Miscellaneous

Topic	Description	Formula / Key Concept
Work-Energy Theorem	States that the work done on an object is equal to the change in its kinetic energy.	$W = \Delta KE = \frac{1}{2}m(v^2 - u^2)$ where $v$ is final velocity, $u$ is initial velocity, $m$ is mass.
Conservation of Energy	Energy cannot be created or destroyed, only transformed from one form to another.	$E_{\text{total}} = \text{Kinetic Energy} + \text{Potential Energy}$
Power	The rate at which work is done or energy is transferred.	$P = \frac{W}{t} \quad \text{or} \quad P = \frac{E}{t}$ (SI Unit: Watt, W = J/s)
Momentum	The product of mass and velocity, representing the quantity of motion of an object.	$p = mv$
Impulse	Change in momentum of an object when a force is applied over a period of time.	$J = F \Delta t = \Delta p$
Circular Motion	Motion of an object in a circular path, with constant or changing speed.	$a_c = \frac{v^2}{r} \quad \text{or} \quad a_c = \omega^2 r$ (Centripetal acceleration, $v$ = velocity, $r$ = radius)
Gravitational Force	The force of attraction between two masses.	$F = G \frac{m_1 m_2}{r^2}$ (where $G$ = gravitational constant = $6.674 \times 10^{-11} \, \text{N m}^2/\text{kg}^2$)
Pressure	The force applied per unit area on a surface.	$P = \frac{F}{A}$ (SI Unit: Pascal, Pa = N/m²)
Buoyancy	The upward force exerted by a fluid on a submerged or floating object.	$F_B = \rho_{\text{fluid}} g V_{\text{displaced}}$ where $\rho$ is fluid density, $g$ is acceleration due to gravity, and $V$ is volume displaced.
Surface Tension	The force per unit length exerted along the surface of a liquid.	$\gamma = \frac{F}{L}$ (SI Unit: N/m)
Heat Transfer	The transfer of heat from a warmer object to a cooler one. Types include conduction, convection, and radiation.	Conduction: $Q = \frac{kA(T_1 - T_2)}{d}$ <br> Convection: $Q = hA(T_1 - T_2)$ <br> Radiation: $P = \sigma A T^4$
Capacitance	The ability of a system to store charge per unit voltage.	$C = \frac{Q}{V}$ (SI Unit: Farad, F)
Magnetic Field	A field produced by moving charges or magnetic materials that exerts a force on other charges.	$B = \frac{\mu_0 I}{2 \pi r}$ (for a long straight current-carrying wire)
Electromagnetic Induction	The process by which a changing magnetic field induces an electromotive force (EMF) in a conductor.	$\mathcal{E} = -\frac{d\Phi_B}{dt}$ (Faraday's Law)
Capacitor in Series and Parallel	The arrangement of capacitors in series or parallel affects their total capacitance.	Series: $\frac{1}{C_{\text{total}}} = \frac{1}{C_1} + \frac{1}{C_2} + \dots$ <br> Parallel: $C_{\text{total}} = C_1 + C_2 + \dots$
Energy Stored in Capacitor	The energy stored in a capacitor when charged by a voltage.	$E = \frac{1}{2} C V^2$
Laws of Thermodynamics	The fundamental laws governing energy and heat transfer.	First Law: $\Delta U = Q - W$ <br> Second Law: Entropy of an isolated system tends to increase. <br> Third Law: As temperature approaches absolute zero, entropy approaches a minimum.
Thermodynamic Cycles	A series of processes in which the system returns to its original state. Used in heat engines and refrigerators.	Carnot Cycle: Efficiency = $1 - \frac{T_{\text{cold}}}{T_{\text{hot}}}$
Einstein’s Theory of Relativity	Describes the relationship between space, time, and gravity, especially at high velocities.	$E = mc^2$ (Energy-mass equivalence)
Wave-Particle Duality	The concept that every particle or quantum entity can exhibit both wave-like and particle-like properties.	de Broglie Wavelength: $\lambda = \frac{h}{mv}$ (where $h$ is Planck's constant, $m$ is mass, and $v$ is velocity)
Photoelectric Effect	The phenomenon where electrons are emitted from a material when it is exposed to light.	$E_{\text{photon}} = h f$ (where $h$ is Planck's constant, and $f$ is frequency)
Quantum Mechanics	The branch of physics dealing with phenomena at atomic and subatomic scales.	Schrödinger’s Equation: $i \hbar \frac{\partial}{\partial t} \Psi = \hat{H} \Psi$
Heisenberg Uncertainty Principle	States that one cannot simultaneously know both the exact position and momentum of a particle.	$\Delta x \Delta p \geq \frac{\hbar}{2}$
Young’s Modulus	Describes the elasticity of a material, representing its ability to deform under stress.	$Y = \frac{\text{Stress}}{\text{Strain}} = \frac{F/A}{\Delta L/L}$

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Recap: Key Points to Remember

• Work-Energy Theorem: Work done on an object equals the change in its kinetic energy.
• Capacitance: The ability of a capacitor to store charge.
• Thermodynamics: Governs energy conservation, heat transfer, and entropy.
• Wave-Particle Duality: Describes the nature of particles at quantum scales.
• Photoelectric Effect: The emission of electrons from a material when illuminated by light.