Key formulae — Mechanics

Summary of classical mechanics formulae (ch. 1–8, 4b). Derivations and limits of validity are in the respective chapters.

Uniformly accelerated motion $v = v_0 + at$ $\Delta s = v_0 t + \tfrac12 a t^2$ $v^2 = v_0^2 + 2a\,\Delta s$

Dynamics (Newton’s second law) $\pq{F} = m\pq{a}$

Work and energy $L = \pq{F}\cdot\pq{s} \qquad E_k = \tfrac12 m v^2 \qquad E_p = mgh$

Conservation of mechanical energy

In the presence of only conservative forces: $E_k + E_p = \text{cost}$ .

Momentum $\pq{p} = m\pq{v} \qquad \Delta\pq{p} = \pq{F}\,\Delta t$

Oscillations $T = 2\pi\sqrt{m/K} \quad\text{(molla)} \qquad T = 2\pi\sqrt{\ell/g}\quad\text{(pendolo)}$

Gravitation $F = G\,\frac{m_1 m_2}{r^2} \qquad \frac{T^2}{r^3} = \text{cost}\quad\text{(III legge di Keplero)}$

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Topics: Kinematics · Dynamics · Work and energy · Gravitation