Dimensions from Graphs and Slopes
For a graph of y against x, the slope Delta y/Delta x has dimensions [y][x]^-1 and the signed area integral y dx has dimensions [y][x], subject to the plotted variables and scale factors.
Why this shows up in the exam
Interpreting motion graphs · Extracting material constants · Checking experimental linearisation
Learn the idea
A graph's slope carries ordinate dimensions divided by abscissa dimensions, and its area carries their product. Axis labels are part of the physics: steepness and enclosed area inherit units from both axes rather than from either plotted quantity alone.
🧠 Memory hook: Slope is vertical over horizontal; area is vertical times horizontal.
Get this one clearly and it pays off every single time it shows up in the paper. 🎯
Formulas & facts to keep ready
- [slope] = [y][x]⁻¹ — dimension of graph slope
- [area] = [y][x] — dimension of area under a y-x graph
How to approach it
- 1Read both axis quantities and scale factors
- 2Form vertical change over horizontal change
- 3For area, multiply ordinate by the horizontal differential
Common slip-ups that cost marks
- •Using the angle drawn on paper as physical slope
- •Ignoring scaled axes
- •Giving graph area only the ordinate unit
🌟 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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