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Index / Outline * Mechanics and Kinematics ‘ Thermodynamics and Heat ‘ Electromagnetism and Circuits ‘ Optics and Wave Phenomena ‘ Modern Physics and Atomic Theory Mechanics and Kinematics:- ‘ Equations of Motion: Relates velocity, displacement, and time under constant acceleration using v = u + at ond s = ut + Bat? - Newton's Second Law: The net force applied to an object is egual to the product of its mass and acceleration CF = ma). * Work and Energy: Work done is calculated as Force times displacement (W = Fad cos@), where Kinetic Energy is Amv’. ‘ Gravitation: The Universal Law of Gravitation is expressed as F = G (CHE ae where G ts the gravitational constant. * Power: The rate of doing work, measured in Watts, detined by the formula P = Wit. Thermodynamics and Heat:- Richiles daceribias th lationchio bet haat bt , energy. : Specific Heat Capacity: Amount of thermal energy reguired to change temperature, calculated as Q@ = mc. ‘ Ideal Gas Law: Relates pressure, volume, and temperature via PV = wRT, where R Is the universal gas constant. : First Law of Thermodynamics: The change in Internal Energy (AU) is equal to heat added (Q) minus work done CW). ‘ Entropy: A measure of system disorder, where the change Is AS = AQ/T for reversible processes. Electromagnetism and Circuits:- rormulas for electric ch ic fields, and current flow in electrical components, ‘ Coulomb's Law: Defines the electrostatic force between two point charges as F = k@getr* * Ohm's Law: The relationship between Voltage (V), Current (1), and Resistance CR) given by V = IR. Capacitance: The ability to store electric charge, defined as C = Q/V and measured In Farads. ‘ Magnetic Force: The force on a moving charge in a magnetic teld is F = gvB sind, ' Faraday's Law: The induced Electromotive Force (EMF) is egual to the negative rate of change of magnetic flux. Optics and Wave Phenomena:- * Snell's Law: Governs the refraction of light between two media using m sin®1 = M2 sinQ2. * Mirror and Lens Formula: 7he ee between focal length CO, object distance (uw, and image distance Cy a is lh = IW + Ifa. PART - 1 Mechanics and Kinematics * Thermodynamics and Heat « Electromagnetism and Circuits * Optics and Wave Phenomena ¢ Modern Physics and Atomic Theory Mechanics and Kinematics:- ‘ Equations of Motion: Used for constant acceleration; equations include v = u + at, s = ut + Wat? and v? = 4? + 2as. ‘ Newton's Second Law: Defines Force (F) as the product of mass (m) and acceleration (a), expressed as F = ma. * Work and Energy: Work is W = Fal cosO; Kinetic Energy is 1/2mv7; Potential Energy is mgh. * Momentum: Defined as p = mv, the Conservation of Momentum states total momentum remains constant In Isolated systems. Thermodynamics and Heat:- The ctely of haat 2 P ee . th bi f matter, : First Law of Thermodynamics: Energy conservation law stated as AU = @ - Wd), where AU is Internal Energy change. ‘ Ideal Gas Law: Relates pressure, volume, ana temperature via PV = nRT, using the Universal Gas Constant. ‘ Specific Heat Capacity: The heat reguired to change temperature is Q = mcAT; Latent Heat handles phase changes (@ = mt). an isolated system always increases. Electromagnetism and Circuyits:- ‘he kibsitet of aucte c field | eesteatn emeae components. Coulomb's Law: Force between charges is F = k@Glg2/r?), governed by the Electrostatic Constant. ‘ Ohm's Law: Defines the relationship V = /R; Resistance in series adds up, while in parallel, reciprocals add. Capacitance: Calculated as C = Q/V: represents the ability to store Electric Charge. ‘ Magnetic Force: Force on a moving charge is F = qvB sin@; Electromagnetic Induction is detined by Faraday's Law. Optics and Wave Phenomena:- fnalysic of light behav blecti hracti ) period ; » Snell's Law: Governs Retraction: n/ sm@/ = n2 sinO2, where n is the refractive index. ‘ Mirror and Lens Formula: The eguation I/f = IW + I/u relates Focal Length to object and image distances. ‘ Wave Speed: Calculated as v = fA, where f is Freguency and i is wavelength. ‘ Interference: Occurs when waves overlap; Constructive Interference increases