HSC Physics 1 Initial Notes

Part II Physics — First Paper 11

Chapter 5 Physical World and Measurement 5.1 Key Concepts & Theoretical Foundations Physics is the study of matter, energy, and their interactions, expressed quantitatively. Every quantitative statement rests on measurement: the comparison of a physical quantity with a chosen standard called a unit. Physical quantity A property of a body or phenomenon that can be measured and expressed as (numerical value) × (unit). Quantities are fundamental (base) or derived (built from base quantities by multiplication/division). The SI system defines seven mutually independent base quantities. All others—area, velocity, force, energy—are derived. The dimension of a quantity records how it is built from the base quantities mass [M], length [L], time [T], current [I], temperature [Θ], amount [N] and luminous intensity [J]. Dimensional analysis Writing a quantity as [MaLbT c . . . ] lets us (i) check equations for homogeneity—every additive term must share the same dimensions; (ii) derive the form of a relation up to a dimensionless constant; and (iii) convert units between systems. Its limitation: it cannot find dimensionless constants (like 1 2 or 2π) and fails for equations with more unknowns t

HSC 2027 Science — Teacher’s Guide 13 5.2 Master Formula Sheet Master Formula Sheet Vernier LC = 1 MSD −1 VSD = 1 MSD n Screw-gauge LC = pitch no. of circular divisions Reading = main scale + (coincidence × LC) Relative error = ∆x x , Percentage error = ∆x x × 100% If Q = ApBq Cr : ∆Q Q = p∆A A + q ∆B B + r∆C C [Force] = [MLT −2], [Energy] = [ML2T −2], [Pressure] = [ML−1T −2] Symbols: n = number of vernier divisions; MSD/VSD = main/vernier scale division; ∆x = absolute error. Units are SI throughout. 5.3 Tables, Diagrams & Visual Layouts Base quantity SI unit Symbol / dimension Length metre m, [L] Mass kilogram kg, [M] Time second s, [T] Electric current ampere A, [I] Temperature kelvin K, [Θ] Amount of substance mole mol, [N] Luminous intensity candela cd, [J] 0 1 2 3 4 5 6 7 8 Main Vernier zero mark Figure 1.1 — Vernier calliper: reading = main-scale value + (coinciding vernier line × LC). 5.4 Worked Mathematical Problems Worked Problem 5.1 (Dimensional derivation) The period T of a simple pendulum may depend on length ℓ, mass m, and gravitational acceleration g. Use dimensions to find the form of T. Solution. Assume T = k ℓambgc with k dimensionless. Dimensionally, [T] = [L]a[M]