THE UNIVERSITY OF MALTA MATSEC SUPPORT UNIT

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1 THE UNIVERSITY OF MALTA MATSEC SUPPORT UNIT PHYSICS FORMULAE AND DATA BOOKLET This booklet is not to be removed from the examination room or marked in any way.

3 THE UNIVERSITY OF MALTA MATSEC SUPPORT UNIT PHYSICS FORMULAE AND DATA BOOKLET The following equations and formulae may be useful in answering some of the questions in the examination.

4 Table of Contents Uniformly accelerated motion... 3 Mechanics... 3 Circular motion and rotational dynamics... 3 Simple harmonic motion... 4 Ray optics... 4 Current electricity... 5 Alternating current... 5 Stationary waves... 6 Wave motion... 6 Fields... 6 Capacitance... 7 Inductance... 7 Electromagnetism... 8 Temperature... 8 First and second laws of thermodynamics... 9 Gases... 9 Materials... 9 Heat transfer Quantum phenomena Radioactivity Mathematical Formulae Physical Constants

5 Uniformly accelerated motion Equations of motion: v = u + at v 2 = u 2 + 2as u + v s = ( 2 ) t s = ut at2 Mechanics Newton s second law: Kinetic Energy: Potential Energy: Mechanical Work Done: Power: Momentum: F = ma = d(mv) dt KE = 1 2 mv2 PE = Δ(mgh) W = FΔd P = Fv p = mv Circular motion and rotational dynamics Angular speed: Angular acceleration: Centripetal acceleration: ω = dθ dt = v r α = dω dt = a r a = v2 r 3

6 Centripetal force: Period: Torque: F = mv2 r T = 2π r v τ = Iα Work done in rotation: τθ = Δ ( 1 2 Iω2 ) Simple harmonic motion Displacement: Velocity: x = x 0 sin(ωt + φ) v = ωx 0 cos(ωt + φ) v = ±ω x 0 2 x 2 Acceleration: Period: Mass on a light spring: a = kx = ω 2 x T = 1 f = 2π k = 2π ω T = 2π m k Ray optics Refractive index: n 1 sin θ 1 = n 2 sin θ 2 1n2 = sin θ 1 = v 1 sin θ 2 v 2 1n3 = 1 n 2 2 n 3 Thin lenses: 1 f = 1 u + 1 v 4 (real is positive)

7 Magnification: 1 f = 1 v 1 u m = v u = h i h o m = v u = h i h o (Cartesian) (real is positive) (Cartesian) Current electricity Ohm s Law: Current: Resistors in series: Resistors in parallel: Power: Resistivity: V = IR I = nave R TOTAL = R 1 + R = R TOTAL R 1 R 2 P = IV = I 2 R = V2 R ρ = RA l Temperature coefficient: α = R θ R 0 R 0 θ Alternating current For sinusoidal alternating current: Root mean square for sinusoidal alternating current and voltage: I = I 0 sin 2πft I rms = I V rms = V 0 2

8 Reactance: X L = 2πfL X C = 1 Stationary waves 2πfC Speed of waves on strings: v = T μ Wave motion Velocity of a wave: Two slit interference: Diffraction grating: Single slit diffraction: Diffraction of circular aperture: v = fλ s = λd d d sin θ = nλ θ = λ a sin θ θ = 1.22 λ a Fields Electric field strength: E = F +q = dv dr Uniform field: Force between point charges: Electric field strength of a point charge: E = F +q = V d Q 1 Q 2 F = 4πε o r 2 Q E = 4πε o r 2 6

9 Force between point masses: F = G M 1M 2 r 2 Electric potential: V = Q 4πε 0 r Gravitational potential: V G = GM r Work: W = QV = Δ ( 1 2 mv2 ) Capacitance Charge on a capacitor: Capacitance of parallel plates: Capacitors in parallel: Capacitors in series: Energy stored: Charging: Discharging: Q = CV C = ε 0ε r A d C TOTAL = C 1 + C = C TOTAL C 1 C 2 W = 1 2 CV2 Q = Q 0 (1 e t RC) Q = Q 0 e t RC Inductance Mutual inductance: M = E di dt 7

10 Self-inductance: L = E di dt Energy stored: W = 1 2 LI2 Electromagnetism Force on wire: Torque on a rectangular coil: Force on moving charge: Magnetic flux: Field inside a solenoid: Field near a long straight wire: Induced emf: Emf induced in a moving conductor: Simple alternator emf: Hall voltage: F = BIl τ = BANI F = BQv Φ = BA B = μ 0 μ r ni I B = μ 0 2πr E = N d dt E = Blv V = V 0 sin (ωt + φ) V H = BI nqt Temperature Temperature (K): T = P P tr K 8

11 Celsius scale: θ( C) = T(K) K First and second laws of thermodynamics First law of thermodynamics: Ideal heat engine: ΔU = ΔQ + ΔW η = 1 T c T h Gases Ideal gas equation: Kinetic theory of an ideal gas: Boltzmann s constant: Principal molar heat capacities of an ideal gas: Adiabatic process: PV = nrt PV = 1 3 Nm c2 k = R N A γ = C P C V PV γ = constant C P C V = R Materials Hooke s law: Stress: Strain: Young s modulus: F = kδx σ = F A ε = Δl l Y = σ ε 9

12 Energy stored in a stretched wire: Heat transfer Thermal conduction: E = 1 2 k( l)2 dq dt = ka dθ dx Quantum phenomena Quantum energy: E = hf Mass-energy: E = mc 2 Photoelectric effect: hf = φ + ( 1 2 mv2 ) max Energy levels: ΔE = E 2 E 1 = hf = hc λ De Broglie wavelength: λ = h mv Radioactivity Decay rate: Half-life: Absorption law for gamma radiation: dn dt = λn A = λn N = N 0 e λt T1 = ln 2 2 λ I = I 0 e μd 10

13 Mathematical Formulae Surface area of a sphere: S = 4πr 2 Volume of a sphere: V = 4 3 πr3 Surface area of a cylinder: S = 2πrh + 2πr 2 Volume of a cylinder: Logarithms: V = πr 2 h ln(x n ) = nlnx ln(e kx ) = kx Equation of a straight line: y = mx + c Relationship between cosine and sine: Small angles: sin(90 θ) = cos θ sin θ tan θ θ(in radians) 11

14 Physical Constants Acceleration of free fall on and near the Earth s surface Gravitational field strength on and near the Earth s surface Mass of the Earth Radius of the Earth Boltzmann constant Molar gas constant Avogadro s constant g = 9.81 m s 2 g = 9.81 N kg 1 M E = kg r E = m k = J K 1 R = 8.31 J K 1 mol 1 N A = mol 1 Coulomb s law constant k = 1 4πε 0 = N m 2 C 2 Charge of an electron Rest mass of an electron Rest mass of a proton Rest mass of a neutron Electronvolt Gravitational constant Permittivity of free space Permeability of free space Planck constant Speed of light in a vacuum e = C m e = kg m p = 1.67(3) kg m n = 1.67(5) kg 1 ev = J G = N m 2 kg 2 ε 0 = F m 1 μ 0 = 4π 10 7 H m 1 h = J s c = m s 1 12

15 Unified atomic mass unit 1 u = kg 13

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