Advanced Higher Physics Formula Sheet

Advanced Higher Physics Formula Sheet: A Comprehensive Guide

This article serves as a comprehensive guide to the key formulas encountered in Advanced Higher Physics. It's designed to be a valuable resource for students preparing for exams, offering a structured overview of essential equations across various topics. Remember, understanding the underlying principles and derivations is crucial alongside memorizing the formulas. This sheet acts as a helpful tool, but not a replacement for thorough understanding.

Mechanics

Kinematics

• Displacement: Δx = **v_avg**t (where v_avg = (v_i + v_f)/2)
• Velocity: v = Δx/Δt
• Acceleration: a = Δv/Δt
• Equations of Motion (constant acceleration):
  • v = u + at
  • s = ut + ½at²
  • v² = u² + 2as
  • s = ½(u + v)t (where u = initial velocity, v = final velocity, a = acceleration, s = displacement, t = time)
• Projectile Motion:
  • Horizontal velocity (v_x) remains constant.
  • Vertical velocity (v_y) changes due to gravity.
  • Range (R) = (u²sin2θ)/g (where θ = launch angle, g = acceleration due to gravity)
  • Maximum height (H) = (u²sin²θ)/(2g)
• Relative Velocity: v_AB = v_A - v_B (where v_AB is the velocity of A relative to B)

Dynamics

• Newton's Second Law: F_net = ma (where F_net is the net force, m is mass, a is acceleration)
• Weight: W = mg (where g is acceleration due to gravity)
• Friction: F_f ≤ μR (where F_f is frictional force, μ is the coefficient of friction, R is the normal reaction force)
• Work done: W = Fscosθ (where F is force, s is displacement, θ is the angle between force and displacement)
• Kinetic Energy: KE = ½mv²
• Potential Energy (gravitational): PE = mgh (where h is height)
• Power: P = W/t = Fv (where P is power, t is time, v is velocity)
• Momentum: p = mv
• Impulse: I = Δp = FΔt
• Conservation of Momentum: m₁u₁ + m₂u₂ = m₁v₁ + m₂v₂ (in a closed system)
• Elastic Collision: Kinetic energy is conserved.
• Inelastic Collision: Kinetic energy is not conserved.
• Circular Motion:
  • Centripetal acceleration: a_c = v²/r = ω²r (where r is radius, ω is angular velocity)
  • Centripetal force: F_c = mv²/r = mω²r

Gravitation

• Newton's Law of Universal Gravitation: F = Gm₁m₂/r² (where G is the gravitational constant, m₁ and m₂ are masses, r is the distance between their centers)
• Gravitational Field Strength: g = GM/r² (where M is the mass of the gravitating body)
• Gravitational Potential: V = -GM/r
• Escape Velocity: v_e = √(2GM/r)

Waves

Wave Properties

• Wave speed: v = fλ (where v is wave speed, f is frequency, λ is wavelength)
• Intensity: I ∝ A² (where A is amplitude)
• Doppler Effect: f_o = f_s(v ± v_o)/(v ± v_s) (where f_o is observed frequency, f_s is source frequency, v is wave speed, v_o is observer velocity, v_s is source velocity; + for approaching, - for receding)

Superposition

• Principle of Superposition: The resultant displacement of two or more waves is the vector sum of their individual displacements.
• Interference: Constructive (waves in phase), Destructive (waves out of phase).
• Diffraction: Bending of waves around obstacles.
• Standing Waves: Formed by the superposition of two waves travelling in opposite directions.
• Nodes and Antinodes: Points of zero and maximum amplitude, respectively.

Electricity

Electrostatics

• Coulomb's Law: F = kq₁q₂/r² (where k is Coulomb's constant, q₁ and q₂ are charges, r is the distance between them)
• Electric Field Strength: E = F/q (where F is force, q is charge)
• Electric Potential: V = W/q (where W is work done)
• Electric Potential Energy: U = kq₁q₂/r

Current Electricity

• Ohm's Law: V = IR (where V is voltage, I is current, R is resistance)
• Resistance: R = ρL/A (where ρ is resistivity, L is length, A is cross-sectional area)
• Power: P = IV = I²R = V²/R
• Kirchhoff's Laws:
  • Junction Rule: The sum of currents entering a junction equals the sum of currents leaving the junction.
  • Loop Rule: The sum of potential differences around a closed loop is zero.
• Capacitance: C = Q/V (where Q is charge, V is voltage)
• Energy stored in a capacitor: E = ½CV²

Magnetism

• Magnetic Flux Density: B = F/(Il sinθ) (where F is force, I is current, l is length of conductor, θ is angle between B and I)
• Force on a moving charge in a magnetic field: F = Bqv sinθ (where q is charge, v is velocity)
• Force on a current-carrying conductor in a magnetic field: F = BIL sinθ

Nuclear Physics

• Radioactive Decay: N = N₀e^-λt (where N is the number of undecayed nuclei, N₀ is the initial number of nuclei, λ is the decay constant, t is time)
• Half-life: t_½ = ln2/λ
• Activity: A = λN
• Energy released in nuclear reactions: E = mc² (where m is mass defect, c is the speed of light)

Thermal Physics

• Ideal Gas Law: PV = nRT (where P is pressure, V is volume, n is number of moles, R is the gas constant, T is temperature)
• Kinetic Theory of Gases: KE_avg = (3/2)kT (where k is Boltzmann constant)
• Specific Heat Capacity: Q = mcΔT (where Q is heat energy, m is mass, c is specific heat capacity, ΔT is temperature change)
• Latent Heat: Q = mL (where L is latent heat)

Quantum Physics

• Photoelectric Effect: E_k = hf - φ (where E_k is kinetic energy of emitted electrons, h is Planck's constant, f is frequency, φ is work function)
• de Broglie Wavelength: λ = h/p (where p is momentum)
• Energy levels of a hydrogen atom: E_n = -13.6/n² eV (where n is the principal quantum number)

Further Considerations

This formula sheet provides a foundational overview. Advanced Higher Physics often requires deeper understanding of concepts, vector mathematics, and the application of these formulas in complex scenarios. Always refer to your course materials and textbooks for complete information and worked examples. Remember to practice applying these formulas through problem-solving to solidify your understanding and build confidence. Consistent effort and a systematic approach are key to success in Advanced Higher Physics. Good luck!