Physical World, Units, Measurement and Kinematics
What this domain tests
Base units and dimensions, error propagation, significant figures, vernier and screw gauge readings, then straight-line and projectile kinematics with graph interpretation.
Core rules
- Seven SI base units: metre, kilogram, second, ampere, kelvin, mole, candela.
- Dimensional homogeneity: every term of a valid equation carries the same dimensions. Dimensional analysis cannot supply dimensionless constants or trigonometric factors.
- Errors: absolute errors add for sums and differences; relative (fractional) errors add for products and quotients; a power n multiplies the relative error by n.
- Vernier least count = 1 MSD − 1 VSD; screw gauge least count = pitch ÷ number of circular divisions.
- Uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
- Projectile: T = 2u sinθ/g, H = u²sin²θ/2g, R = u²sin2θ/g; maximum range at 45°.
Worked example
A ball is thrown at 20 m/s at 30° to the horizontal, with g = 10 m/s². Find the range and maximum height. R = u²sin2θ/g = (400 × sin60°)/10 = (400 × 0.866)/10 ≈ 34.6 m. H = u²sin²θ/2g = (400 × 0.25)/20 = 5.0 m. Note that sin²30° = 0.25, not 0.5.
Traps that cost marks
- Adding absolute errors when the quantities are multiplied.
- Carrying centimetres through a calculation instead of converting to metres first.
- Applying the uniform-acceleration equations when acceleration varies.
- Forgetting that horizontal velocity is constant while vertical velocity changes throughout a projectile's flight.