• The metre rule and half-metre rule are used to measure lengths to a precision of 0.1 cm.

• A vernier caliper is used to measure lengths to a precision of 0.01 cm.• A micrometer is used to measure length to a precision of 0.01 mm.

1.5 How do we measure length?

• Correct way to read the scale on a ruler• Position eye perpendicularly at the mark on the scale

to avoids parallax errors • Another reason for error: object not align or arranged

parallel to the scale

1.5 How do we measure length?

Zero Error• Many instruments do not read exactly zero when nothing is being

measured• Happen because they are out of adjustment or some minor fault in the

instrument• Add or subtract the zero error from the reading shown on the scale to

obtain accurate readings

1.5 How do we measure length?

• The table below shows the range and precision of some measuring instruments

Instrument Range of measurement

Accuracy

Measuring tape 0 − 5 m 0.1 cm

Metre rule 0 − 1 m 0.1 cm

Vernier caliper 0 − 15 cm 0.01 cm

Micrometer screw gauge

0 − 2.5 cm 0.01 mm

1.5 How do we measure length?

Vernier Caliper• allows measurements up to 0.01 cm• Consists of a 9 mm long scale divided into 10 divisions

1.5 How do we measure length?

Vernier Caliper• The object being measured is between 2.4 cm and 2.5 cm long.• The second decimal number is the marking on the vernier scale which

coincides with a marking on the main scale

1.5 How do we measure length?

Vernier Caliper•Here the eighth marking on the vernier scale coincides with the marking at C on the main scale•Therefore the distance AB is 0.08 cm, i.e. the length of the object is 2.48 cm

1.5 How do we measure length?

1.5 How do we measure length?Using the Vernier Caliper

Micrometer Screw Gauge• Used to measure diameter of fine wires, thickness of paper and small

lengths• The micrometer has two scales:

– Main scale on the sleeve – Circular scale on the thimble

• There are 50 divisions on the thimble.• One complete turn of the thimble moves the spindle by 0.50 mm.

1.5 How do we measure length?

Micrometer Screw Gauge• Two scales: main scale and circular scale• One complete turn moves the spindle by 0.50 mm.• Each division on the circular scale = 0.01 mm

1.5 How do we measure length?

1.5 How do we measure length?Using the micrometer

Precautions when Using a Micrometer1. Never tighten thimble too much

– Modern micrometers have a ratchet to avoid this2. Clean the ends of the anvil and spindle before making a measurement

– Any dirt on either of surfaces could affect the reading3. Check for zero error by closing the micrometer when there is nothing

between the anvil and spindle– The reading should be zero, but it is common to find a small

zero error– Correct zero error by adjusting the final measurement

1.5 How do we measure length?

Time• Measured in years, months, days, hours, minutes and

seconds• The SI unit for time is the second (s).

1.6 How do we measure time?

Stopwatch• Measure short intervals of time• Two types: digital stopwatch, analogue stopwatch• Digital stopwatch more accurate as it can measure time in intervals

of 0.01 seconds.• Analogue stopwatch measures time in intervals of 0.1 s.

1.6 How do we measure time?

Errors Occur in Measuring Time • If a digital stopwatch is used to time a race, should

not record time to the nearest 0.01 s. • This is because the reaction time in starting and

stopping the watch will be more than a few hundredths of a second.

• Here an analogue stopwatch would be just as useful.

1.6 How do we measure time?

Ticker-tape Timer

• An electrical device making use of the oscillations of a steel strip to mark short intervals of time

• Steel strip vibrates 50 times a second and makes 50 dots a second on a paper tape being pulled past it

1.6 How do we measure time?

Ticker-tape Timer• Time interval between two consecutive dots is 0.02 s.• If there are 10 spaces on a pieces of tape, time taken is 10 × 0.02 s

= 0.20 s • Counting of the dots starts from zero.• A 10–dot tape is shown below.

1.6 How do we measure time?

Period of a pendulum• The oscillation of a simple pendulum is an example of

a regularly repeating motion.• The time for 1 complete oscillation is referred to as

the period of the oscillation.

1.6 How do we measure time?