it’s going.
Dance Analogy:
Your “oomph” traveling across the floor. A heavier dancer moving quickly has more drive — and more stopping difficulty.
Equation:
\[ T = \dfrac{1}{2} I \omega^2\]
Plain English:
The energy stored in turning depends on rotational inertia and spin speed.
Dance Analogy:
The “engine” of pivots and spins. Think of Viennese Waltz: the faster the turn, the more energy you’re managing.
Equation: \(F = m a\)
Plain English:
Force equals mass times acceleration.
Dance Analogy:
How much push the Leader needs to start motion. A heavier partner requires more force to accelerate.
Equation: \(p = m v\)
Plain English:
Momentum is mass in motion — once moving, it resists stopping or changing direction.
Dance Analogy:
Quickstep or Foxtrot glide: momentum carries you forward smoothly, but also makes sudden halts harder.
Equation: \(\tau = r \times F\)
Plain English:
Rotational force depends on how far from the pivot the push is applied.
Dance Analogy:
Leading from the hand: a small input at the arm creates big rotation through the frame.
Equation: \(L = T - V\)
Plain English:
The balance between motion energy (T) and stored energy (V).
Dance Analogy:
The principle of “Least Action” in dancing: smooth movement happens when motion balances energy losses. See also:
Equation:
\[ \mathcal{D} = \dfrac{1}{2} c \dot{q}^2\]
Plain English:
Energy lost due to friction, drag, or damping.
Dance Analogy:
The hidden costs: shoe friction, floor resistance, or muscle fatigue and anything else that results in an energy loss.
See also:
Terms such as
\(velocity\_vector(θ) = \dfrac{d}{dθ} [ arc\_point(θ) ]\)
Replace with expanded form:
\(arc\_point(θ) = (R * \cos(θ), R * \sin(θ))\)
\(velocity\_vector(θ) = (-R * \sin(θ), R * \cos(θ))\)
Shorthand
\(unit\_velocity(θ) = \dfrac{velocity\_vector(θ)}{||velocity\_vector(θ)||}\)
is really:
\(unit\_velocity(θ) = (-\sin(θ), \cos(θ))\) (magnitude = R cancels out)