amplitude. Modern Physics and Atomic Theory:- Quantum concepts, nuclear reactions, and the structure of the atom. cud Le, E Motion in O Two Di _— : Distance and Displacement: Distance /s the total path length covered, whereas Displacement is the shortest vector distance between the initial and Final positions. ‘ Average and Instantaneous Velocity: Average velocity is total displacement over total time, Instantaneous Velocity 1s detined as the derivative of positron with respect to time (v = dx/at). * Acceleration: The rate of change of velocity. For Uniform Acceleration, the velocity changes by egual amounts in egual time intervals. Eguations of Uniformly Accelerated Motion:- » First Equation: v = u + at, where u' is Initial Velocity and \' is final velocity. : Second Eguatiom s = ut + Bat’, representing Displacement as a function of time. ‘ Third Equation: v? = u? + 2as, used when Time is not explicitly given. Nth Second Displacement: S_n = 4 + a/2C2n - 1), calculating distance in a specitic One-Second Interval. Projectile Motion Dynamics:- ‘ Time of Flight (1): 7 = (2u sin@) / 9; this Is the total time the object remains in the Air. + Maximum Height (#): 4 = (? sin'®) / 29, reached when the Vertical Velocity component becomes zero. ‘ Horizontal Range (R): k = Cy? sin20) / 9; the maximum range is achieved at a Launch Angle of 4§ degrees. ' Equation of Trajectory: y = x tan® - gx?) / Cu? cos), proving the path is a Parabola. Newton's Laws of Motion and Forces:- ~7- + Law_of Inertia: An object maintains tts state of rest or uniform motion unless Second Law (F=ma): The force applied is equal to the rate of change of Linear Momentum (P = mv). ‘ Impulse: J = F x At = AP: a large force acting for a very short duration causes a Change in Momentum. ‘ Friction: f = uN, where wu is the coefticrent of friction and N Is the Normal Reaction Force. Static friction is generally higher than kinetic frictron. Work, Energy, and Power:- * Work Done: W = F + s cosO. Work is zero if the force is Perpendicular to displacement. : Kinetic Energy (K.E): KE = Amv it is the energy possessed by an object due to its Motion. ‘ Potential Energy (P.E): Gravitational P.E = moh, associated with the Position or contiguration of the object. * Work-Energy Theorem: The total work done by all forces on a body is egual to the change in its Kinetic Energy. » Power: P = Wit = F « v; the rate at which Work is performed. S/ unit Is the Watt CW). Circular Motion:- ‘ Centripetal Acceleration: a_c = v’/r = w%, directed toward the Center of the circular path. ‘ Centripetal Force: F_c = mv’/r; this /s not a new force but a Reguirement for circular motion provided by tension, friction, or gravity. Thermometry and Thermal Expansion:- ‘ Temperature Scales: The relation between Celsius, Fahrenheit, and Kelvin Is given by (CLS) = (F-32)19 = (K-273.1S/S. The Absolute Zero temperature is 0 Kelvin or -273.1S degrees Celsius, where molecular motion ceases. * Linear Expansion: Defined as the change in length Al = La&T, where a Galpha) is the coefficient of linear expansion. - Areal and Volume Expansion: Areal expansion AA = ABPAT and volume expansion AV = VAT. The relationship between coefficients isaiPp iy =1s2 +3 for isotropic solrds. : Anomalous Expansion of Water: Water exhibits a unique property where its Maximum Density occurs at 4 degrees Celsius. Calorimetry and Heat Transfer:- : Specific Heat Capacity: The amount of heat required to raise the temperature of unit mass by one degree, expressed as @ = mcAT, + Latent Heat: Heat absorbed or released during a phase change without temperature change, calculated as @ = mL. The Latent Heat of Fusion for ice Is 80 calfg. « Thermal Conduction: The rate of heat How H = d@fdt = KACTI - T2)/L, where K represents thermal conauctivity. « Stefan-Boltzmann Law: The total radiant energy emitted by a blackbody Is proportional to the fourth power of its absolute temperature, E = oT". ‘ Wien's Displacement Law: The wavelength corresponding to maximum emissron /s tnversely proportional to temperature, Am T = b, where b is Wien's constant. Laws of Thermodynamics:- 0 + Z2eroth Law: /f two systems are in