ALL THE BACKGROUND INFO YOU NEED TO KNOW Chapter 1

Standards of Length, Mass and Time We will use a standard system of units, called SI (Systeme International) adapted from the metric system. The fundamental units of length, mass and time in the SI system are:  Meter (m)  Kilogram (kg)  Second (s) There are a few other fundamental units, but we’ll get to them later. THE MKS SYSTEM – Don’t forget it! THE MKS SYSTEM – Don’t forget it! TEXT: Look up definitions of the meter, kilogram and second. We will use a standard system of units, called SI (Systeme International) adapted from the metric system. The fundamental units of length, mass and time in the SI system are:  Meter (m)  Kilogram (kg)  Second (s) There are a few other fundamental units, but we’ll get to them later. THE MKS SYSTEM – Don’t forget it! THE MKS SYSTEM – Don’t forget it! TEXT: Look up definitions of the meter, kilogram and second.

Other Measurement Systems If you are using smaller measurements, you might use the Gaussian or cgs system where the units of length, mass and time are:  Centimeter (cm)  Gram (g)  Second (s) The U.S. Customary system uses:  Foot (ft.)  Slug  Second (s) But, we’re going to stick with the MKS system. TEXT: Complete the following tables.

Prefixes Used with SI Units PowerPrefixAbbreviation femtof picop nanon microµ millim centic decid 10 1 dekada 10 3 kilok 10 6 megaM 10 9 gigaG teraT

Dimensions The dimensions of length, mass and time are used in many different combinations throughout physics. Length, mass and time are considered base units. (They cannot be broken down into any more “basic” units.) Think about some quantities that you know of that combine these units. Some examples:  Speed : mile/hour (mph), meter/second (m/s)  Volume : cubic meter (m 3 )  Area : meters squared (m 2 )  Density : kg/m 3  Acceleration : (m/s 2 ) These are called derived units.

Dimensional Analysis Dimensional analysis uses the fact that dimensions can be treated as algebraic quantities. Examples: Show that the expression v = v o + at is dimensionally correct where v is velocity (m/s), a is acceleration (m/s 2 ), t is time (s) Find a relationship between acceleration (a), velocity (v), and distance (r) for a particle traveling around a circle.

Significant Figures When taking measurements, we can measure to the smallest increment of the instrument and then estimate one more digit.  For example, for a ruler that can measure to 1.0 cm, a reading might be 16.4 ±0.5 cm.  The ±value indicates the accuracy of the measurement, which depends on the:  Instrument  Skill of the user  Number of times the measurement is repeated

When are numbers significant? Nonzero digits are always significant All final zeros after the decimal point are significant, e.g ( 7 sig figs) Zeros between two other significant digits are always significant, e.g (6 sig figs) Zeros used solely as placeholders are not significant, e.g (1 sig fig) or, any zeros preceding a non-zero digit are not significant.

Rules for Sig Figs Multiplying and Dividing:  The answer has the same number of sig figs that as the least accurate measurement in the equation. Adding and Subtracting:  The answer has the same number of decimals places as the measurement with the least number of decimal places. Scientific Notation and Sig Figs:  The format for scientific notation is:  M x 10 n where 1  M  10 and n is an integer  The M value contains the sig figs in the number.

Conversions ALWAYS USE THE FACTOR LABEL METHOD TO CONVERT. Steps:  List the conversion factors that are needed. (You can skip this step after you are good at converting.)  Make fractions with the conversions that will cancel the units we don’t want.  Multiply the quantity you are converting by the conversion fraction(s).  Cancel units as you would algebraic quantities.

Conversion Examples Examples:  If a car is traveling at a speed of 28.0 m/s, is the driver exceeding the speed limit of 55.0 mi/hr?  The traffic light turns green, and the driver of a high performance car slams the accelerator to the floor. The accelerometer registers 22.0 m/s 2. Convert this reading to km/min 2.

Coordinate Systems Cartesian Coordinate System (Rectangular Coordinate System):  Points are labeled with the coordinates (x, y)

Coordinate Systems (cont.) Plane Polar Coordinates:  (u, θ)  The standard references are usually the (0,0) point of a graph and the positive x-axis.  We’ll talk more about this later.

Trigonometry Basic trig is a very important tool in solving physics problems. Pythagorean theorem:  r 2 = x 2 + y 2 Trig functions:  sin α = y/r (opposite/hypotenuse)  cos α = x/r (adjacent/hypotenuse)  tan α = y/x (opposite/adjacent) r y x α

Trigonometry Example A person measures the height of a building by walking out a distance of 46.0 m from its base and shining a flashlight beam toward the top. When the beam is elevated at an angle of 39.0 with respect to the horizontal, as shown in the picture, the beam strikes the top of the building. Find the height of the building and the distance the flashlight beam has to travel before it strikes the top of the building m 39.0 ْ

Graphing Data Independent variable: x-axis Dependent variable: y-axis Title written: y vs. x Set minimums and maximums on axes based on your data. Title your axes with value name and value units, e.g. Time (seconds). Always draw BEST FIT straight line or smooth curve. DO NOT use a series of straight line segments that “connect the dots”. If using a computer program:  Find equation of the line or curve.  Substitute appropriate variables for x and y.  Add appropriate units after equation coefficients.

Distance (m) vs. Time (s) Time (s) Distance (m)