Numeracy for Physics

Defined quantities

Defined quantities are the standard units we use. We have a single global definition of each of the standard units. The standardization of units allow for mass understanding of basic quantities. Such quantities that can be defined are the most basic extensions along the dimensions, or the most basic measurement of a phenomena, (however they might not be defined as simply as what they intend to define).

Length is defined by the meter (m). One meter is about the distance from your desk to the floor.

Time is defined by the second (s). It took 1 second to read this.

Mass is defined as the amount of matter in a body (how much stuff (no matter what it's made of) is in a thing)

Mass is defined by the kilogram in everyday life. 1 kilogram is the mass of a bag of sugar

Temperature is a basic quanitity which is easier measured than defined.

It is usual to measure temperature in ^oC, 1^oC is ¹/₁₀₀ of the difference in temperature between the 'freezing' point of water and the 'boiling' point of water

Energy

Derived Quantities

When we want to measure other things of interest we can usually combine the set units.

This depends on what we want to measure.

lets take 3 common examples

Speed

You all understand the concept of speed, a faster body will cover more ground in a set time or cover a set distance in less time.

As the units of Distance are the meter, and the standard unit of time being the second, we see that the units of speed will be meters per second, which is more often wrote as ^m/_s., or more simply as just m/s.

Acceleration

Acceleration is defined as the 'rate of change of velocity (speed) with respect to time.

where v & u are the two speeds (both measured in m/s) and t is the time again measured in seconds.

So we now have (m/s)/s ... write this in your copy as a fraction .... and work it out.

unit of acceleration = (m/s²)

Force

So the units of force will be the units of mass times the units of acceleration

kg x m/s² = kgm/s² this is the true basic units of force, but somebody decided to honor Issac Newton and name 1 kgm/s² the Newton (N) .

Powers

power of 10

what is 10² ?

what is 10³ ?

and 10

what happens when we put 10 to the power of a real number ?

what is 10¹?

what is 10⁰?

Use your calculator to determine the

10^-3

a unit divided by a unit ms^-1 ...

The table of prefixes

Tera 10¹²

Giga 10⁹

^{Mega 106}

^{kilo 103}

Significant digits and Unit Manipulation