Mechanical Quantity Dimensions
Mechanical dimensions are obtained by substituting [x]=L, [m]=M, and [t]=T into defining equations such as F=ma, p=mv, W=Fs, pressure=F/A, and power=W/t.
Why this shows up in the exam
Verifying mechanics formulas · Interpreting material properties · Comparing energy and torque dimensions
Learn the idea
Force, momentum, energy, pressure, and power dimensions follow directly from Newtonian definitions. A short chain from length, mass, and time is safer than memorising a long table of mechanical dimensions.
🧠 Memory hook: Rebuild mechanics from F = ma and work = force times distance.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- [F] = M L T⁻² — force
- [p] = M L T⁻¹ — linear momentum
- [E] = M L² T⁻² — work or energy
- [P] = M L² T⁻³ — power
How to approach it
- 1Start from a definition
- 2Substitute M, L, and T
- 3Simplify exponents before matching
Common slip-ups that cost marks
- •Confusing momentum p with pressure P
- •Giving torque a different dimension from energy
- •Losing a time power when moving from energy to power
🌟 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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