| Constants | |
|---|---|
| Gravity | $ g = -9.8 \frac{m}{s^2} $ |
| Equations | |
|---|---|
| $ x = x_0 + v_0 t + \frac{1}{2}at^2 $ | |
| $ v = \frac{Δs}{t} $ | |
| $ a = \frac{Δv}{t} $ | |
| $ v = v_0 + at $ | |
| $ v^2 = v_0^2 + 2a( x - x_0 ) $ | |
| $ \vec{a} ⋅ \vec{b} = |a| × |b| × cos(\theta) $ | |
| $ \vec{a} × \vec{b} = a_x b_x + a_y b_y $ | |
| $ |\vec{a}| = \sqrt{ a_x^2 + a_y^2 } $ | |
| $ Δv = \frac{Δx}{t} $ | |
| $ Δx = x_2 - x_1 $ | |
| $ W = K_f - K_i $ | |
| $ K = \frac{1}{2}mv^2 $ | |
| $ W_g = -mg Δy $ |
| Constants | |
|---|---|
| Vacuum permittivity | $ ε_0 = 8.9875517873681764 × 10^{-12} { F \over m } $ |
| Mass of electron | $ 9.10938356 × 10^{-31} kg $ |
| Mass of proton | $ 1.6726219 × 10^{-27} kg $ |
| Coulomb's constant | $ k = 8.9875517873681764 × 10^9 { N m^2 \over C^2 } $ |
| Elementary electric charge | $ 1.60217662 × 10^{19} \ C $ |
| Equations |
|---|
| $$ F = ma = k \frac{{ q_1 q_2 }}{r^2} = Eq $$ |
| $$ E = k \frac{q}{r^2} $$ |
| $$ \tau = r F sin(\theta) $$ |
| $$ E_{\text{ring}} = k \frac{qz}{{ z^2 + r^2 }^{\frac{3}{2}}} $$ |
| $$ λ = \frac{q}{2 π r} $$ |
| $$ σ = \frac{q}{π r^2} $$ |
| $$ E_{\text{disk}} = 2 π k σ \left(\frac{1 - z}{\sqrt{z^2 + r^2}}\right) $$ |
| $$ E_{\text{dipole}} = \frac{2 k q d}{z^3} $$ |
| $$ Φ = \frac{q_{\text{enc}}}{ε_0} $$ |
| $$ E_{\text{inf. rod}} = \frac{1}{2 π ε_0}\frac{λ}{d} $$ |
| $$ E_{\text{inf. sheet}} = \frac{σ}{2 ε_0} $$ |