1. A-level Physics
Unit G481:
Mechanics
Units of
measurement

2. Units of measurement LOs
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)
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3. Lesson focus
• Units of measurement
Learning objectives
At 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.
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4. 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.
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5. Units of measurement LOs
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.
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6. Units of measurement LOs
Write the unit symbol and name for each of these frequently met
quantities:
length speed
area energy
electrical charge
volume
resistance
time interval
mass
angle
Motion To past paper compilation (units)

7. The SI system and base units LOs
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.
*Système Internationale
Motion To past paper compilation (unit conversion)

8. Prefixes and standard form LOs
decimal number number (word) prefix name of prefix standard form
equivalent
quadrillion P
trillion T
billion
1 000 000
1000 thousand k x 103
m
0.000001 millionth μ
f
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9. Converting units 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:
a) 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.
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10. 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
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11. Converting units LOs
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
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
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12. Derived units and base units LOs
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
force = mass x acceleration (F = ma)
units: N = kg x ms-2
So, one newton is equivalent to one kilogram metre per second squared
( 1 N = 1 kgms-2 ).
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13. Derived units and base units LOs
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
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14. Derived units and base units LOs
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
power =
time
J
Units: W =
s
So, one watt is equivalent to one joule per second ( 1 W = 1 J s-1 )
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15. Derived units and base units LOs
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 )
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16. Estimation LOs
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.
Motion To past paper compilation