Olympiad Wallah

⚡ KINETIC ENERGY — FORMULA SHEET 🔹 Kinetic Energy (KE) KE = ½mv² where, m = mass v = velocity 🔹 Work-Energy Theorem W = ΔKE W = KE₂ − KE₁ 🔹 Translational Kinetic Energy KE = ½mv² 🔹 Rotational Kinetic Energy KE = ½Iω² where, I = moment of inertia ω = angular velocity 🔹 Total Kinetic Energy (Rolling Motion) KE = ½mv² + ½Iω² 🔹 Relation Between Momentum and Kinetic Energy KE = p²/2m where, p = momentum 🔹 Velocity in Terms of Kinetic Energy v = √(2KE/m) 🔹 Momentum in Terms of Kinetic Energy p = √(2mKE) 🔹 Change in Kinetic Energy ΔKE = ½m(v₂² − v₁²) 🔹 Average Power P = ΔKE/t

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⚡ NEWTON'S LAWS OF MOTION — FORMULA SHEET 🔹 Newton's First Law ΣF = 0 Body remains at rest or in uniform motion unless acted upon by an external force. 🔹 Newton's Second Law F = ma where, F = Force m = Mass a = Acceleration 🔹 General Form F = dp/dt where, p = Momentum 🔹 Momentum p = mv 🔹 Impulse J = FΔt 🔹 Impulse-Momentum Theorem J = Δp = p₂ − p₁ 🔹 Weight of a Body W = mg 🔹 Normal Reaction Horizontal Surface: N = mg 🔹 Lift Moving Upward N = m(g + a) 🔹 Lift Moving Downward N = m(g − a) 🔹 Apparent Weightlessness N = 0 when, a = g 🔹 Tension in a Light String For a body of mass m: T = m(g ± a) (Depending on direction of acceleration) 🔹 Pseudo Force Fₚ = ma₀ where, a₀ = acceleration of non-inertial frame 🔹 Friction Maximum Static Friction: fₛ(max) = μₛN Kinetic Friction: fₖ = μₖN

🧭 VECTORS — FORMULA SHEET 🔹 Magnitude of a Vector |A| = √(Aₓ² + Aᵧ²) 🔹 Unit Vector  = A/|A| 🔹 Resolution of a Vector Aₓ = A cosθ Aᵧ = A sinθ 🔹 Resultant of Two Vectors R = √(A² + B² + 2ABcosθ) 🔹 Direction of Resultant tanα = (Bsinθ)/(A + Bcosθ) 🔹 Dot Product A·B = ABcosθ A·B = AₓBₓ + AᵧBᵧ + A𝓏B𝓏 🔹 Cross Product A × B = ABsinθ 🔹 Unit Vector Relations i·i = 1 j·j = 1 k·k = 1 i·j = j·k = k·i = 0 🔹 Cross Product Relations i × j = k j × k = i k × i = j j × i = -k k × j = -i i × k = -j 🔹 Area of Parallelogram Area = |A × B| 🔹 Area of Triangle Area = ½|A × B| 🔹 Projection of A on B Projection = (A·B)/|B|

🚀 KINEMATICS — FORMULA SHEET 🔹 Speed Speed = Distance / Time v = s/t 🔹 Velocity Velocity = Displacement / Time v = Δx/Δt 🔹 Acceleration a = (v − u)/t where, u = initial velocity v = final velocity 🔹 First Equation of Motion v = u + at 🔹 Second Equation of Motion s = ut + ½at² 🔹 Third Equation of Motion v² = u² + 2as 🔹 Fourth Equation of Motion s = [(u + v)/2]t 🔹 Average Velocity Average Velocity = Total Displacement / Total Time For Uniform Acceleration: v_avg = (u + v)/2 🔹 Relative Velocity Velocity of A with respect to B: V_AB = V_A − V_B 🔹 Projectile Motion Horizontal Range: R = (u² sin2θ)/g Maximum Height: H = (u² sin²θ)/(2g) Time of Flight: T = (2u sinθ)/g 🔹 Free Fall v = gt s = ½gt² v² = 2gs 🔹 Graph Relations Slope of Position-Time Graph = Velocity Slope of Velocity-Time Graph = Acceleration Area under Velocity-Time Graph = Displacement 🎯 MUST REMEMBER v = u + at s = ut + ½at² v² = u² + 2as R = (u² sin2θ)/g H = (u² sin²θ)/(2g) T = (2u sinθ)/g

🌊 WAVES — FORMULA SHEET 🔹 Wave Speed (v) v = fλ where, v = wave speed f = frequency λ = wavelength 🔹 Frequency (f) f = 1/T where, T = time period 🔹 Time Period (T) T = 1/f 🔹 Angular Frequency (ω) ω = 2πf ω = 2π/T 🔹 Wave Number (k) k = 2π/λ 🔹 General Wave Equation y = A sin(kx − ωt) where, A = amplitude k = wave number ω = angular frequency 🔹 Speed of Transverse Wave on a String v = √(T/μ) where, T = tension in string μ = mass per unit length 🔹 Intensity of a Wave I ∝ A² Intensity is directly proportional to the square of amplitude. 🔹 Phase Difference ϕ = 2π(Δx/λ) 🔹 Path Difference Δx = nλ Constructive Interference Δx = (2n+1)λ/2 Destructive Interference 🔹 Beat Frequency fᵦ = |f₁ − f₂| 🔹 Doppler Effect (Source Moving) f' = f[v/(v ∓ vₛ)] where, f' = apparent frequency f = actual frequency v = speed of sound vₛ = speed of source

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Science most important questions ❓ 🥳 you should learn ! 1. How does a carbon atom attain a noble-gas configuration? A carbon atom attains a noble-gas configuration by forming four covalent bonds with other atoms, allowing it to share its four valence electrons. By sharing electrons, carbon effectively achieves the stable octet configuration of neon (eight electrons in its outer shell). 2. Define catenation. Catenation is the ability of an element to form long chains or rings by bonding to atoms of the same element through covalent bonds. Carbon shows strong catenation, which enables the formation of complex organic molecules. 3. Write the number of covalent bonds present in propane. Propane (C3H8) contains 10 covalent single bonds: 2 C–C bonds and 8 C–H bonds, for a total of 10. 4. Define the term oxidising agent. An oxidising agent (oxidant) is a substance that gains electrons in a chemical reaction and, in doing so, causes another substance to be oxidised. Oxidising agents often contain an element in a relatively high oxidation state. 5. Write the formula for the first member of the ketone family. The simplest ketone is propanone (commonly called acetone), with formula C3H6O and structural formula CH3COCH3.

Gravitation - Formula Sheet 🔹 Universal Law of Gravitation: F = G(m₁m₂)/r² 🔹 Gravitational Field Intensity (g): g = GM/r² 🔹 Gravitational Potential (V): V = -GM/r 🔹 Gravitational Potential Energy (U): U = -GMm/r 🔹 Escape Velocity (vₑ): vₑ = √(2GM/R) 🔹 Orbital Velocity (vₒ): vₒ = √(GM/r) 🔹 Satellite Time Period (T): T = 2π√(r³/GM) 🔹 Relation Between Escape & Orbital Velocity: vₑ = √2 × vₒ

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