1a Measurements & units
2022年11月24日 11:07
Number Prefixes
Prefix Meaning 10x notation
T (𝑡𝑒𝑟𝑎) 1000 000 000 000 1012
G (𝑔𝑖𝑔𝑎) 1000 000 000 109
M (𝑚𝑒𝑔𝑎) 1000 000 106
k (𝑘𝑖𝑙𝑜) 1000 103
d (𝑑𝑒𝑐𝑖) 1/10 10-1
c (𝑐𝑒𝑛𝑡𝑖) 1/100 10-2
m (𝑚𝑖𝑙𝑙𝑖) 1/1000 10-3
μ (𝑚𝑖𝑐𝑟𝑜) 1/1000 000 10-6
n (𝑛𝑎𝑛𝑜) 1/1000 000 000 10-9
p (𝑝𝑖𝑐𝑜) 1/1000 000 000 000 10-12
SI Units
Quantity Unit Symbol
mass kilogram kg
length metre m
time second s
current ampere A
temperature kelvin K
Amount of substance mole mol
luminous candela cd
Significant figures
• Use the lowest significant figure of data in the calculation
Measuring length
Large objects (several metres) Tape Low precision
~ few mm to 1 cm
Medium (several centimetres) Ruler Medium precision
~ 1 mm
Small (several millimetres) Vernier calipers High precision
~ 0.1 mm
Small (several millimetres) Micrometer Highest precision
~ 0.01 mm
Measuring time
• Time intervals of seconds or minutes can be measured using a stopclock or stopwatch.
• When humans are involved measuring short time intervals (a few seconds or less) can be difficult –
this is because of human reaction time (215 ms on average)
• This can be overcome in two ways:
○ Automated timing
○ Measuring time of several repeats
Page 1
, 1b Volume & density
2022年11月24日 11:07
Volume
• A measure of how much space an object takes up
• Volume units
• SI unit = m3
• 1 litre = 10-3 m3
• 1 millilitre = 10-6 m3 = 1 cm3
Measuring volume
Liquid Measuring cylinder
Regular solids Calculated using mathematics
Irregular solids Displacement
Large objects Displacement can
Mass and weight
• Mass: a measure of the amount of substance in an object
• All objects are attracted to the Earth by gravity - the greater the mass of an object, the stronger the
Earth's pull
• Weight: the Earth's gravitational force on an object
• All objects resist attempts to make them go faster, slower, or in a different direction - the greater
the mass of an object, the stronger the resistance to change in motion
Measuring mass
A several grams Balance
Kilograms Newton scales
Density
• A measure of how much mass can fit in a volume.
𝑚𝑎𝑠𝑠 𝑚
• density = ⎯⎯⎯⎯⎯⎯⎯ 𝜌 = ⎯⎯
𝑣𝑜𝑙𝑢𝑚𝑒 𝑣
• SI derived unit of density = kg/m3
• 1 g/cm3 = 1000 kg/m
Page 2
, 2a Speed, velocity & acceleration
2022年11月24日 11:07
• Speed: How fast something is moving
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑
• average speed = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• Velocity: The speed of something in a particular direction
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
• average velocity = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• Acceleration: A measure of how fast something changing its velocity (vector)
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣−𝑢
• average acceleration = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯𝑎 = ⎯⎯⎯⎯⎯
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 𝑡
Page 3
, 2b Motion graphs
2022年11月24日 11:07
Distance time Speed time
Horizontal line Stationary Moving at constant speed
Straight line Moving at constant speed Constant acceleration
Curve Accelerating Changing acceleration
Gradient Speed Acceleration
Area / Distance traveled
Page 4
2022年11月24日 11:07
Number Prefixes
Prefix Meaning 10x notation
T (𝑡𝑒𝑟𝑎) 1000 000 000 000 1012
G (𝑔𝑖𝑔𝑎) 1000 000 000 109
M (𝑚𝑒𝑔𝑎) 1000 000 106
k (𝑘𝑖𝑙𝑜) 1000 103
d (𝑑𝑒𝑐𝑖) 1/10 10-1
c (𝑐𝑒𝑛𝑡𝑖) 1/100 10-2
m (𝑚𝑖𝑙𝑙𝑖) 1/1000 10-3
μ (𝑚𝑖𝑐𝑟𝑜) 1/1000 000 10-6
n (𝑛𝑎𝑛𝑜) 1/1000 000 000 10-9
p (𝑝𝑖𝑐𝑜) 1/1000 000 000 000 10-12
SI Units
Quantity Unit Symbol
mass kilogram kg
length metre m
time second s
current ampere A
temperature kelvin K
Amount of substance mole mol
luminous candela cd
Significant figures
• Use the lowest significant figure of data in the calculation
Measuring length
Large objects (several metres) Tape Low precision
~ few mm to 1 cm
Medium (several centimetres) Ruler Medium precision
~ 1 mm
Small (several millimetres) Vernier calipers High precision
~ 0.1 mm
Small (several millimetres) Micrometer Highest precision
~ 0.01 mm
Measuring time
• Time intervals of seconds or minutes can be measured using a stopclock or stopwatch.
• When humans are involved measuring short time intervals (a few seconds or less) can be difficult –
this is because of human reaction time (215 ms on average)
• This can be overcome in two ways:
○ Automated timing
○ Measuring time of several repeats
Page 1
, 1b Volume & density
2022年11月24日 11:07
Volume
• A measure of how much space an object takes up
• Volume units
• SI unit = m3
• 1 litre = 10-3 m3
• 1 millilitre = 10-6 m3 = 1 cm3
Measuring volume
Liquid Measuring cylinder
Regular solids Calculated using mathematics
Irregular solids Displacement
Large objects Displacement can
Mass and weight
• Mass: a measure of the amount of substance in an object
• All objects are attracted to the Earth by gravity - the greater the mass of an object, the stronger the
Earth's pull
• Weight: the Earth's gravitational force on an object
• All objects resist attempts to make them go faster, slower, or in a different direction - the greater
the mass of an object, the stronger the resistance to change in motion
Measuring mass
A several grams Balance
Kilograms Newton scales
Density
• A measure of how much mass can fit in a volume.
𝑚𝑎𝑠𝑠 𝑚
• density = ⎯⎯⎯⎯⎯⎯⎯ 𝜌 = ⎯⎯
𝑣𝑜𝑙𝑢𝑚𝑒 𝑣
• SI derived unit of density = kg/m3
• 1 g/cm3 = 1000 kg/m
Page 2
, 2a Speed, velocity & acceleration
2022年11月24日 11:07
• Speed: How fast something is moving
𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑚𝑜𝑣𝑒𝑑
• average speed = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• Velocity: The speed of something in a particular direction
𝑑𝑖𝑠𝑝𝑙𝑎𝑐𝑒𝑚𝑒𝑛𝑡
• average velocity = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
• Acceleration: A measure of how fast something changing its velocity (vector)
𝑐ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑣𝑒𝑙𝑜𝑐𝑖𝑡𝑦 𝑣−𝑢
• average acceleration = ⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯⎯𝑎 = ⎯⎯⎯⎯⎯
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛 𝑡
Page 3
, 2b Motion graphs
2022年11月24日 11:07
Distance time Speed time
Horizontal line Stationary Moving at constant speed
Straight line Moving at constant speed Constant acceleration
Curve Accelerating Changing acceleration
Gradient Speed Acceleration
Area / Distance traveled
Page 4
