Part of JME-07 — Units, Measurements & Error Analysis

Key Formulae Quick Reference

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Common Dimensional Formulae:

  • Force: [MLT2MLT^{-2}], Energy: [ML^{2T}^{-2}], Power: [ML^{2T}^{-3}]
  • Pressure: [ML^{-1}$$T^{-2}], Momentum: [MLT1MLT^{-1}]
  • Planck's constant: [ML^{2T}^{-1}], G: [M^{-1}$$L^{3T}^{-2}]

Error Propagation:

  • Z = A +/- B: Delta(Z) = Delta(A) + Delta(B)
  • Z = A * B or A/B: DeltaZZ\frac{Z}{Z} = DeltaAA\frac{A}{A} + DeltaBB\frac{B}{B}
  • Z = AnA^n: DeltaZZ\frac{Z}{Z} = |n| * DeltaAA\frac{A}{A}
  • Z = ApA^p * BqB^q / CrC^r: DeltaZZ\frac{Z}{Z} = |p|*DeltaAA\frac{A}{A} + |q|*DeltaBB\frac{B}{B} + |r|*DeltaCC\frac{C}{C}

Unit Conversion: n2n_2 = n1n_1 * M1M2\frac{M_1}{M_2}^a * L1L2\frac{L_1}{L_2}^b * T1T2\frac{T_1}{T_2}^c

Instruments:

  • Vernier LC = 1 MSD - 1 VSD
  • Screw gauge LC = Pitch / Circular divisions

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