Conversion Between Unit Systems
If Q has dimensions M^aL^bT^c..., numerical measures n_1 and n_2 in two coherent systems satisfy n_1 M_1^aL_1^bT_1^c... = n_2 M_2^aL_2^bT_2^c..., expressing invariance of Q.
Why this shows up in the exam
SI-CGS conversion · Checking legacy data · Changing custom base-unit systems
Learn the idea
A physical quantity keeps its magnitude while its numerical value changes inversely with the chosen unit size. The same table can be 1 metre or 100 centimetres long; a smaller unit requires a larger numeral to represent the same physical amount.
🧠 Memory hook: Quantity stays fixed: numeral and unit scale inversely.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- n₂ = n₁ (M₁/M₂)ᵃ (L₁/L₂)ᵇ (T₁/T₂)ᶜ — numerical-value conversion between unit systems
- n₁ u₁ = n₂ u₂ — same physical quantity in two units
How to approach it
- 1Find the dimensional exponents
- 2Write each old base unit in new bases
- 3Apply every factor with its exponent
Common slip-ups that cost marks
- •Converting only the length factor of a compound unit
- •Reversing old-unit and new-unit ratios
- •Changing the physical value during conversion
🌟 That's the whole idea — you've got this. Try the practice set below; every question you attempt makes it stick a little harder.
Original chapter practice
Original questions for this chapter, not past-paper questions or an exact mapping to this individual concept.
A quantity Q is defined as Q = force^1 / speed^2. Which dimensional formula represents Q?
More from Physical World and Measurement
Dimensional analysis and formulas
Understand dimensional formulas, the principle of homogeneity, dimensional consistency, and how to use dimensional analysis to check equations and derive relationships.
Physical quantities and units
Learn about fundamental and derived physical quantities, SI units, supplementary units, and how units relate to the measurement of physical quantities.
Measurement tools and techniques
Explore the use and principles of common measuring instruments like vernier calipers and screw gauge, including least count, zero error, and practical measurement methods.
Errors in measurement
Study the types of errors in physical measurements, their classification, and how errors propagate in calculations and experiments.
Significant figures and calculations
Learn the rules for determining significant figures and applying them correctly in mathematical operations like multiplication and division.
Applications of units and dimensions
Apply your knowledge of units and dimensions to solve problems involving physical constants, mechanical and electromagnetic properties, and real-world scenarios like thermal expansion.