Module 2 of 9Lesson 1 of 21 · P01 Measuring length and time: SI units, vernier, micrometer, pendulum
BGCSE Science Double Award · Physics · Form 4 · Section 1 General physics
Lesson P01 · about 10 minutes

Measuring length and time: SI units, vernier, micrometer, pendulum

Put a 50 thebe coin on a ruler and you can only say “a couple of millimetres thick”. Close a micrometer on the same coin and it reads to one hundredth of a millimetre. Scientists, mechanics and jewellers all need that kind of accuracy — and the BGCSE examiners test measuring skills every year.

Prof KitsoIn 2024 most candidates got the Paper 1 micrometer question wrong. They ignored one small half-millimetre mark. After this lesson, you will not.
50 thebe coin ruler: to 1 mmmicrometer:to 0.01 mm 28.40 measure small things — and time many swings
Papers 1, 3 and 4Pendulum asked in 2 practical papers (2010, 2019)🔬 Scale reader + pendulum lab

Learn5 cards

Fundamental quantities and SI units

Every measurement is a number and a unit. have their own base . All other quantities are built from them.

Speed (m/s), volume (m³) and density (kg/m³) are derived quantities, not fundamental ones.

quantitySI unit lengthmetrem masskilogramkg timeseconds temperaturekelvinK electric currentampereA amount of substancemolemol
Learn these six pairs by heart.

Reading a vernier caliper

A reads to 0.01 cm (0.1 mm). First read the main scale just before the vernier zero: 2.4 cm.

Then find the one vernier line that lines up exactly with a main-scale line: here line 6. Add 6 × 0.01 cm.

2.4+0.06=2.46 cm2.4+0.06=2.46\text{ cm}
234cm0510main scale before the 0: 2.4 cmline 6 lines up → + 0.06 cm = 2.46 cm
Main scale first, then the matching vernier line.

Reading a micrometer

A reads to 0.01 mm. Read the sleeve first — and look for the 0.5 mm marks below the line.

One turn of the thimble moves 0.5 mm, so each of its 50 divisions is 0.01 mm. Add the thimble division on the datum line.

5.5+0.28=5.78 mm5.5+0.28=5.78\text{ mm}
05253028sleevethimblesleeve: 5.5 mm (half mark showing)thimble: 28 × 0.01 mm → 5.78 mm
The red half mark is the one most candidates miss.

Errors and accuracy

Close the jaws first. If the reading is not zero, that is a : subtract it from every reading.

Avoid : put your eye directly in line with the mark, at 90° to the scale.

The of an instrument is its smallest division. Record to it: 24.0 cm on a mm rule.

56789 ✓ eye in line: 7.0✗ eye to oneside: 7.5 eye at 90° to the scale
Same pointer, two eyes, two readings.

Timing a pendulum

The T is the time for one complete : A → B → A.

Your reaction time (about 0.2 s) adds an error each time you start or stop the stopwatch. So time 20 oscillations and divide by 20. Count each time the bob passes a mark at the centre.

T=time for 20 oscillations20T=\dfrac{\text{time for 20 oscillations}}{20}
AB lmarkone oscillation: A → B → A
Time many swings, then divide.

See it live

In the reader, set a random vernier or micrometer and type your reading. It tells you which part you misread. Try at least three micrometer settings with the half mark showing.

In the pendulum lab, time 1 swing, then 20 swings. See how much smaller the reaction-time error becomes, and test whether a heavier bob changes the period.

Vernier and micrometer readerNew scales every time — including the 0.5 mm trap
Pendulum timingTime 20 swings, divide by 20, beat your reaction time

Worked example3 examples

Example 1Grade C
A student measures the diameter of a small glass marble with a vernier caliper. The scales are shown. Find the diameter.
123cm0510
The vernier zero is between 1.3 and 1.4 cm. Line 4 lines up.
main scale1.3 cm (just before the vernier zero)
vernierline 4 lines up: 4×0.01=0.04 cm4\times0.01=0.04\text{ cm}
add1.3+0.041.3+0.04
answer1.34 cm1.34\text{ cm} (= 13.4 mm)
CheckIs 1.34 cm a sensible size for a small marble? Yes. Always ask whether your answer is a sensible size — it catches misreadings.
Example 2Grade B
When the micrometer is closed with nothing in it, it reads +0.02 mm. A student then measures a copper wire. The sleeve shows 0 mm and the 0.5 mm mark; thimble division 23 is on the datum line. Find the true diameter of the wire.
sleeve0.5 mm0.5\text{ mm} (the half mark is showing)
thimble23×0.01=0.23 mm23\times0.01=0.23\text{ mm}
reading0.5+0.23=0.73 mm0.5+0.23=0.73\text{ mm}
formulatrue reading = reading − zero error
substitute0.73−0.020.73-0.02
answer0.71 mm0.71\text{ mm}
Negative zero error?If the closed micrometer reads −0.03 mm, the rule is the same: reading − (−0.03), so you add 0.03 mm.
Example 3Grade A
A student times 20 oscillations of a pendulum. The stopwatch shows 00:28.40. Her reaction time is about 0.2 s.

