Class 11 Physics (CBSE NCERT)

Cheatsheet Content

1. Physical World & Measurement Physics: Study of nature and natural phenomena. Fundamental Forces: Gravitational, Electromagnetic, Strong Nuclear, Weak Nuclear. Units: SI system (MKS). Dimensions: $[M^a L^b T^c]$ for physical quantities. Homogeneity Principle: Dimensions of terms on both sides of an equation must be same. Significant Figures: Rules for counting and arithmetic operations. Errors: Absolute, Relative, Percentage Error. 2. Kinematics 2.1 Motion in a Straight Line Distance vs. Displacement: Scalar vs. Vector. Speed vs. Velocity: Scalar vs. Vector. $v = \frac{dx}{dt}$. Acceleration: $a = \frac{dv}{dt}$. Equations of Motion: (for constant acceleration) $v = u + at$ $s = ut + \frac{1}{2}at^2$ $v^2 = u^2 + 2as$ 2.2 Motion in a Plane Vectors: Addition (Triangle, Parallelogram Law), Resolution of Vectors. Dot Product: $\vec{A} \cdot \vec{B} = AB \cos\theta$. Cross Product: $\vec{A} \times \vec{B} = AB \sin\theta \hat{n}$. Projectile Motion: Max Height $H = \frac{u^2 \sin^2\theta}{2g}$ Time of Flight $T = \frac{2u \sin\theta}{g}$ Range $R = \frac{u^2 \sin(2\theta)}{g}$ Uniform Circular Motion: Angular Velocity $\omega = \frac{v}{r}$ Centripetal Acceleration $a_c = \frac{v^2}{r} = \omega^2 r$ 3. Laws of Motion Newton's First Law: Inertia. Newton's Second Law: $F = ma$. Impulse $J = \Delta p = F \Delta t$. Newton's Third Law: Action-Reaction. Conservation of Momentum: For an isolated system, $\sum \vec{p} = \text{constant}$. Friction: Static ($f_s \le \mu_s N$), Kinetic ($f_k = \mu_k N$). $\mu_s > \mu_k$. Banking of Roads: $\tan\theta = \frac{v^2}{rg}$ (for no friction). 4. Work, Energy, and Power Work: $W = \vec{F} \cdot \vec{d} = Fd \cos\theta$. Kinetic Energy: $K = \frac{1}{2}mv^2$. Potential Energy: $U = mgh$ (gravitational), $U = \frac{1}{2}kx^2$ (spring). Work-Energy Theorem: $W_{net} = \Delta K$. Power: $P = \frac{dW}{dt} = \vec{F} \cdot \vec{v}$. Conservation of Mechanical Energy: $E = K+U = \text{constant}$ (for conservative forces). Collisions: Elastic: Momentum & KE conserved. Inelastic: Momentum conserved, KE not conserved. 5. System of Particles & Rotational Motion Center of Mass (CM): $\vec{R}_{CM} = \frac{\sum m_i \vec{r}_i}{\sum m_i}$. Moment of Inertia: $I = \sum m_i r_i^2$. Parallel Axis Theorem: $I = I_{CM} + Md^2$. Perpendicular Axis Theorem: $I_z = I_x + I_y$ (for planar objects). Torque: $\vec{\tau} = \vec{r} \times \vec{F} = I\vec{\alpha}$. Angular Momentum: $\vec{L} = \vec{r} \times \vec{p} = I\vec{\omega}$. Conservation of Angular Momentum: If $\vec{\tau}_{ext} = 0$, then $\vec{L} = \text{constant}$. Rolling Motion: $K_{total} = K_{translational} + K_{rotational} = \frac{1}{2}mv_{CM}^2 + \frac{1}{2}I_{CM}\omega^2$. 6. Gravitation Newton's Law of Gravitation: $F = G \frac{m_1 m_2}{r^2}$. Acceleration due to Gravity: $g = \frac{GM}{R^2}$. Variation with height: $g' = g(1 - \frac{2h}{R})$ (for $h \ll R$). Variation with depth: $g' = g(1 - \frac{d}{R})$. Gravitational Potential Energy: $U = -\frac{GMm}{r}$. Escape Velocity: $v_e = \sqrt{\frac{2GM}{R}} = \sqrt{2gR}$. Orbital Velocity: $v_o = \sqrt{\frac{GM}{r}}$. Kepler's Laws: Orbits are ellipses. Equal areas in equal times. $T^2 \propto R^3$. 7. Properties of Bulk Matter 7.1 Mechanical Properties of Solids Stress: $\sigma = \frac{F}{A}$. Strain: $\epsilon = \frac{\Delta L}{L_0}$, $\frac{\Delta V}{V_0}$, $\phi$. Hooke's Law: Stress $\propto$ Strain. Young's Modulus: $Y = \frac{\text{Tensile Stress}}{\text{Tensile Strain}}$. Bulk Modulus: $B = \frac{\text{Volume Stress}}{\text{Volume Strain}}$. Shear Modulus: $G = \frac{\text{Shear Stress}}{\text{Shear Strain}}$. Poisson's Ratio: $\nu = \frac{\text{Lateral Strain}}{\text{Longitudinal Strain}}$. 