Essential Physics Formulas

1. Classical Mechanics

Kinematics

• $x$ — position
• $x_0$​ — initial position
• $v$ — velocity
• $v_0$ — initial velocity
• $a$ — acceleration
• $t$ — time

Kinematics (uniform acceleration only)

$$v = \frac{dx}{dt} \quad a = \frac{dv}{dt}$$ $$x = x_0 + v_0 t + \frac{1}{2}at^2 \quad v^2 = v_0^2 + 2a(x-x_0)$$

Dynamics

$$\vec{F} = m\vec{a} \quad\text{(constant mass)}$$ $$\vec{F} = \frac{d\vec{p}}{dt} \quad \vec{p} = m\vec{v}$$

Gravitation (point masses / spherical symmetry):$$F = G\frac{m_1 m_2}{r^2}$$​​

Work, Energy, Power

$$W = \int \vec{F}\cdot d\vec{r}$$ $$K = \frac{1}{2}mv^2 \quad U_g = mgh \;\text{(near Earth, constant \(g\))}$$ $$U_s = \frac{1}{2}kx^2 \;\text{(Hookean regime)}$$$$E = K + U \quad P = \vec{F}\cdot\vec{v}$$

Rotation

$$\vec{L} = \vec{r}\times\vec{p} \quad \vec{\tau} = \frac{d\vec{L}}{dt}$$​ $$I = \sum mr^2 \;(\text{discrete}) \quad K_{rot} = \frac{1}{2}I\omega^2$$

Oscillations (simple harmonic motion)

$$F = -kx \quad \omega = \sqrt{\frac{k}{m}}$$ $$x(t) = A\cos(\omega t + \phi)$$