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Metric Units: (adapted from http://en.wikipedia.org/wiki/Metric_system ) CGS centimeter gram second system MKS meter kilogram second system Variants of the metric system Quantity CGS MKS length (l) centimeter (cm) meter (m) Meter = 100 centimeters mass(m) gram (g) kilogram (kg) The kilogram (SI symbol: kg), also known as the kilo, is the base unit of mass in the International time (t) second (s) second System of Units. (kilogram = 1000 gram(g) ) velocity(v) cm/s m/s acceleration (a) cm/s² m/s² 1 dyne = 1 g·cm/s² = 10−5 kg·m/s² = 10−5 Newton force (F) dyne (dyn) newton (N) 1Newton = 1 kg·m/s2 pressure (p) barye (Ba) pascal (Pa) 1 Ba = 0.1 Pascal = 0.1 Newton/m2 = 1 g·cm-1s-2 2 2 −7 energy (W) erg (erg) joule (J) 1 erg = g·cm /s = 10 joules (1 erg = 1 dyne cm = 1 g·cm2/s2) 1 joule = 107 erg power (P) erg/s watt (W) 1 watt = one joule per second (power measures viscosity (µ) poise (p) Pa·s the rate of energy conversion) 1 poise = 1 g·cm-1·s-1 (1 Pascal·s = 1Pa·s = 1 -1 -1 kg·m ·s (the extent to which a fluid resists a tendency to flow) The International System of Units (System international units or SI) is the current international standard metric system and the system most widely used around the world. Mass can be defined as a quantitative measure of an object's resistance to the change of its speed. In addition to this, gravitational mass can be described as a measure of magnitude of the gravitational force which is 1. exerted by an object (active gravitational mass), or 2. experienced by an object (passive gravitational force) Whenever the mass, m, appears in our formulas, we substitute the ratio of the convenient force-acceleration pair (w/g), and measure the mass in lbs. per ft./sec.2 or in grams per cm./sec. Recall that weight is a force, so the metric unit of weight (or any other force - such as that of a stretched spring, or a bat striking a ball, or a locomotive pulling a train) is the dyne or Newton. .

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Summer 2018 Astron 9 Week 2 FINAL
ORDER OF MAGNITUDE PHYSICS RICHARD ANANTUA, JEFFREY FUNG AND JING LUAN WEEK 2: FUNDAMENTAL INTERACTIONS, NUCLEAR AND ATOMIC PHYSICS REVIEW OF BASICS • Units • Systems include SI and cgs • Dimensional analysis must confirm units on both sides of an equation match • BUCKINGHAM’S PI THEOREM - For a physical equation involving N variables, if there are R independent dimensions, then there are N-R independent dimensionless groups, denoted Π", …, Π%&'. UNITS REVIEW – BASE UNITS • Physical quantities may be expressed using several choices of units • Unit systems express physical quantities in terms of base units or combinations thereof Quantity SI (mks) Gaussian (cgs) Imperial Length Meter (m) Centimeter (cm) Foot (ft) Mass Kilogram (kg) Gram (g) Pound (lb) Time Second (s) Second (s) Second (s) Temperature Kelvin (K) Kelvin (K)* Farenheit (ºF) Luminous intensity Candela (cd) Candela (cd)* Amount Mole (mol) Mole (mol)* Current Ampere (A) * Sometimes not considered a base cgs unit REVIEW – DERIVED UNITS • Units may be derived from others Quantity SI cgs Momentum kg m s-1 g cm s-1 Force Newton N=kg m s-2 dyne dyn=g cm s-2 Energy Joule J=kg m2 s-2 erg=g cm2 s-2 Power Watt J=kg m2 s-3 erg/s=g cm2 s-3 Pressure Pascal Pa=kg m-1 s-2 barye Ba=g cm-1 s-2 • Some unit systems differ in which units are considered fundamental Electrostatic Units SI (mks) Gaussian cgs Charge A s (cm3 g s-2)1/2 Current A (cm3 g s-4)1/2 REVIEW – UNITS • The cgs system for electrostatics is based on the assumptions kE=1, kM =2kE/c2 • EXERCISE: Given the Gaussian cgs unit of force is g cm s-2, what is the electrostatic unit of charge? # 2 ! = ⟹ # = ! & 2 )/+ = g cm/ s1+ )/+ [&]2 REVIEW – BUCKINGHAM’S PI THEOREM • BUCKINGHAM’S PI THEOREM - For a physical equation involving N variables, if there are R independent dimensions, then there are N-R independent dimensionless groups, denoted Π", …, Π%&'.
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Reference: www. rockmass.net 620(7(&+1,&$/81,76 7KH,QWHUQDWLRQDO 6, V\VWHPRIXQLWV Its seven basic units, from which other units are derived, are given in the table below. Dimension Symbol SI unit Comment Name Unit Length l metre m Mass m kilogram kg Time t second s Electric current I ampere A Temperature T kelvin K Luminous intensity Iv candela cd Molar heat capacity n mol mol BASIC UNITS IN SI SYSTEM Angle a radian rad Additional unit Frequency f hertz Hz s-1 Force F newton N 1 N = 1 kgm/s2 Pressure, stress p, σ, pascal Pa 1 Pa = 1 N/m² UNITS Energy, work, heat E, W, Q joule J 1 J = 1 N × m DIVERTED SI- Effect P watt W 1 W = 1 J/s 'HFDGHSUHIL[HV prefix symbol value prefix symbol value tera T 1012 deci d 10-1 giga G 109 centi c 10-2 mega M 106 milli m 10-3 kilo k 103 micro µ 10-6 hecto h 102 nano n 10-9 deca da 101 pico p 10-12 7KH*UHHNDOSKDEHW Α α, ∝ ∗) alpha (a) Ι ι iota (i) Ρ ρ rho (r, rh) Β β beta (b) Κ κ kappa (k) Σ σ sigma (s) Γ γ gamma (g, n) Λ λ lambda (l) Τ τ tau (t) ∆ δ, ∂ ∗) delta (d) Μ µ mu (m) Υ υ upsilon (y, u) Ε ε epsilon (e) Ν ν nu (n) Φ φ, ϕ*) phi (ph) Ζ ζ zeta (z) Ξ ξ xi (x) X χ chi (ch, h) Η η ëta (e, ë) Ο ο omicron (o) Ψ ψ psi (ps) Θ θ, ϑ ∗) theta (th) Π π pi (p) Ω ω omega (o, õ) *) Old-style character 2 9DULRXVXQLWVDQGFRQYHUVLRQV 'LPHQVLRQ 1DPH 6\PERO 8QLW &RQYHUVLRQ Time minute min s 1 h = 60 s hour h h 1 h = 60 min day day day 1 day = 24 h week wk wk 1 wk = 7 days year yr yr 1 yr = 365.242 days = 52.17 wk Length Angstrom A m 1 A = 10-10 m nautical mile n mile 1 n mile = 1852 m wave length λ m Force load G (P,W) N 1 kp = 9.807 N 2 o o 2 gravity g N 1 gn = 9.80665 m/s (exact, at 45 N; at 60 N g = 9.82 m/s ) atmosphere atm 1 atm Modulus elasticity modulus E Pa 1 kPa = 0.1 N/cm = 0.102 ton/m2 deformation modulus G Pa 1 MPa = 10,2 kg/cm2 shear modulus K Pa Density mass density ρ kg/m3 force density γ kN/m3 Flow Lugeon Lugeon l/min/m 1 Lugeon = approx.
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