Scientific units

A-level Physics

Unit G481: Mechanics

Units of measurement

Motion

To do - in pairs

Write a list of units – names and symbols if possible – and as many as you can.

To get you started: the volt (symbol: V)

Units of measurement LOs

Learning objectivesAt the end of the lesson you will be able to:

• explain that some physical quantities consist of a numerical magnitude and a unit;

• use correctly the named units listed in the specification;

• use prefixes correctly;

• make suitable estimates of physical quantities.

Lesson focus• Units of measurement

Motion

Learning outcomes

All can• recall the SI base units for length, time, mass, and the derived units for speed,

velocity, acceleration, force and energy;

• recall the prefixes for a thousand, million, thousandth and millionth, and can express them in standard form;

• estimate the mass of a typical human, and dimensions of a classroom.

Most can• recall six SI base units and the derived units for power, resistance, acceleration,

force and energy;

• recall the standard form equivalents of giga, tera, nano and pico;

• estimate the speed of sound in air.

Motion

Motion

Physics can be regarded as the study of matter, energy, fields and waves, and

has been described as the science of measurement. Measurements are

usually made by counting. Saying, for example, that a running track is 400 m

long means that its length is 400 lots of 1m or, in other words, 400 x 1m.

Key ideas:

• A measurement is the product of a pure number and a unit.

• Units of measurement are written in the singular (e.g. 400 m not 400

ms)

• A measurement must have its unit specified.


Motion

Write the unit symbol and name for each of these frequently met

quantities:

length

area

volume

time interval

mass

angle

speed

energy

electrical charge

resistance

To past paper compilation (units)


The sizes of physical quantities are expressed using the SI* system. All SI units are

expressed in terms of seven, independent basic quantities, each with its own unit.

These are: quantity quantity symbol unit unit symbol

mass m kilogram kg

length l metre m

time t second s

temperature T kelvin K

electrical current I ampere A

amount of substance n mole mol

luminous intensity Iv candela cd

The seven SI base units are: kg, m, s, K, A, mol and cd.

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*Système Internationale

To past paper compilation (unit conversion)

The SI system and base units LOs

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decimal number number (word) prefix name of prefix standard form equivalent

quadrillion P

trillion T

billion

1 000 0001000 thousand k x 103

m0.000001 millionth μ

f

Prefixes and standard form LOs

Exercises

Express these quantities using the most appropriate prefix:

a) 0.0034 m b) 2378 N c) 1 245 000 J

d) 0.000 000 062 m e) 5900 g f) 0.005 s

g) 345 000 W h) 0.000 02 m

Convert the following numbers to standard form:

e) 3470 b) 68 000 000 c) 27

d) 0.594 e) 0.000 92 f) 264.2

g) 5555 h) 0.005555 i) 0.8354

k) 954 million l) 1/23 m) 1/354

n) A quarter of a million.

Motion

Converting units LOs

Convert

1. 25 cm to m 2. 37 mm to m 3. 0.1 cm to m

4. 0.5 mm to m 5. 200 m to cm 6. 5.6 m to mm

7. 0.5 mm2 to m2 8. 2.4 cm2 to m2 9. 4.0 m2 to cm2

10. 0.2 m2 to mm2

11. 6 340 000 000 J to kJ, MJ and GJ

12. 42 MJ to kJ and J

13. 4.5 x 10-4 m to mm

14. 3.6 x 10-3 m to mm

15. Give the volume of a cube of side 0.1 mm in m3

Motion


Convert each of the following quantities and express the answers in standard form (if appropriate):

a) 400 cm to m b) 24 x 104 mm into m c) 0.050 watt in mW

d) 2.5 x 10-3 kN to N e) n kW to W f) n milliwatt to W

g) 3.5 x 2.2 mA to A h) 3.4 x 103 x y gram to kg

Motion

Trickier

1. Convert an area of a) 350 cm2 to m2 b) 0.06 m2 to cm2

2. Convert a volume of b) 2.5 mm3 to m3 b) 0.07 m3 to mm3

3. Convert a density of 8 g per cm3 to kg per m3


Motion

Most units can be expressed as combinations of other, base, units. They are said

to be derived from these units. In the SI system, base units include the metre (m;

length), kilogram (kg; mass) and second (s; time). To convert a unit first find a

suitable equation. For example:

Q. Express the newton in base SI units.

A. The newton is the derived unit of force and

mass x acceleration (F = ma) force =

kg x ms-2

So, one newton is equivalent to one kilogram metre per second squared ( 1 N = 1 kgms-2 ).

units: N =

Derived units and base units LOs

Motion

Try converting these derived units into base units:

1. The pascal (Pa – the SI unit of pressure)

2. The joule (J – the SI unit of energy)

3. The watt (W – the SI unit of power)

Useful equations: p = F/A energy = ? P = E/t


Motion

Some units can be expressed as combinations of other, base units. In the

SI system the base units include the metre (m; length), kilogram (kg; mass)

and second (s; time). To convert a unit first find a suitable equation. For

example:

Q. Express the watt in base SI units.

A. The watt is the unit of power and

energy transferred

timepower =

J

sW =Units:

So, one watt is equivalent to one joule per second ( 1 W = 1 J s-1 )


Now try these:

Work out each SI derived unit in terms of the seven base units

1. frequency SI derived unit: Hz

2. force SI derived unit: N

3. pressure SI derived unit: Pa

4. energy SI derived unit: J

5. electrical resistance SI derived unit: Ω (hint: 1 V = 1 J/C and 1 C = 1 As )

Motion


Motion

To do – in pairs

Estimate the following (don’t forget the unit!):

1. the width of a football goal

2. the area of a tennis court

3. the volume of this lab

4. the time taken by a sprinter to run 200 m

5. the mass of a typical sixth form student

6. the angle made by the Sun (or Moon) at your eye

7. the speed of sound

8. the kinetic energy of an apple falling from a tree, just before it hits the ground.

To past paper compilation

Estimation LOs

Documents

Scientific units