Work & Energy Theorem: Work done by a force over displacement is $W = \vec{F}\cdot\vec{d} = F d \cos\theta$. Net work done equals kinetic energy change: $W_{\text{net}} = \Delta KE = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$.
Gravitational Potential Energy: $PE = mgh$ in uniform gravitational fields.
Mechanical Power & Efficiency: Power is rate of energy transfer: $P = \frac{dW}{dt} = \vec{F}\cdot\vec{v}$. Thermodynamic efficiency is $\eta = \frac{P_{\text{out}}}{P_{\text{in}}} \times 100\%$.
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