thermal eguilbrium with a third system, temperature, : First Law (Law of Conservation of Energy): The heat supplied to a system CQ) is equal to the sum of the increase in internal energy CU) and work done CW) by the system: dQ = dv + dW. * Work Done in Processes: /n an /sothermal process, W = nRT In(V2/VI). In an Adiabatic Process, work done is W = (PIV) - P2V2)y - V. Second Law: Heat cannot spontaneously flow trom a colder body to a hotter boay. This law introduces the concept of Entropy, which always increases in an /solated system. Kinetic Theory of Gases (KTG):- ‘ Ideal Gas Equation; Represented by PV = nRT, where R is the Universal Gas Constant (8.319 TbnolK). * Root Mean Square (RMS) Speed: The velocity is calculated as v_rms = CRT) or I RTI), where k is the Boltzmann Constant. * Degrees of Freedom: For a Monatomic gas f = 3, and for a Diatomic Gas f = S Cat room temperature). Internal energy U = G12) nRT. : Molar Specific Heats: The relation Cp - Cv = R is known as Mayer's Formula, The ratio y = Cp/Cv = 1 + If. Heat Engines and Refrigerators;- : Efficiency of Heat Engine: n = (Work Done / Heat Input) = 1 - (Q_out / @_in). For a Carnot Engine, n = 1 - (T_low / Thigh). : Coefficient of Performance (COP); For a refngerator, B = Q_low / W) = T_low / high - T_low). A Perfect Refrigerator with infinite COP is physically Wnpossible. -11- closed loop is egual to Yo times the total current passing through that loop: GB-a) = pol. Magnetic Field of a Solenoid: /nside a long, tightly wound Solenoid, the field /s uniform and given by B = woul, where n is the number of turns per unit length. ‘ Lorentz Force: 7he total force on a charge g moving with velocity v in both electric field E and magnetic teld Bis F = gE +v x B). * Magnetic Force on a Current-Carrying Conductor: A wire of length L carrying current | in a magnetic field B experiences a force F = ILB sin®. ‘ Torgue on a Current Loop: The torgue acting on a loop of area A and N turns in a magnetic field is t = MAB sin®, or in vector form, t = m x B where m is the magnetic dipole moment. Electromagnetic Induction (EMI):- . isn dadliccedl Eh ve Fi ‘EME) * Magnetic Flux: The total magnetic field passing through a surface is b= BA c0s0, measured in Webers (wh). + Faraday’s Law: The magnitude of the induced EMF is egual to the time rate of change of magnetic flux: € = -dbfdt. * Len2’s Law: The dlirection of the induced current is such that it opposes the change in magnetic Hux that produced it. * Motional EME; EMF induced in a conductor of length L moving with velocity v perpendicular to freld Bis e = Bly. « Self-Inductance (L): The property where a coil opposes change in its own current; e = -L Cifdt). For a ane, uf = yon Al. « Mutual Inductance (M): EMF romans: tn one coll due to current change iv an DC and AC Circuits:- Direct Current (DC) Fundamentals : Ohm’s Law: The potential difference across a conductor Is proportional to the current. V = IR. : Kirchhoff’s Current Law (KCL): The algebraic sum of currents at any Junction is zero (ZI = O. * Kirchhoff’s Voltage Law (KVL): The sum of potential changes around any Closed Loop is zero (ZV = 0). ‘ Power Dissipation: The rate of heat production in a resistor is P= Wi = IR = VR. tics hlin + CAC) Principl « Root Mean Square (RMS) Values: Effective values of voltage and current: Vrms = Vo2 and Irms = lh 2. . Reactance (X): /nauctive reactance X_L = wl and capacitive reactance X_€ = 1/ (we). * Impedance (2): Total opposition in an LCR circuit: 2 = SLR? + KL - X_C)*), * Resonance Conditiom: Occurs when X_L = X_G resulting in minimum /mpedance. Resonant treguency to = 1/ ln JQC)]. * Power Factor: Defined as cosp = R/2. True power P = Vrms Irms cos. * Transformers: Based on mutual induction: VsMp = Ns/Np = Ip/ts where N is the number of turns. -14- : Snell’s Law: For retraction, the ratio of sines of the angles of incidence and retraction is constant: nl sin @1 = n2 sin @2. Refractive Index: Detined as the ratio of speed of hight im vacuum to the speed in a medium, n = ch. ‘ Critical Angle: The angle of incidence for which the angle of refraction is 90 degrees: sin Be = n2fal (where nl > n2). Lenses