Coherent Derived Units
A coherent SI derived unit is obtained from a quantity equation without an extra numerical factor, so its expression in base units is a product of integer or rational powers of SI base units.
Why this shows up in the exam
Reading engineering specifications · Checking equation outputs · Converting named units to base form
Learn the idea
Named units such as newton, joule, pascal, and watt are compact names for products of SI base units. A named derived unit is only shorthand; opening the shorthand exposes the mechanics or field equation that defines it.
🧠 Memory hook: Open the unit name before comparing it.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- N = kg m s⁻² — newton from F = ma
- J = kg m² s⁻² — joule from work or energy
- Pa = kg m⁻¹ s⁻² — pascal from force per area
- W = kg m² s⁻³ — watt from energy per time
How to approach it
- 1Write the defining quantity equation
- 2Replace each quantity by base units
- 3Collect powers and compare
Common slip-ups that cost marks
- •Comparing unit names without expansion
- •Confusing joule and watt
- •Dropping inverse powers in pascal
🌟 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?
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