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# Physics 211 Notes Week 1 PY 211

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This 4 page Class Notes was uploaded by Mitchell on Saturday January 9, 2016. The Class Notes belongs to PY 211 at North Carolina State University taught by Chueng Ji in Spring 2016. Since its upload, it has received 11 views. For similar materials see College Physics 1 in Physics 2 at North Carolina State University.

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Date Created: 01/09/16

Physics 211 Week 1: Units and Significant Figures Fundamental Units and Derived Units Fundamental Units: Units of measurement that are independent of other types of measurement. They are set by a standard and are the basis for creating derived units. There are 4 fundamental units of interest in this course: Length (meters), Mass (grams), Time (seconds), and Current (ampere) Derived Units: Units of measurement that are composites of fundamental units, or are in some way related to the fundamental units. Example being speed, which is distance (length) over time. There are many different derived units. Fundamental Units: SI (metric system) Notation English Units Length Meters (m) [L] Feet (ft) Mass Grams (g) [M] Pounds (lb) Time Seconds (s) [T] Seconds (s) Prefixes 18 10 1,000,000,000,000,000,000 exa- 10 15 1,000,000,000,000,000 peta- 12 10 9 1,000,000,000,000 tera- 10 1,000,000,000 giga- 10 6 1,000,000 mega- 3 10 1,000 kilo- 10 2 100 hecto- 10 deka- 1 10 -1 .1 deci- -2 10 .01 centi- 10-3 .001 milli- -6 10 .000,001 micro- 10-9 .000,000,001 nano- 10-12 .000,000,000,001 pico- -15 10 .000,000,000,000,001 femto- 10-18 .000,000,000,000,000,001 atto- Order of Magnitude = (ex.) 1.2 x 10 the Order of Magnitude refers to the scale or power of 10 that the number is in. It is important in scientific notation to be able to identify the order of magnitude. Useful Conversions Physics 211 SI EU EU SI 1 meter = 3.28 feet 1 foot = .305 meters 1 cm = .3937 inch 1 inch = 2.54 cm 1 km = .6214 miles 1 mile = 1.609 km 1 kg = 2.2046 lb 1 pound = .4536 kg 1 liter = 1.0567 qt 1 quart = .9464 L Significant Figures (“Sig Figs”) Significant Figures are a way to remain consistent when dealing with uncertainty in measurements. The last number in a measurement always carries a degree of uncertainty. There are rules for counting significant figures and operating with them. ● All non-zero numbers count as sig figs Ex) 1563 = 4 sig figs ● Trapped zeros count Ex) 2003 = 4 sig figs ● Preceding zeros don’t count Ex) .0043 = 2 sig figs ● leading zeros sometimes do, sometimes don’t* Ex) 2500 = 4 sig figs Ex) 2500 = 2 sig figs ● if the leading zeros are after a decimal, they always count Ex) .004500 = 4 sig figs *to avoid confusion, stick with scientific notation when dealing with numbers greater than 1,000 When operating with significant figures, always round the answer to the same number of sig figs as the input with the fewest number of sig figs Ex) 12.01 (4 sig figs) + 15 (2 sig figs) = 27 (2 sig figs) Review of Math and One-Dimensional Motion: Displacement and Velocity Calculating and Converting Units with the “Fraction Method” We use the fraction method to cancel out units and convert from one unit to another. This involves setting up a long fraction with multiple parts that end up with the units we want left after cancelling. Ex.) How many meters are in 1 mile? 1 mile 5280 ft. .305 meters = 1 x 5280 x .305 = 1610 m 1 mile 1 ft. Set starting units on the left Relate each unit to another until you have the units you need on the right Multiply, divide, and cancel out as necessary Physics 211 Trigonometry Mathematics using relationships between angles and sides of triangles to find missing values. a Sin θ = Opposite = Hypotenuse c c a Cos θ = Adjacent = b Hypotenuse c θ Tan θ = Opposite = a Adjacent b b Pythagorean Theorem: For any right triangle, the sum of the squares of the two right sides will equal the square of the hypotenuse. 2 2 2 a + b = c This can apply to the trigonometry functions above, as well. Divide both sides by c , substitute the relevant trigonometric function, and you have: sin θ + cos θ = 1 Ex.) x = 12.5 m Tan θ = y/x θ = 22.5° Tan (22.5) = y/12.5 y θ y = ? 12.5 • Tan (22.5) = y x y = 5.17 m Motion on the X-Axis Vector: A quantity with both direction and magnitude Scalar: A quantity with magnitude, but no direction Physics 211 Position: The location of an object, usually denoted by x Displacement: The distance between the final position of an object and the initial position after a certain period of time, usually denoted by Δx (note that Displacement is a vector, therefore direction must be indicated by an arrow and the sign of the quantity is of importance) X 0 initial position X f final position ΔX = displacement ΔX = X f X 0 X 0 X f ΔX 2 m 5 m Xf X0 2 – 5 = -3 ΔX = -3m Time = t Elapsed Time = Δt t0= initial time tf= final time Δt = elapsed time Δt = t f t 0 Velocity: displacement over elapsed time. Not to be confused with speed. Velocity is also a vector. Velocity is often denoted by v and measured by m/s. A derived unit Speed: Distance travelled over elapsed time. Speed is a scalar. v = average velocity Δx v = Δt

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