and Optical Instruments:- * Lens Maker’s Formula: Relates focal length to refractive index and radii of curvature: WE = Cn - D) LURI - 17R2]. « Thin Lens Formula: The standard equation Is Iff = If - Ife. ‘ Lens Power: /nverse of focal length measured in meters, expressed in Dioptres O). P= ‘ Magnifying Power (Microscope): For a simple microscope at least distance of distinct vision, M = 1 + BF. : Astronomical Telescope: Magnifying power is given by M = -foffe and length L=for fe. Wave Optics:- ‘ Path difference and Phase Difference: Phase aifference Ap = Cén/) Ax, where Ax Is the path difference. ‘ Interference Conditions: Constructive interference occurs when Ax = mh; Destructive occurs when Ax = (n + WW2)A. - Young’s Double Slit Experiment: The fringe width Bp = AD/d, where D is screen distance and d is slit separation. : Brewster's Law: Relates refractive index to polarizing angle: n = tanGp). : Malus’s Law: Intensity of transmitted polarized light 1 = 10 cos. 16" Wave Motion and Sound:- + @), where k = 2nf and w = 2nf. ‘ Velocity of Transverse Wave: On a stretched string, velocity v = J (Th) where T is tension and ui Is linear mass density. : Velocity of Sound: /n a gas, Laplace correction gives v = SGyPhp). + Doppler Effect: The observed treguency f' = f Lv + vo) / W = vs)J, where vo 1s observer speed and vs 1s source speed. : Beats: The beat frequency is the absolute difference between two source frequencies: fb = [fl - 2]. PART - 6 Modern Physics and Atomic Theory Thi bi Mh , radiati ee ¢ matter, and the structural dynamics of the atom and nucleus. Dual Nature of Radiation and Matter:- ‘ Photon Energy and Momentum: The energy of a photon is given by E = bv = deh, and its momentum Is p = Efe = bh. : Einstein’s Photoelectric Eguation: The maximum kinetic energy of emitted =|7= electrons is Kmax = bv - D, where V is the work function of the metal. X-Rays and Moseley’s Law:- : Cut-off Wavelength: The minimum wavelength of X-rays is Amin = hefev. ‘ Moseley’s Law: For characteristic X-rays, the frequency v follows Jv = a2 - 4), where 2 is the atomic number. PART -7 Equations of Motion: Relates velocity, displacement, and time under constant acceleration using v= u+ at and s = ut+ “at?. The Fait o Moti £ iiiidad th eicviba th Lidisicshin ‘bu bysical bith s ee , time, provided the object moves with a Constant Acceleration, Fundamental Kinematic Variables:- » Initial Velocity Cu): The velocity of the object at the starting point of the observation, measured in m/s. « Final Velocity (v): The velocity of the object after a specitic time interval t has elapsed. -19- « Acceleration (a): The rate of change of velocity, which must remain Uniform : Displacement (s): The change in position of the object, which is a Vector Quantity. : Time (t): The duration during which the motion is being studied. The Three Primary Equations of Motion:- ' First Equation (v = yu + at): Known as the Velocity-Time Relation, it calculates the final velocity when initial velocity, acceleration, and time are known. * Second Equation (s = ut + at): Known as the Position-Time Relation, it determines the displacement of an object over a given timetrame. : Third Eguation (v? = u? + 2as): Known as the Velocity-Displacement Relation, this eguation is independent of time and relates the square of velocity to displacement. Special Case: Displacement _in the n-th Second:- » Formula (Sn = u + af2(2n - 1)): Used to calculate the distance traveled specitically during the n-th Second of motion rather than the total displacement. Motion Under Gravity:- When_an object is in Free Fall, the acceleration a' is replaced by 9' (acceleration due to gravity), where 9 # ¢.2 m/s? « Upward Motion: Acceleration /s taken as -g because gravity acts opposite to the direction of motion. ‘ Downward Motion: Acceleration is taken as +9 as the object speeds up toward the Earth. Important Sign Conventions:- « Directional Consistency: /f the initial direction of motion is positive, then any vector (velocity or acceleration) in the opposite direction must be Negative. -20- : Retardation: Wher an object slows down, the acceleration fs negative, also 
