1.3. Units and Significant Figures

The Scientific Method starts with making observations = precise and accurate measurements

• 1.3.1. SI Units

• 1.3.2. Unit Prefixes

1.3.1. Units of Measurement

• In physics, the metric system is (almost) always used.

• Standard: SI Units (Système International) – MKS:

• Meter (m) – Length

• Kilogram (kg) – Mass

• Second (s) – Time

– CGS: • Centimeter (cm) – Length

• Gram (g) – Mass

• Second (s) – Time

The Primary Base Units

Property SI Unit Symbol

Length Meter m

Time Second s

Mass Kilogram kg

Electric current* Ampere A

Temperature Kelvin ˚K or K

Almost everything is physics can be described by combinations of these 5 base units.

The magnitude of these units is arbitrary and historical. The important thing is that everyone uses consistent standards!

*IMHO should be: Electric charge Coulomb C

Standards of Calibration for Units

Length: the meter

Then: one ten-millionth of the distance from the North Pole to

the equator (1793)

Now: the distance traveled by light in a vacuum in

1/299,792,458 of a second

Mass: the kilogram

Then: the mass of one liter of water

Now: the mass of a particular platinum-iridium cylinder kept at

the Intl. Bureau of Weights and Standards in Sèvres, France.

Time: the second

Then: 1 day = 24 hours, 1 hour = 60 min, 1 min = 60 s

Now: the time for a particular radio wave from a cesium-133

atom to complete 9,192,631,770 oscillation cycles.

Unit Conversions

Length in Physics

Exponential Notation

Example

Exponential multiplication and division

Mass in Physics

Mass vs. Weight

• Mass is a measure of the amount of matter (primarily protons and neutrons) in an object – It is an intrinsic, unchanging property

– It is a measure of the “inertia” of an object

• Weight is a measure of the gravitational force acting on an object – It varies depending on the object’s location

So, a 1 kg object weighs more on Earth than on the Moon. In orbit, it appears to be “weightless”.

Time in Physics

Unit Prefixes designate powers of 10

Example: Diameter of a red blood cell: 8 × 10-6 m = 8 µm Convention to use powers of 103: Mass (≈weight) of a honeybee: 1.5 × 10-4 kg = 1.5 × 10-1 g = 0.15 g or 150 mg These prefixes can be used with Non-metric units: 1 GB = 109 bytes

a) Speed of light 3.0 × 108 m/s = 0.30 Gm/s b) Radius of Earth 6380 km = 6.38 Mm c) Stefan-Boltzmann

constant 5.7 × 10-8 W m-2 K-4 = 57 nW m-2 K-4

Exercise: Apply Standard Unit Prefixes

Changing a unit prefix can be done just like a unit conversion, by multiplying a fraction:

Applying Standard Unit Prefixes

Unit Prefix Conversions

Relevant Prefixes

• Does it make sense to describe the length of this room in nm, m or km?

• The radius of the Earth?

• The size of a virus?

Using appropriate prefixes can be helpful.

Using non-SI Units is Sometimes Allowed

Sometimes exceptions are made when using non-SI units makes physical interpretation easier:

“The average human lifetime is 2.4 Gs.” versus “The average human lifetime is 75 years.” Life expectancy at birth for 1987, NC for Health Statistics

Accessible interpretation is important for validation, and to build an understanding of magnitudes, relative relationships and phenomenology.

Question