(a) Find the period.

time00:28.40 = 28.40 s
formulaT=total timenumber of oscillations{T=\dfrac{\text{total time}}{\text{number of oscillations}}}
substituteT=28.4020{T=\dfrac{28.40}{20}}
answerT=1.42 sT=1.42\text{ s}

(b) Compare the timing error with timing just one oscillation.

one swing0.21.42×100\dfrac{0.2}{1.42}\times100
≈ 14 % error
20 swings0.228.40×100\dfrac{0.2}{28.40}\times100
≈ 0.7 % error
answertiming 20 swings makes the error about 20 times smaller
Stopwatch displaysChange the display to seconds before you calculate: 01:05.30 means 1 min 5.30 s = 65.30 s.

Misconception busterfrom the BEC examiner reports

Micrometer read as 5.28 mm — the 0.5 mm mark below the line was ignored.
Read both sides of the sleeve line: 5 mm + 0.5 mm + 0.28 mm = 5.78 mm.

Examiner report: 2024 Paper 1, Item 1

Length recorded as “24 cm” from a metre rule.
Record to the accuracy of the instrument: 24.0 cm (the rule reads to 0.1 cm).

Examiner report: 2023 Paper 4, Q1(a)

Weight, volume, density or speed named as a fundamental quantity.
Fundamental: length, mass, time, temperature, current, amount of substance. Speed and density are derived.

Examiner report: Physics (0571) 2023 Paper 1, item 3

“Avoid parallax error.” — and nothing more.
Say how: “place the eye directly in line with (perpendicular to) the reading on the scale.”

Examiner report: Physics (0571) 2023 Paper 4, Q2

Prof KitsoFor a “source of error” question, name a real cause — reaction time, zero error, parallax — and say how to reduce it. “Human error” earns nothing.

Quick check5 questions · Paper 1 style

1Which of these is a fundamental quantity?

  1. ✗ Not this one. Speed=distancetime{\text{Speed}=\dfrac{\text{distance}}{\text{time}}}, so it is derived from length and time.
  2. ✗ Not this one. Volume is length × length × length — derived.
  3. ✗ Not this one. Density=massvolume{\text{Density}=\dfrac{\text{mass}}{\text{volume}}} — derived.
  4. ✓ Right. Time is fundamental; its SI unit is the second (s).

2A micrometer sleeve shows 6 mm and the 0.5 mm mark below the line. Thimble division 15 is on the datum line. What is the reading?

  1. ✓ Right. 6 + 0.5 + 0.15 = 6.65 mm.
  2. ✗ Not this one. This ignores the 0.5 mm mark below the line — the 2024 Paper 1 trap.
  3. ✗ Not this one. This forgets to add the thimble reading.
  4. ✗ Not this one. The thimble 15 means 15 × 0.01 = 0.15 mm, not 15 mm.

3Which instrument measures the diameter of a thin wire (about 0.7 mm) most accurately?

  1. ✗ Not this one. A metre rule reads only to 1 mm — bigger than the wire itself.
  2. ✗ Not this one. A vernier reads to 0.1 mm: good, but not the best here.
  3. ✓ Right. A micrometer reads to 0.01 mm, the smallest division of these.
  4. ✗ Not this one. A tape reads to 1 mm at best and bends.

4A pendulum makes 20 oscillations in 30.0 s. What is its period?

  1. ✗ Not this one. This multiplies 30.0 by 20 instead of dividing.
  2. ✓ Right. T=30.020=1.50 s{T=\dfrac{30.0}{20}=1.50\text{ s}}
  3. ✗ Not this one. This is 2030.0\dfrac{20}{30.0} — upside down. It gives oscillations per second, not the period.
  4. ✗ Not this one. This divides by 10, not by the 20 oscillations counted.

5Why does a student time 20 oscillations instead of one?

  1. ✗ Not this one. The period depends on the length, not on how many swings you count.
  2. ✗ Not this one. Errors are reduced, never removed completely.
  3. ✓ Right. About 0.2 s of error in 30 s is far smaller than 0.2 s in 1.5 s.
  4. ✗ Not this one. For small swings the period stays the same.

