Let’s use the right units !!!!

• In Physics we use the SI system of units.– (International System)

– This means:

yard pound (distance) (mass)

We use: meter kilogram second (distance) (mass) (time)

But how do I convert to SI Units ?

To give you a basic idea:

1 meter (m) ~ 3.3 ft1 kilogram (kg) ~ 2.2 lbs

and time is always in seconds (s) in all systems.

SI Prefixes

In the SI system:

centi means 1/100milli means 1/1000kili means 1000

I like the SI System

So, here are the major conversions within the SI System:

1000m (meter) = 1km (kilometer)100cm (centimeter) = 1m (meter)1000mm (millimeter) = 1m (meter)

1000g (gram) = 1kg (kilogram)

Other conversions that you will need . . .

1 inch = 2.54cm1 mile = 1600m

Unit conversionsaka. (Factor Analysis / Unit Analysis / Dimensional Analysis)

If you need to convert numbers based on their units (such as from inches to meters) do the following:

(Starting quantity) * (conversion factor) = (ending quantity)

EXAMPLE:How many kilograms are in 3.6 lbs? (remember 1kg ~ 2.2 lb)

3.6 lbs X 1 kg = 1.6 kg 2.2 lb

Starting quantity

Conversion factorEnding quantity

Let’s try a few . . . Remember: (Starting quantity) * (conversion factor) = (ending quantity)

• How many Kilograms are in 243 grams? 243 grams x 1 kilogram = 0.243 kilograms 1000 grams

• How many centimeters are there in 0.5 meters? 0.5 meters x 100 centimeters = 50 meters

1 meter

• How many meters are there in 2387 millimeters?2387 millimeters x 1 meter = 2.387 meters

1000 millimeters

Alright, let’s get a little harder . . .Pair up - Work with a neighbor and calculate these values

Remember: (Starting quantity) * (conversion factor) = (ending quantity)

• If you run a 6K race (6 kilometer), how many inches did you travel?

• If you climb a building 120 stories tall (1 story is about 3 meters high), how many centimeters did you climb?

• If a competition Frisbee has a mass of 165g, how many pounds is it?

Significant Figures

are the number of digits in a number to show the accuracy of a measurement

Sig Fig RULES: (here they are – don’t copy them in class)

1. All non-zero digits are significant.

2. All zeros between non-zero digits are significant.

3. All zeros to the right of a decimal point are significant.

4. In the absence of any information, whole numbers with zeros to the left of the decimal point are not significant. They are place holders

Sig Fig RULES Continued . . .

5. With appropriate information, whole numbers with zeros to the left of the decimal may be significant.

6. In decimal fractions smaller than 1, the leading zeros (to the left of the first non-zero digit) are not significant. They are place holders.

7. In scientific notation the zeros are always significant.

8. In performing all mathematical operations (multiplication, division, addition, subtraction, etc), the number with the least number of significant figures will determine the significant figures of the final answer.

9. In performing label factor, the conversion factors are exact. They do not determine the number of significant figures in the final answer.

Here’s a basic rule to follow . . .

In general, whenever you do a problem in Physics, NEVER put more than two digits after the decimal point in your answer. (unless working with really small numbers)

For example: 3.14 7 4.1 5.97 0.2362

0.5 7.2534 8.0 6.8677 2.69

You cannot be more accurate than 1/100 ths in most cases!

Scientific Notation

VERY LARGE and VERY SMALL

numbers are hard to work with. So, you will sometimes use scientific notation. It helps make it easier.

1.23 x 104 = 12,300 (the positive 4 means to move the decimal point 4 places to the RIGHT)

4.6 x 10-3 = 0.0046 (the negative 3 means to move the decimal point three places to the LEFT)

Scientific Notation MATH

Addition: (5.5x102) + (3x102) = 8.5x102

Subtraction: (5.5x102) - (3x102) = 2.5x102

Multiplication: (4.1x102) x (6x10-3) = 24.6x10-1

Division: (4.1x102) ÷ (6x10-3) = 0.68x105

Why do we use Scientific Notation in Physics ????

• A typical star has a mass of about 2×1030 kg, which is about 1×1057 atoms of hydrogen per star. A typical galaxy has about 400 billion stars so that means each galaxy has 1×1057 × 4×1011 = 4×1068 hydrogen atoms. There are possibly 80 billion galaxies in the Universe, so that means that there are about 4×1068 × 8×1010 = 3×1079 hydrogen atoms

in the observable universe.

Get the picture ????

Accuracy:How close a number is to a known value. For example, the value of π Is known to be 3.1415927. Is it accurate to use 3.14? Is it more accurate to use 3? (No)

Precision:How closely grouped (or close together) number values are. For instance,5, 4.5, and 4.7 are closely grouped. They are precise data. The numbers 2, 5.6, and 14.1 are less precise.

Think about a dart board . . .

Is player Green or Red more precise?Green

Which player is the most accurate?Blue

Error Analysis(Comparing Two Numbers)

Percent Difference – used when comparing any two numbers when an exact value is not known. It determines EXACTLY how precise the two numbers are.

% Diff. = | value #1 – value #2 | x 100% average of the values

Percent Error - used when comparing a number to a known or actual value. It determines EXACTLY how accurate a number is.

% Error = | actual value - number| x 100% actual value

Error Analysis (Comparing two numbers)

So you have two numbers and you don’t know if either of them is correct. The best you can do is compare them to each other to see how close they are. (Percentage difference)

For example: 2.5 and 2.75

% Diff. = | 2.5 – 2.75 | x 100% = 9.52% 2.625

(they are pretty close but could be better)

So you have a number and you want to know if it is close to the known (or correct) value. (Percentage error)

For example: 3.2 compared to π (3.14)

% Diff. = | 3.2 – 3.14 | x 100% = 1.91% 3.14

they are really close, so3.2 is an accurate representation for π.

Error Analysis (Comparing two numbers)

Approximately Equal to . . .

In Physics class, the actual and correct answer is ALWAYS the BEST. However, sometimes you don’t need to get bogged down in numbers.

You can round off numbers and use the

≈ symbol instead of = to signify “approximately equal to”

For example: π ≈ 3

BE CAREFUL This can lead to significantERROR

I like to be

exact ! exact !

Commonly Used Graphs in Physics

Linear ( y = m x + b ) Power ( y = m xk )

Inverse ( y = 1 / xk ) Root ( y = k√x )

Measurement

If we want to observe the world around us, we need to quantify it some way. We do this by measuring things . . .

However, measurements are not always very good.

Imagine measuring the length of an ant with a yard stick – not very good.

How about measuring the length of a football field in inches – too tedious!

What if you pumped 23.7639857678545532 gallons of gas into your car. Does this measurement seem a little over-kill?

In Physics class, we need to make GOOD Measurements !!!!

Error in Measurement

When we measure, we need to make sure we use the appropriate scale. Which would provide a better measurement?

distance ≈ 1.5 inches distance = 1.4 inches

What is the Percent Error in calculating the object with a left ruler?

1.5 – 1.4 x 100 = 7.14% Error not bad, but not that great either! 1.4