A living appendix translating physics equations into plain English and dance insights.
Equation:
\[ T = \tfrac{1}{2} m v^2\]
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:
\[ T = \tfrac{1}{2} I \omega^2\]
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:
\[ V = \tfrac{1}{2} k (z - z_0)^2\]
Plain English:
Energy stored like a spring when displaced from equilibrium.
Dance Analogy:
Rise & Fall. When you rise above natural level, you’re “charging” energy that releases back into the lowering.
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 stored rise/fall energy.
Equation:
\[ \mathcal{D} = \tfrac{1}{2} c \dot{q}^2\]
Plain English:
Energy lost due to friction, drag, or damping.
Dance Analogy:
The hidden costs: shoe friction, floor resistance, or muscle fatigue. Why nothing is perfectly efficient.