Physical Quantities And Measurement Techniques

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Measurement of Length

Rulers measure small distances (cm) to the nearest millimetre.
Tape measures measure lengths of tens of centimetres.
Trundle wheels measure lengths of tens of metres.
For small objects, measure multiple (e.g., 4 ball-bearings) and divide by the number to find one dimension.

Trundle wheel

Measurement of Volume

Measuring cylinders measure the volume of liquids directly.
The volume of an irregular solid is found by the displacement method: measure the change in liquid volume.
Read the bottom of the meniscus at eye level for accuracy.

Measuring cylinders showing before and after readings

Measurement of Time

Stop-clocks and stopwatches measure time intervals.
Human reaction time (≈0.25 s) can cause significant error for short intervals.
To reduce uncertainty, measure the time for multiple oscillations (e.g., 10 swings) and divide by the number.
Use a fiducial marker (e.g., a line at equilibrium) to improve timing accuracy.

Two stopwatches showing the start and end of a lap

Multiple Readings & Accuracy

Taking multiple readings reduces the impact of random errors.
Example: measure thickness of 100 sheets of paper, then divide by 100 for average thickness of one sheet.
Two measurements are considered equal within experimental accuracy if they differ by less than 10%.

Taking multiple readings to improve accuracy

Scalars & Vectors

Scalar quantities have magnitude only (e.g., mass, distance, speed, energy).
Vector quantities have both magnitude and direction (e.g., weight, displacement, velocity, force).
Distance is the total path length (scalar); displacement is the straight‑line distance from start to finish (vector).
Speed is distance per unit time (scalar); velocity is displacement per unit time (vector).
An object can have constant speed but changing velocity if it changes direction.

Distance vs displacement

Examples of Scalars & Vectors

Scalars: distance, speed, mass, energy, volume, density, temperature, power.
Vectors: displacement, velocity, weight, force, acceleration, momentum.
Mass is a scalar; weight is a vector (force due to gravity).
Mass does not change with location; weight depends on gravitational field strength.

Examples of scalar and vector quantities

Slides

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Practice questions

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1.The diagram shows four identical ball-bearings placed between two blocks on a steel ruler. The total length of the four ball-bearings is 8 cm. Calculate the diameter of one ball-bearing in cm.
Easy
- A1
- B2
- C3
- D4
2.A stopwatch reads 0:55:10 at the start of a lap and 1:45:10 at the end. Calculate the time taken for the lap in seconds.
Easy
- A45
- B55
- C50
- D60
3.State the typical human reaction time for an alert person.
Easy
4.What is a scalar quantity?
Easy
5.What is a vector quantity?
Easy
6.Distance is a scalar quantity.
Easy
True or false?
7.Displacement is a scalar quantity.
Easy
True or false?
8.Match each quantity to its type (scalar or vector).
Easy
- distance
- displacement
- speed
- velocity
- scalar
- vector
- scalar
- vector

More questions

9.Complete the sentence.
Easy
The time for 10 swings of a pendulum is measured and divided by 10 to reduce the effect of ____.
10.Which of the following is a vector quantity?
Easy
- Amass
- Benergy
- Cweight
- Dvolume
11.Which instrument is used to measure the volume of a liquid accurately?
Easy
- AMeasuring cylinder
- BRuler
- CTape measure
- DTrundle wheel
12.A scalar quantity has both magnitude and direction.
Easy
True or false?
13.A student measures the time for 20 oscillations of a pendulum and obtains 30.0 s. What is the time period of the pendulum?
Easy
- A0.67 s
- B1.5 s
- C30.0 s
- D600 s
14.Which of the following are scalar quantities? (Select all that apply)
Medium
- AEnergy
- BWeight
- CAcceleration
- DVolume
- EMomentum
15.Arrange the following steps in the correct order to accurately measure the thickness of a single sheet of paper using a ruler.
Medium
- Measure the thickness of a stack of 100 sheets of paper.
- Divide the measured thickness by 100.
- Record the measurement.
- Place the stack on a flat surface.
16.A student places 8 identical coins in a pile. The height of the pile is 2.4 cm. What is the average thickness of one coin?
Easy
- A0.3 cm
- B0.4 cm
- C3.0 cm
- D19.2 cm
17.Select all the scalar quantities from the list below.
Medium
- AWeight
- BSpeed
- CAcceleration
- DVolume
- EDisplacement
18.Arrange the following steps in the correct order to accurately measure the time period of a pendulum using a stopwatch and a fiducial marker.
Medium
- Set the pendulum swinging
- Place a fiducial marker at the equilibrium position
- Start the stopwatch as the pendulum passes the marker
- Measure the time for 10 oscillations
- Calculate the time period by dividing by 10
19.A car travels 200 m north, then 100 m south. What is the displacement of the car from its starting point?
Medium
- A100 m north
- B100 m south
- C300 m north
- D300 m south
20.Which of the following are vector quantities? (Select all that apply)
Medium
- Aweight
- Benergy
- Cacceleration
- Dmomentum
- Edensity
21.A stopwatch reads 1:20.00 at the start of an experiment and 2:05.50 at the end. Calculate the time interval in seconds.
Medium
22.A student measures the time for 50 drops of water to fall from a tap as 20 s. Calculate the average time between two drops falling.
Easy
23.A student collects 0.21 kg of water. Calculate the weight of this water. (Take gravitational field strength g = 10 N/kg)
Easy
24.State the instrument used to measure the volume of a liquid accurately.
Easy
25.A student measures the time for 30 oscillations of a pendulum and records 42.0 s. Calculate the time for one oscillation. Give your answer to 3 significant figures.
Medium
26.Complete the sentence:
Easy
The instrument used to measure the volume of a liquid accurately is a ____.
27.A student uses a stopwatch to measure the time for 20 flashes of an LED. The stopwatch reading at the start is 0.00 s and at the end is 16.4 s. Calculate the average time between flashes.
Medium
28.Explain why taking multiple readings of the time for a pendulum to complete 10 oscillations gives a more accurate value for the time period than measuring just one oscillation.
Medium
29.Describe how to determine the volume of an irregularly shaped solid using a measuring cylinder and water.
Medium
30.A stopwatch reads 1:20.00 at the start of an experiment and 2:05.50 at the end. Calculate the time interval in seconds.
Medium
- A50 s
- B54.5 s
- C45.5 s
- D41 s
31.A student measures the time for 50 drops of water to fall from a tap as 20 s. Calculate the average time between two drops falling.
Medium
- A1.4 s
- B-0.6 s
- C0.4 s
- D2.4 s
32.A student collects 0.21 kg of water. Calculate the weight of this water. (Take gravitational field strength g = 10 N/kg)
Easy
- A1.1 N
- B3.1 N
- C2.1 N
- D4.1 N
33.A student measures the time for 30 oscillations of a pendulum and records 42.0 s. Calculate the time for one oscillation. Give your answer to 3 significant figures.
Medium
- A1.4 s
- B3.4 s
- C0.4 s
- D2.4 s
34.A student uses a stopwatch to measure the time for 20 flashes of an LED. The stopwatch reading at the start is 0.00 s and at the end is 16.4 s. Calculate the average time between flashes.
Medium
- A-0.18 s
- B2.82 s
- C0.82 s
- D1.82 s

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