7.2 Mechanical Properties of Fluids Pressure: $P = \frac{F}{A}$. Pascal's Law: Pressure applied to an enclosed fluid is transmitted undiminished. Archimedes' Principle: Buoyant force $F_B = \rho_{fluid} V_{sub} g$. Equation of Continuity: $A_1v_1 = A_2v_2$. Bernoulli's Principle: $P + \frac{1}{2}\rho v^2 + \rho gh = \text{constant}$. Viscosity: $F = \eta A \frac{dv}{dz}$. Stokes' Law: $F_v = 6\pi \eta r v$. Surface Tension: $S = \frac{F}{L}$. Surface Energy $E_s = S \times A$. Capillary Rise: $h = \frac{2S \cos\theta}{\rho rg}$. 7.3 Thermal Properties of Matter Heat: Form of energy transfer. Temperature: Measure of hotness/coldness. Thermal Expansion: Linear: $\Delta L = L_0 \alpha \Delta T$. Area: $\Delta A = A_0 \beta \Delta T$, where $\beta = 2\alpha$. Volume: $\Delta V = V_0 \gamma \Delta T$, where $\gamma = 3\alpha$. Specific Heat Capacity: $Q = mc\Delta T$. Latent Heat: $Q = mL$. (Fusion, Vaporization) Heat Transfer: Conduction: $\frac{dQ}{dt} = -KA \frac{dT}{dx}$. Convection: Transfer by mass movement. Radiation: Stefan-Boltzmann Law $P = \epsilon \sigma A T^4$. Wien's Displacement Law $\lambda_m T = b$. 8. Thermodynamics Thermodynamic System: Collection of matter. Zeroth Law: Thermal equilibrium implies same temperature. First Law of Thermodynamics: $\Delta U = Q - W$. (Conservation of Energy) Thermodynamic Processes: Isothermal: $\Delta T = 0$. Adiabatic: $Q = 0$. $PV^\gamma = \text{constant}$. Isobaric: $\Delta P = 0$. Isochoric: $\Delta V = 0$. Heat Engine: Efficiency $\eta = 1 - \frac{Q_2}{Q_1}$. Refrigerators/Heat Pumps: Coefficient of Performance $COP = \frac{Q_2}{W}$ (refrigerator), $COP = \frac{Q_1}{W}$ (heat pump). Second Law of Thermodynamics: Entropy never decreases for an isolated system. (Clausius & Kelvin-Planck statements). 9. Kinetic Theory Ideal Gas Equation: $PV = nRT = Nk_B T$. Assumptions of KTG: Point particles, elastic collisions, random motion, negligible intermolecular forces. Pressure of an Ideal Gas: $P = \frac{1}{3}\frac{nm\overline{v^2}}{V}$. Kinetic Energy of Gas: Avg KE per molecule $ = \frac{3}{2}k_B T$. Degrees of Freedom ($f$): Monatomic (3), Diatomic (5). Law of Equipartition of Energy: Energy per degree of freedom is $\frac{1}{2}k_B T$. Specific Heats: $C_V = \frac{f}{2}R$, $C_P = (\frac{f}{2}+1)R$. Mayer's Relation: $C_P - C_V = R$. Ratio of Specific Heats: $\gamma = \frac{C_P}{C_V} = 1 + \frac{2}{f}$. Mean Free Path: $\lambda = \frac{1}{\sqrt{2}n\pi d^2}$. 10. Oscillations and Waves 10.1 Oscillations Simple Harmonic Motion (SHM): $x(t) = A \sin(\omega t + \phi)$. Velocity: $v(t) = A\omega \cos(\omega t + \phi)$. Acceleration: $a(t) = -A\omega^2 \sin(\omega t + \phi) = -\omega^2 x$. Time Period: $T = \frac{2\pi}{\omega}$. Energy in SHM: $E = \frac{1}{2}kA^2 = \frac{1}{2}m\omega^2 A^2$. (KE + PE). Simple Pendulum: $T = 2\pi \sqrt{\frac{L}{g}}$. Spring-Mass System: $T = 2\pi \sqrt{\frac{m}{k}}$. 10.2 Waves Wave Equation: $y(x,t) = A \sin(kx - \omega t + \phi)$. Wave Speed: $v = f\lambda = \frac{\omega}{k}$. Transverse Waves: $v = \sqrt{\frac{T}{\mu}}$ (string). Longitudinal Waves: $v = \sqrt{\frac{B}{\rho}}$ (fluid), $v = \sqrt{\frac{Y}{\rho}}$ (solid). Speed of Sound in Air: $v = \sqrt{\frac{\gamma P}{\rho}}$. Superposition Principle: Resultant displacement is vector sum of individual displacements. Stationary Waves: Formed by superposition of two identical waves traveling in opposite directions. Nodes (zero displacement), Antinodes (max displacement). Open organ pipe: $f_n = \frac{nv}{2L}$, $n=1,2,3...$ Closed organ pipe: $f_n = \frac{nv}{4L}$, $n=1,3,5...$ Beats: $f_{beat} = |f_1 - f_2|$. Doppler Effect: $f' = f \left( \frac{v \pm v_o}{v \mp v_s} \right)$.