Dimensional Analysis

Conversions of Units

UNITS

• The world-wide scientific community uses the metric system to make measurements.

• SI units: System International d’Unites

• SI units are related by powers of 10 (making it easy to convert between)

Fundamental Units

• Time: seconds (s)

• Length: metres (m)

• Mass: kilograms (kg)

• Other quantities can be described using these three units. Derived units are combinations of fundamental units.

• i.e. Speed: m/s

Definitions

• Note: You are NOT responsible for these definitions! They are just for knowledge sake!

• Distance (m): “The metre is the length of the path travelled by light in a vacuum during a time interval of 1/299 792 458 of a second.”

Definitions

• Note: You are NOT responsible for these definitions! They are just for knowledge sake!

• Mass (kg): “The kilogram is equal to the mass of the international prototype of the kilogram.”

Definitions

• Note: You are NOT responsible for these definitions! They are just for knowledge sake!

• Time (s): “The second is the duration of 9 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium 133 atom.”

Why do we need to convert units?

• They are EXACT so we can compare worldwide (even the USA).

• They are used by the scientific community and have been used since 1960.

Dimensional Analysis

• Identify the given or known data (information).

• Identify the unknown. • Plan the solution or calculations by either:

– setting up a series of conversion factors OR– using a formula

• Check your work by cancelling out units.

Example 1: Conversion within Fundamental SI units

• A space shuttle orbits the Earth at an altitude of 300 000 m. What is its altitude in:

• A) mm

• B) km

Example 2: Conversions between SI units and non-SI units

• Calculate the number of cm in 20 inches if you know that 1 inch = 2.54 cm.

Example 3: Multiple step conversions

• A person on a diet might lose 2.3 kg per week. Express the mass loss rate in mg per second.

Questions for you…

• How many seconds are in 1 year? (note: 1 year is 365.25 days …)

• Both the 100 yard and the 100m dash are used in track events. Which is longer and by how much? (note: 1 yd = 0.9144 m)