Physics lab at home

Why this matters

Physics is an experimental science. Every equation in this course was accepted because measurements agreed with it, and every engineer and scientist spends part of their career collecting data, estimating its uncertaintyAn estimate of how far a measured result could be from the true value. and deciding whether it supports a conclusion. This lab uses a string, a small weight and a stopwatch to measure the acceleration due to gravity, g, to within a couple of percent. The method (plan, measure several times, reduce error, compare with a model) is the same one used in research and test labs.

The model

From the waves lesson, a simple pendulum of length L swinging through small angles has periodThe time for one full swing of the pendulum, found by timing many swings and dividing.

T = 2π · √(L / g)

Rearranged for g:

g = 4π² · L / T²

So measuring L and T gives g. Three assumptions hide in the model, and the procedure is designed to respect them:

1. Small angles. The formula is very accurate below about 15°. Pull the weight only a short way to the side (for a 1 m string, about 20 cm).
2. A point mass on a light string. Use a small, dense weight such as a large metal nut, a bundle of keys or a fishing sinker, on thin string or dental floss. Measure L to the centre of the weight.
3. No friction or drag. A dense weight keeps air drag small, and the swings should die away only slowly.

Measuring the period well

Your reaction timeThe delay in starting and stopping a stopwatch, roughly 0.1–0.2 s, which timing many swings spreads out. when starting and stopping a stopwatch is roughly 0.1–0.2 s. That error is huge compared with a single period of about 2 s. The fix is to time many swings and divide:

20 swings in 35.9 s   →   T = 35.9 / 20 = 1.795 s

The reaction-time error is now shared across 20 swings, so it drops to about 0.01 s per period. Start timing as the weight passes the lowest point (where it moves fastest, so the moment is easiest to judge) and count "zero" at that first pass.

Repeat each timing three times. If the three values differ by more than a few tenths of a second, you probably miscounted.

Worked example

L = 0.800 m and the average of three timings gives T = 1.795 s:

g = 4π² × 0.800 / 1.795² = 31.58 / 3.222 = 9.80 m/s²

How good is the answer?

A result without an uncertainty is only half an answer. For a formula like g = 4π²L/T², the relative uncertainties add, with the period counted twice because it is squared:

δg / g ≈ δL / L + 2 · δT / T

If you can measure L to ±0.5 cm (0.005 m) and T to ±0.01 s:

δL / L = 0.005 / 0.800 = 0.6%
2·δT/T = 2 × 0.01 / 1.795 = 1.1%
total  ≈ 1.7%   →   g = 9.80 ± 0.17 m/s²

The accepted value, about 9.81 m/s² (it varies slightly with latitude and altitude), lies well inside that range, so the experiment agrees with the model. If yours does not, look for a cause: a wrong length (measured to the knot instead of the centre of the weight), large swings, or a miscount.

A better method: several lengths

Measuring at one length tests one point. Measuring at three to five lengths and plotting T² against L is stronger. The model predicts a straight line through the origin with slopeThe gradient of the T²-versus-L line, which the model predicts equals 4π²/g. 4π²/g, so

g = 4π² / slope

A line fitted through several points averages out random errors, and a curve or an offset reveals systematicErrors that push results the same way every time, revealed by a curve or offset in a fitted line. ones. That is the habit to keep: test a model across a range, not at a single point. You can fit the slope by hand on graph paper, in a spreadsheet, or with a few lines of Python later in the Scientific Python course.

Optional: phone sensors

The free phyphox app (from RWTH Aachen University) turns a phone's accelerometer, gyroscope and microphone into lab instruments and includes a pendulum experiment. Only use the phone as the swinging weight if it is securely held in a bag hanging just above a bed or cushion, so a slip cannot damage it. Otherwise, use the phone simply as a stopwatch.

Safety

This lab is safe at home if you keep it simple: hang the string from a sturdy table edge, shelf bracket or door frame you can reach from the floor (no standing on chairs), keep the swing small, and keep it clear of glass, pets and young children.

Where this leads

This course gives you the physics vocabulary that engineering mechanics, thermodynamics, circuits and computational physics build on. The careers it serves require far more than any online course can provide. Engineers usually need a bachelor's degree in engineering (an ABET-accredited program is the standard route to licensure), and those whose work affects public safety pass the FE and PE exams and work under or as a licensed Professional Engineer: see NCEES (https://ncees.org). Physicists, chemists and materials scientists need at least a bachelor's degree with real laboratory coursework, and research roles usually need a graduate degree. Checked on 2026-10-23. Real designs always need review by a licensed engineer; the calculations in this course build intuition, not sign-off.

Quick recap

• g = 4π²L/T²; measure L to the centre of the weight and keep swings small.
• Time many swings to shrink reaction-time error.
• Relative uncertainty: δg/g ≈ δL/L + 2δT/T.
• Several lengths and a T²-versus-L plot test the model better than one point.

Try it

Open the Do tab and follow the steps to measure g at home.