INTRODUCTION

The “stuff” every Physics student should know…

The Metric System

• Based on powers ten• Standards of the metric system: SI units –

provides a set of standards of measurement, because it is convenient.

• Fundamental unit – the base units from which all quantities can be described.

• Examples: Length – meter(m) Mass – kilogram(kg) Time – second(s)

• Derived Unit – combinations of the base units

• Examples: m/s, m/s/s, Joule

• Can you think of any others?

The Metric System

• Prefixes for the Metric System:Femto (F) 10-15

Pico (p) 10-12 Tera (T) 1012

Nano (n) 10-9 Giga (G) 109

Micro () 10-6 Mega (M) 106

Milli (m) 10-3 Kilo (k) 103

Centi (c) 10-2 Hecto (h) 102

Deci (d) 10-1 Deka (da) 101

The Metric System

Conversions – when moving to a larger unit from a smaller unit, move the decimal point to the left the number of spaces (steps) between the prefixes, When moving to a smaller unit from a larger unit, move the decimal point to the right the number of spaces (steps) between the prefixes.

DRUL RULE: down to the right, up to the left

The Metric System

The Factor- Label Method – converting from one unit to another using a conversion factor.

• A conversion factor is a fraction that is equal to the number 1.

• See the worksheet labeled Unit Conversions and Factor Label Method

The Metric System

Uncertainty In Measurement

All measurements are subject to uncertainties. For example:• Parallax – the apparent shift in the position of an

object when it is viewed from different anglesTo avoid this and other discrepancies, we need:Precision – the degree of exactness of a

measurement• It is limited by the smallest division on the

measurement scale

Accuracy – how well the results of an experiment agree with the standard value.

• Because precision of measuring devices is limited, so is the number of digits in the measurement.

• See overhead and handout on Accuracy and Precision

Uncertainty In Measurement

Significant Figures – “Sig Figs”

Sig figs – the valid digits in a measurement• All digits 1-9 are significant (123 – three sig

figs)• Zeros between sig. digits are always

significant (5.007 – 4 sig figs)• Trailing zeros in a number are only

significant if the number contains a decimal point. ( 100.0 – 4 sig figs but 100 – 1 sig fig)

• Zeros in the beginning of a number whose only function is to place the decimal point are not significant (0.0025 – 2 sig figs)

• Zeros following a decimal significant fiure are significant (0.000470 – 3 sig figs, 0.47000 – 5 sig figs)

Significant Figures – “Sig Figs”

Rules for calculations using Significant Figures• When multiplying and dividing, limit and round to

the least number of significant figures in any of the factors.

• When adding and subtracting, limit and round your answer to the least number of decimal places in any of the numbers that make up your answer.

Significant Figures – “Sig Figs”

To avoid confusion with significant figures, we put measurements in scientific notation.

This way all significant figures come before the power of ten.

Examples: 156,000 1.56 x 105

0.026 2.6 x 10-2

0.1260 1.260 x 10-4

When performing operations with sig figs, the answer is only as precise as the lesser precise value. See w.s. on calculations with sig figs

Significant Figures & Scientific Notation

Graphing Data

Independent Variable – the variable that is changed or manipulated, the experimenter can control directly (x –axis)

Dependent Variable – the responding variable, this depends on the independent variable (y – axis)

Slope = rise = y

run x

Linear relationship – the dependent variable varies linearly with the independent; the two are directly proportional

y = mx + b

• Direct relationship – as one increases, so does the other

• Indirect (Inverse) relationship – as one increases, the other decreases

Graphing Data

Quadratic relationship – one variable depends on the inverse of the other (the graph is called the parabola)

y = mx2 y = kx2

• Inverse relationship – one variable depends on the inverse of the other

y = k(1/X) = k/x or k = xy or y = kx-1

Graphing Data