Mechanics • Electrodynamics • Optics • Modern Physics • Thermodynamics
Condition for pure rolling on incline: friction $f_s \le \mu_s N$.
Acceleration: $$a_{\text{cm}} = \frac{g \sin\theta}{1 + \frac{I_{\text{cm}}}{M R^2}}$$
Frictional force required: $$f = \frac{M g \sin\theta}{1 + \frac{M R^2}{I_{\text{cm}}}}$$
Partial dielectric slab: $$C = \frac{\varepsilon_0 A}{d - t(1 - 1/K)}$$
Stored electrostatic energy: $$U = \frac{1}{2} C V^2 = \frac{Q^2}{2C} = \frac{1}{2} Q V$$
Einstein Equation: $$h\nu = \Phi_0 + K_{\max} = h\nu_0 + e V_s$$
Bohr Energy Levels: $$E_n = -\frac{13.6 Z^2}{n^2}\text{ eV}$$
Radius of Bohr orbit: $$r_n = 0.529 \frac{n^2}{Z}\text{ \AA}$$