Exam cornerPaper 4 style · 9 marks

A student finds the period of a simple pendulum. The top of the string is level with the 12.0 cm mark on a vertical metre rule. The centre of the bob is level with the 76.0 cm mark. Fig. 1.1 shows the stopwatch after 20 oscillations.

metre rule 00:31.80 20oscillations
Fig. 1.1
(a)
Calculate the length l of the pendulum. [1]
(b)
Use Fig. 1.1 to calculate the period T of the pendulum. [2]
(c)
Explain why the student timed 20 oscillations, not one. [1]
(d)
State one source of error in measuring the time and how it can be reduced. [2]
(e)
Suggest how the student made sure the reading at the centre of the bob was accurate. [1]
(f)
The student now tests whether the mass of the bob affects the period. State two variables that must be kept constant. [2]
Model answer

(a)

subtract76.0−12.076.0-12.0
answerl=64.0 cml=64.0\text{ cm}

(b)

time00:31.80 = 31.80 s
formulaT=time20{T=\dfrac{\text{time}}{20}}
substituteT=31.8020{T=\dfrac{31.80}{20}}
answerT=1.59 sT=1.59\text{ s}

(c)

The reaction-time error (about 0.2 s) is shared over 20 oscillations, so it is a much smaller fraction of the time measured.

(d)

Error: the reaction time in starting and stopping the stopwatch.
Reduce it: repeat the timing and find the average, counting each time the bob passes a mark at the centre of the swing.

(e)

Placed the eye level with the centre of the bob, at 90° to the rule, to avoid parallax.

(f)

1. The length of the pendulum.
2. The angle from which the bob is released (the amplitude).
Marking key — how the examiner awards the marks
Mark pointMark
(a)64.0 cm (to 1 d.p., the accuracy of the rule)B1
(b)31.8020\dfrac{31.80}{20}C1
1.59 s (unit needed)A1
(c)reaction-time error is a smaller fraction of the total time / gives a more accurate periodB1
(d)error: reaction time in starting / stopping the stopwatch, or miscounting oscillationsB1
reduce: time more oscillations / repeat and find the average / count as the bob passes a mark at the centreB1
(e)eye level with the bob / eye perpendicular to the rule (avoids parallax); or set square from the bob to the ruleB1
(f)length of the pendulumB1
angle of release / amplitude (or number of oscillations timed)B1

Total: 9 marks

Examiner tip. Write the stopwatch time in seconds first. Give every length to the accuracy of the rule (64.0 cm, not 64 cm). For “source of error”, name the cause — never just “human error”.

Rememberone-page card to download

  • Fundamental quantities: length (m), mass (kg), time (s), temperature (K), current (A), amount of substance (mol).
  • Vernier: main scale before the zero + matching line × 0.01 cm. Accuracy 0.01 cm (0.1 mm).
  • Micrometer: sleeve (watch the 0.5 mm marks) + thimble × 0.01 mm. Accuracy 0.01 mm.
  • True reading = reading − zero error. Avoid parallax: eye at 90° to the scale.
  • Period = time for one complete oscillation. Time 20 and divide by 20 to cut the reaction-time error.

Formula card

vernier = main + (line × 0.01 cm)
micrometer = sleeve + (division × 0.01 mm)
true reading = reading − zero error
T=time for n oscillationsn{T=\dfrac{\text{time for }n\text{ oscillations}}{n}}n = number of oscillations
Download this card (PDF)

Science that earnsa skill you can sell

Sorting and labelling bolts for backyard mechanics

Many mechanics and spare-parts sellers keep tins of mixed bolts, nuts, washers and drill bits. Finding the right size wastes time every day.

With a vernier caliper you can measure each part to 0.1 mm, sort them by size (M6, M8, M10…) and label small boxes. Charge per workshop, then return each month to sort new stock.

Example costs
Digital vernier caliper (used for many jobs)P180
40 small plastic boxes and labelsP120
Transport for one monthP60
First-month costsP360
Income: 4 workshops × P150P600
Profit in the first monthP240

After the first month the caliper is paid for, so profit rises. Check your zero error every morning — a mechanic will not trust you twice.

Work only with the owner present, never near running engines or grinders, and wear gloves with oily or sharp parts. Never take parts away from the workshop.

Example figures only — check real prices and agree your charge with each owner first.

Syllabus checklist Tap when you can do it

← S14 Formula bank and the memory plan (no formula sheet in the exam)Next: P02 Distance, speed, velocity and acceleration →

Stadira Training Institute · Gaborone, Botswana · BGCSE Science Double Award (0569) Complete Tutor

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