Review covering scientific notation, calculating slope, metric conversions, dimensional analysis (unit cancellation), basic algebra, and trig functions!

 Many of the numerical values you will be dealing with in Physics are very large or very small numbers. Written in this form, the values of the quantities take up a lot of space and can be very confusing to read and can be awkward to use in calculations. To make things easier, we will always write them in scientific notation by expressing decimal places as powers of 10.   M x 10 n where M is a number between 1 and 10 and n is an integer.  To write numbers in scientific notation, move the decimal point until only one non-zero digit remains to the left. Then count the number of places you moved the decimal point and use that number as the exponent of 10.  Examples:  3,1200,000 = 3.12 x 10 6 (If you move the decimal to the left to make the number smaller your exponent is positive)  = 3.12 x (if you move the decimal to the right to make the number bigger your exponent is negative.  Fun Practice at

 Input the number in scientific notation is put into your calculator correctly. Read the directions for your particular calculator. For basic scientific calculators:  Punch the number (the digit number) into your calculator.  Push the EE or EXP button. Do NOT use the x (times) button!  Enter the exponent number. Use the +/- button to change its sign.  Voila! Treat this number normally in all subsequent calculations.  To check yourself, multiply 6.0 x 10 5 times 4.0 x 10 3 on your calculator. Your answer should be 2.4 x 10 9.

 Slope is equal to the change in the y axis divided by the change in the x axis.  The ∆ symbol means “a change in” so ∆ y means y 2 - y 1 or y final – y initial

 Physics is concerned with the description and understanding of nature, and measurement is one of its most important tools.  Measurements are expressed with a number and a unit (a standard of measurement)  If you were asked how long the room was in terms of your shoe size, each class member would give different answers and it could be confusing. The metric system is based on a system of prefixes corresponding to the powers of 10. Instead of switching names, like when we go from inches to feet, in metrics, we just change the prefix. Another great reason to use the metric system is that because the prefixes are based on the powers of ten, to change prefixes, all we have to do is move the decimal place.  You will be introduced to many units in physics!

Metrics Little GuysBig Guys prefix symbol value

Derived Units

 Used when converting between units. The value is equivalent, but the unit has changed.  You can memorize the metric conversion factors (ex. 1 km = 1,000 m) or an easier solution is to become familiar with the value of each metric prefix and then converting will be a breeze!

 Steps:  1: Write your starting measurement as a fraction  2. Determine a conversion factor (s)  3. Write the conversion factor as a fraction with the unit that you started with in the denominator (so the units cancel out when you multiply).  4. Evaluate. Do the original units cancel so you are left with ONLY the desired units? Multiply both numbers and units.  Example) 80 mi = ___ km?  1) 80 mi 1  2) 1 mi = km  3)  4) = km

 15 mi/h = ______ m/s  1)  2) Conversion Factors: 1 mi = 1609 m 3600 s = 1 hr  3) 4) = = 6.70 m/s =

 1)  2)Conversion Factors: 1 x s = 1µs 1 x 10 6 s = 1 Ms  3)  4)

 Practice 1) Earth’s escape velocity is about 11.2 km/s. How fast is this in mi/h? (1 mi = km)  Practice 2) 7 km = __________µm

 Practice 1) 25,059.0 mi/hr  Practice 2) 7 x 10 9 µs Conversion Factors  1 km = 1000 m  1µm = 1 x m  Follow this link to a great tutorial with practice and instant feedback  Dimensional Analysis Tutorial Dimensional Analysis Tutorial ***Remember your conversion factors should equal the same amount! They are just in different standards of measurement!*****

Be careful when converting squared and cubic units!  Calculate the volume of a box with length = 10 cm, height = 12 cm and width = 15 cm. What would it’s volume be in cubic inches? Note that the cubic centimeters cancel only because the conversion factor is cubed.

This is a good method for finding the resultant of two vectors which make a right angle to each other. For instance, if you walked 11 km North and then walked 11 km east, how far are you from your starting position?

Trig Functions: SOH CAH TOA

 Assume you were in a boat, crossing a river that runs from West to East. If you were moving 12 m/s, 65º N of East, how fast is the river current? To answer this, diagram the problem and look for triangles!!! Make a coordinate system (the black lines) Direction of Water current Boat velocity 12 m/s Current speed? You are given the hypothesis and the angle. You are looking for the adjacent side! How can you find it using one of the trig functions?

 The river current is moving at 5.07 m/s, East.  For more help with this go to

 ax 2 + bx + c = 0  You will, on occasion, have problems in class that will require you to use this method.

 Can you rearrange the following equations? solve for v f

 t = d/v and d = vt  a = 2d/t 2 and  v f = v i + at

 Diagram the problem (helps to visualize)  List the given information  What are you solving for/What is the unknown?  What concepts are involved? What equation(s) will you need to use?  Show all steps  Solve and do not forget a unit!  This is the guess method!