Which of these is a vector?

force. A force acts in a direction. Energy, mass and time only have a size.

A student times 10 swings of a pendulum instead of 1. Why?

It makes the reaction-time error a smaller fraction of the reading. The reaction-time error is about the same either way, so spreading it over 10 swings makes it matter less.

Which instrument is best for measuring the diameter of a wire about 1 mm thick?

a micrometer screw gauge. A micrometer reads to 0.01 mm. A rule only reads to the nearest millimetre.

Forces of 6 N and 8 N act at right angles on an object. What is the resultant force?

10 N. √(6² + 8²) = √100 = 10 N.

30 cm³ of water is in a measuring cylinder. A stone is lowered in and the level reads 42 cm³. What is the volume of the stone?

12 cm³. The stone pushes aside its own volume of water: 42 − 30 = 12 cm³.

Which list contains only scalars?

distance, speed, energy. Distance, speed and energy have no direction. Velocity, force, weight and acceleration all do.

Measuring, scalars and vectors · Cambridge IGCSE Co-ordinated Sciences (Double Award)

In plain words

Some quantities are just an amount: 5 kg, 20 seconds. Those are scalars. Others only make sense with a direction as well: 5 N pushing down, 20 m/s heading north. Those are vectors.

When something is too small or too quick to measure well, measure lots of them together and divide.

Three things to know

A scalar has size only (distance, speed, mass, energy, time). A vector has size and direction (displacement, velocity, force, acceleration, momentum).
Measure a small length or time by measuring many and dividing: the thickness of 100 sheets, the time for 20 swings.
Two vectors at right angles combine by Pythagoras: resultant² = a² + b².

Worked example

A student times 10 swings of a pendulum as 14.5 s. What is the time for one swing?

Ten swings were timed, so divide by 10.
14.5 ÷ 10 = 1.45 s.

Tips and tricks

Vector or scalar? Ask "does it have a direction?" Weight pulls downwards, so it's a vector. Mass doesn't point anywhere, so it's a scalar.
Reading a ruler or a measuring cylinder: put your eye level with the mark, and say so in practical questions. It's a standard mark.

6 questions, about 2 minutes.

It lands in your notebook with its questions as flashcards.

Measuring, scalars and vectors: 6 questions and answers

These are the quiz’s questions. Do the quiz first, then come back here for the ones that got you.

Which of these is a vector?
- energy
- mass
- force (the answer)
- time
A force acts in a direction. Energy, mass and time only have a size.
A student times 10 swings of a pendulum instead of 1. Why?
- It makes the pendulum swing more slowly.
- It makes the reaction-time error a smaller fraction of the reading. (the answer)
- It makes each swing take the same time.
- Stopwatches cannot measure one swing.
The reaction-time error is about the same either way, so spreading it over 10 swings makes it matter less.
Which instrument is best for measuring the diameter of a wire about 1 mm thick?
- a metre rule
- a measuring cylinder
- a micrometer screw gauge (the answer)
- a tape measure
A micrometer reads to 0.01 mm. A rule only reads to the nearest millimetre.
Forces of 6 N and 8 N act at right angles on an object. What is the resultant force?
- 2 N
- 10 N (the answer)
- 14 N
- 48 N
√(6² + 8²) = √100 = 10 N.
30 cm³ of water is in a measuring cylinder. A stone is lowered in and the level reads 42 cm³. What is the volume of the stone?
- 12 cm³ (the answer)
- 30 cm³
- 42 cm³
- 72 cm³
The stone pushes aside its own volume of water: 42 − 30 = 12 cm³.
Which list contains only scalars?
- velocity, mass, time
- force, energy, speed
- distance, speed, energy (the answer)
- weight, distance, acceleration
Distance, speed and energy have no direction. Velocity, force, weight and acceleration all do.

6 questions

Tap an answer and you’ll see straight away whether it’s right, and why.

Worksheet

4 questions, 9 marks. Write your answers on paper, then check them.

Measuring, scalars and vectors

Cambridge IGCSE Co-ordinated Sciences (Double Award) 0654 · 9 marks · papermunch.org

Name ______________________________ Date ______________

A stack of 50 sheets of paper is 6.0 mm thick. Calculate the thickness of one sheet.[2]
Show answerHide answer
0.12 mm. Thickness = 6.0 ÷ 50.
I got this one
A pendulum takes 28.0 s to make 20 complete swings. Calculate the period of one swing.[2]
Show answerHide answer
1.4 s. Period = 28.0 ÷ 20.
I got this one
A boat is driven north by a force of 30 N while the wind pushes it east with a force of 40 N. Calculate the size of the resultant force.[3]
Show answerHide answer
50 N. Resultant = √(30² + 40²) = √2500.
I got this one
State which of these are vectors: mass, weight, speed, velocity, temperature.[2]
Show answerHide answer
Weight and velocity. Both have a direction; the others have size only.
I got this one

Answers: Measuring, scalars and vectors

1. 0.12 mm. Thickness = 6.0 ÷ 50.
2. 1.4 s. Period = 28.0 ÷ 20.
3. 50 N. Resultant = √(30² + 40²) = √2500.
4. Weight and velocity. Both have a direction; the others have size only.