CHAPTER 1

UNITS

• the numerical value of a physical quantity is only meaningful if one specifies the Units in which the quantity is expressed
• the choice of unit is arbitrary, and is dictated by convenience, but any unit must be very clearly and un-ambiguously defined
• unit conversion : as a handy rule, units can be treated as algebraic quantities

remember : one can only convert between units representing the same type of quantiy

Examples : can I convert

1.

seconds into years ?

2.

square feet into liters ?

of course not, but I can do cubic feet into liters

3.

snail hours into light years ? .....

light year : distance covered when moving at the speed of light for one year
snail hour : distance covered when moving at a snail's pace for one hour

Both units measure a distance, therefore it is legitimate to convert one into the other

Multiples and Submultiples

Scientific notation

The "type of quantity" is usually referred to as the dimension.
Fundamental quantities/dimensions (for now):

Quantity Standard Unit

LENGTH meter

MASS kilogram

TIME second

From these, derived quantities can be formed. Specifying the dimension of a quantity also tells us in which unit it should be measured (and viceversa)

Dimensional Analysis
very useful tool (we will use it extensively), for now just a few basic rules :

• in an equation, both sides must have the same dimension
• one can only add or subtract quantities of the same dimension (but they may have different units)
• one can divide or multiply quantities of different dimensions. In doing so, you get a new type of quantity
• arguments of functional operators (sin, exp, etc.) must be dimensionless

Significant figures:

any given quantity is known with a finite precision. This is expressed in terms of significant figures

It is meaningless to express a quantity with more figures than the precision with which it is known.

General rules : book pages 15,16. In practice : use common sense.

Order of Magnitude calculations :

another useful tool, we will just make a couple of examples : problems 1.48, 1.58