**Introduction and Unit Analysis**

**Unit Analysis Learning ****Targets**

- I understand the difference between a variable, unit, and equation
- I can do a basic metric-nonmetric and metric-metric
**conversion** - I can write into and out of
**scientific notation**

**What is Physics?**

**Physics** is the study of the physical world and natural phenomenon.

**Kinematics** - A branch of physics that studies of motion.

Many problems require you to seek out information so you can answer a question.

- How far?
- How long?
- How fast?
- How much faster?

For example this question:

- How fast are you traveling if you travel fifteen meters in five seconds?

Here we are given two knows and one unknown and can begin to create a solvable problem.

Question | Variable | Number and Unit Abbreviation |

How far? | x | 15m |

How long did it take? | t | 5s |

How fast? | v | ? |

Next we would find an equation that has the knowns and unknowns in it, which leads you to the equation v=x/t

After we plug in the values and solve we find the answer to be 3 meters per second or 3 m/s with an abbreviated unit.

The unit m/s was derived by the units for the variables x and t as seen in the picture.

**MKS System**

In physics we use a system of units called MKS derived from the common metric SI units which stands for system international.

**What MKS Stands For:**

- M: Meters
- K: Kilograms
- S: Seconds

Since physics deals with large objects like planets, instead of grams, like in chemistry, we use kilograms as a standard unit of mass.

**Converting**

If the units given are not in the MKS units we will often have to convert.

**Non-Metric to Metric Conversion**

Lets say you were 652 miles away from Atlanta and you were asked to convert this to meters, you would need a conversion ratio.

- 1 mile = 1609.34 m

After converting, we would have to think about significant figures and putting the number into scientific notation as you see in the picture.

**Metric to Metric Conversions**

In science we are measuring in meters and often have a prefix like centi- in front of the unit meter which represents a factor of ten.

Look at a few common prefixes we use in physics which will help you convert.

Here is another example:

**Deimos, a small moon of Mars, has a radius of 11.265 kilometers. How many meters is this?**

After converting you would find that 11.265 km equals 11265 m.

**How to Write Into Scientific Notation**

**When Starting With a Big Number**

- Rewrite the number with only one digit to the left of the decimal point and dropping off the zeros after the last number and add a (x 10)
- If the new number is smaller than the original, count how many decimal places and add that as a positive exponent

**654000000 becomes 6.54 x 10 ^{8}**

**When Starting With a Small Number**

- Rewrite the number with only one digit to the left of the decimal point and dropping off the zeros after the last number and add a (x 10)
- If the new number is bigger than the original, count how many decimal places and add that as a negative exponent

**0.000341 becomes 3.41 x 10 ^{-4}**

**Question: How do you write 0.0051 in scientific notation?**

**How to write out of scientific notation**

**Negative exponent example**: 3.41 x 10^{-4}

If you have a **negative exponent**, drop the (x 10) and move the decimal that many spaces to the left

0.000341

**Positive exponent example**: 4.5 x 10^{5}

If you have a positive exponent, drop the (x 10) and move the decimal that many spaces to the right

450000

**Question: What non-scientific notation number does 4.55 x 10 ^{2} represent?**

**More Practice**

**Practice Problems**

Convert into scientific notation

**1) 4100**

**2) 0.00235**

**3) 3230000**

Express the following numbers in scientific notation

**1) 8.32 x 10 ^{-2}**

**2) 5.4 x 10 ^{4}**

**3) 9.67 x 10 ^{3}**

Convert the following numbers to meters with the correct scientific notation

**1) 320 cm to m**

**2) 5100 km to m**

**3) 0.51 cm to m**

- Continue to part
**1: Scalars and Vectors** - Go to the
**1D Motion Unit Page** - Back to the
**Stickman Physics Home Page** **Equation Sheet**