How to linearize data
Rearrange the equation into the form y = mx + b, where y and x are things you can calculate from the data. For a pendulum, T = 2π√(L/g) becomes T² = (4π²/g)L, so graph T² as a function of L: the slope is 4π²/g. Calculate the new column, plot it, draw one straight best-fit line, and take the slope from two points on the line that are far apart (not from data points). The slope’s units are the vertical-axis unit divided by the horizontal-axis unit. Then solve for the quantity: g = 4π² ÷ slope.
How answers are marked: a slope counts within 5% of the least-squares slope, and the quantity counts when it follows from an accepted slope, including your own. Plot the points for me draws your graph on screen; on paper the grid is blank, so you label the axes and choose the scales, as on the exam.
Example: a pendulum
In set PENDUM, the period for L = 0.50 m is 1.43 s, so T² = 1.43² = 2.04 s². On the graph of T² as a function of L, the best-fit line passes through (0.200, 0.784) and (0.950, 3.84): slope = (3.84 − 0.784) ÷ (0.950 − 0.200) = 4.07 s²/m. Then g = 4π² ÷ 4.07 = 9.70 m/s². Open set PENDUM
Questions
How do you linearize data in physics?
Rearrange the equation so one side is a quantity you can calculate and the other is a constant times another quantity you can calculate. Graph those two quantities. If the equation is right, the points lie on a straight line and the slope is the constant.
What do you graph for a pendulum to get a straight line?
T² as a function of L. Squaring T = 2π√(L/g) gives T² = (4π²/g)L, so the slope is 4π²/g and g = 4π² ÷ slope. Graphing T against √L also works, with slope 2π/√g.
How do you find the slope of a best-fit line?
Pick two points on your line, far apart, that sit on clear grid lines. Do not use data points unless they lie exactly on the line. Slope = (change in vertical) ÷ (change in horizontal), with units.
What are the units of the slope?
The unit on the vertical axis divided by the unit on the horizontal axis. A graph of T² in s² against L in m has a slope in s²/m. A graph of 1/sᵢ against 1/s₀, both in 1/cm, has no unit.
What does the intercept tell you?
It is the value on the vertical axis when the horizontal quantity is zero. For a thin lens graph of 1/sᵢ against 1/s₀ the intercept is 1/f. For most other graphs here it should be close to zero; a large intercept points to a systematic error.
Can I give my class the same data?
Yes. Share with class copies a link with the set code, and everyone who opens it gets the same table. Printed class sets give each student different numbers for the same experiments, each with its own key.
Sources, read October 27, 2026: College Board, AP Physics 1 Course and Exam Description (updated summer 2026: “In the Experimental Design and Analysis question on the exam, students will also be asked to linearize and analyze data”; sample question 3 and its scoring) and AP Physics 2 Course and Exam Description (resistivity, thin lenses, Snell’s law). g = 9.81 m/s².