Physical World, Units, Measurements and Kinematics
This domain covers the SI system, dimensions, errors and instruments, then straight-line motion, projectiles and relative velocity - the toolkit every later mechanics chapter relies on.
Core rules
- Seven SI base units: metre, kilogram, second, ampere, kelvin, mole, candela.
- Dimensional analysis checks equations and converts units, but cannot supply dimensionless constants.
- Error propagation: for z = a^p b^q/c^r, the fractional error is p(Δa/a) + q(Δb/b) + r(Δc/c).
- Vernier callipers least count = 1 MSD − 1 VSD; screw gauge least count = pitch/number of circular-scale divisions.
- Equations of motion: v = u + at, s = ut + ½at², v² = u² + 2as.
- Projectile: T = 2u sinθ/g, H = u² sin²θ/2g, R = u² sin2θ/g, with maximum range at 45°.
- Relative velocity v(AB) = v(A) − v(B).
Worked example
A ball is projected at 20 m s⁻¹ at 30° to the horizontal with g = 9.8 m s⁻². Range R = u² sin2θ/g = 400 × sin60°/9.8 = 400 × 0.866/9.8 ≈ 35 m. Time of flight T = 2 × 20 × 0.5/9.8 ≈ 2.0 s.
Traps
Adding percentage errors without multiplying by the powers; pairing sin2θ = 1 with problems where launch and landing heights differ; applying the screw-gauge zero error with the wrong sign - it is subtracted when positive.