Units, Standards, SI System

Units, Standards, SI System All measured physical quantities have units. Units are VITAL in physics!! In this course (& in most of the modern world, except the USA!) we’ll use (almost) exclusively the SI system of units. SI = “Systéme International” (French) More commonly called the “MKS system” (Meter-Kilogram-Second) or more simply, “The Metric System”

Meter (m) (kilometer = km = 1,000 m) SI or MKS System Standards for Length, Mass, & Time Length Unit: Meter (m) (kilometer = km = 1,000 m) Standard Meter: Modern definition in terms of the speed of light (c = 3  108 m/s) 1 meter  Length of path traveled by light in vacuum in [1/(3  108)]* of a second! *(more precisely, [1/299,792,458]!)

Definition of the Meter The original definition of a meter was in terms of the Earth’s circumference. It was then changed to be based on this platinum-iridium bar (figure). It is now defined in terms of the speed of light, as already mentioned.

SI or MKS System Standards for Length, Mass, & Time Time Unit: Second (s) Standard Second: Modern definition in terms of nuclear decay: 1 Second  Time required for [9.19  109]* oscillations of radiation emitted by cesium atoms! *(more precisely, [9,192,631,770]!)

Standards & Technology. Definition of a Second The value of the second is based on the frequency of light emitted by cesium atoms. Shown in the figure is a cesium clock in the National Institute of Standards & Technology.

SI or MKS System Standards for Length, Mass, & Time Mass Unit: Kilogram (kg) Standard Kilogram  Mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights & Measures in France. (Discussed more later)

Larger & Smaller units are defined from the SI standards by using powers of 10 & Greek prefixes. The table gives the standard SI prefixes for indicating powers of 10. Many (k, c, m, μ) are familiar; Y, Z, E, h, da, a, z, & y are rarely used. __  __  __  __ 

Typical Lengths (approximate)    

Typical Lengths (approximate)              TABLE 1.1 *Red blood cells are not spherical, but are shaped more like flat plates. The value given here is the approximate diameter of the plate.

Typical Times (approximate)              

Typical Times (approximate)      TABLE 1.2     

Definition of a Kilogram Mass is related to the amount of material contained in an object. All masses are defined in terms of a Standard Kilogram, which is composed of an alloy of platinum & iridium.

Typical Masses (approximate)          

Typical Masses (approximate)   TABLE 1.3        

only in the SI system, kilograms, meters, & seconds. Other Systems of Units We will work only in the SI system, in which the base units are kilograms, meters, & seconds.

1. The CGS or “Lesser Metric System” Base Quantities are defined in Other Systems of Units 1. The CGS or “Lesser Metric System” Base Quantities are defined in terms of The SI Base Quantities: Mass Unit = gram (g)  10-3 kg Length Unit = centimeter (cm)  10-2 m Time Unit = second (s) (unchanged from the SI system)

The Engineering System & We will work exclusively in the SI System! Other Systems of Units 2. The British System: Also known as The Engineering System & The (US) Customary System Base Quantities: Foot, Pound, Second (fps) In this system, Force in Pounds is a base unit, instead of mass as used in the SI system. Obviously, there are conversion factors to convert between the British & the SI Systems. These are well known & can be looked up if they are needed. Unit Conversions like this are NOT physics & we will NOT be doing them! We will work exclusively in the SI System!

Fundamental Quantities & Their Units Quantity SI Unit Length meter Mass kilogram Time second Temperature Kelvin Electric Current Ampere Luminous Intensity Candela Amount of Substance mole Physics I, Phys 1403 Physics II, Phys 1404

Units Summary

In this class, we will NOT do unit conversions! We will work exclusively in SI (MKS) units!

Basic & Derived Quantities Basic Quantity  Must be defined in terms of a standard: Meter, Kilogram, Second. Derived Quantity  Defined in terms of combinations of basic quantities Unit of speed (v = distance/time) = meter/second = m/s Unit of density (ρ = m/V) = kg/m3

t = (⅔)hr so, x = (90 km/hr)  [(⅔)hr] = 60 km Units and Equations In dealing with equations, remember that the units must be the same on both sides of an equation (otherwise, it is not an equation)! Example: You go 90 km/hr for 40 minutes. How far did you go? A Ch. 2 equation: x = vt. v = 90 km/hr, t = 40 min. To use this equation, first convert t to hours: t = (⅔)hr so, x = (90 km/hr)  [(⅔)hr] = 60 km The hour unit (hr) has (literally!) cancelled out in the numerator & denominator!

1 m/s  3.6 km/hr; 1 km/hr  (1/3.6) m/s Converting Units As in the example, units in the numerator & the denominator can cancel out (as in algebra) Illustration: Convert 80 km/hr to m/s Conversions: 1 km = 1000 m; 1hr = 3600 s  80 km/hr = (80 km/hr) (1000 m/km) (1hr/3600 s) (Cancel units!) 80 km/hr  22 m/s (22.222…m/s) Some useful conversions: 1 m/s  3.6 km/hr; 1 km/hr  (1/3.6) m/s

Order of Magnitude & Rapid Estimating: “Fermi Problems” Sometimes, we are interested in only an approximate value for a quantity. We are interested in obtaining rough or Order of Magnitude Estimates. Order of Magnitude Estimates are made by rounding off all numbers in a calculation to 1 sig fig, along with power of 10. Can be accurate to within a factor of 10 (often better) Sometimes these are called “Fermi Problems”.

Example: V = πr2d Example: Estimate! Estimate the volume of the water in a particular lake, which is roughly circular, about 1 km across, & you guess it has an average depth of about 10 m. Example: Estimate!

Example: Thickness of a Page You don’t need one of these! Estimate the thickness of a page of your textbook. Hint: You don’t need one of these! Figure 1-8. Caption: Example 1–6. Micrometer used for measuring small thicknesses. Answer: Measure the thickness of 100 pages. You should find that the thickness of a single page is about 6 x 10-2 mm.

Example: Height by Triangulation. Estimate the height of the building shown by “triangulation,” with the help of a bus-stop pole and a friend. (See how useful the diagram is!) Figure 1-9. Caption: Example 1–7. Diagrams are really useful! Answer: The building is about 15 m tall.

Dimensions & Dimensional Analysis The dimensions of a quantity are the base units that make it up. Generally they are written using square brackets. Example: Speed = distance/time Dimensions of Speed: [L/T] Quantities that are being added or subtracted must have the same dimensions. In addition, a quantity calculated as the solution to a problem should have the correct dimensions.

 The correct units can easily be found! ρ = m/V Density unit = kg/m3 Dimensional Analysis If the formula for a physical quantity is known  The correct units can easily be found! Example: Volume: V = L3  Volume unit = m3 A cube with L =1 mm  V = 1 mm3 = 10-9 m3 Example: Density: ρ = m/V Density unit = kg/m3 ρ = 5.3 kg/m3 = 5.3 10-6 g/mm3

 The correct formula can be “guessed”! Acceleration unit = m/s2 Dimensional Analysis If the units of a physical quantity are known  The correct formula can be “guessed”! Examples: Velocity: A car’s velocity is 60 km/h Velocity unit = km/h  Formula: v = d/t (d = distance, t = time) Acceleration: A car’s acceleration is 5 m/s2 Acceleration unit = m/s2  Formula: a = v/t (v = velocity, t = time)

Example: Is this the correct equation for velocity? Dimensional Analysis = Checking dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions. Example: Is this the correct equation for velocity?

Example: Is this the correct equation for velocity? Dimensional Analysis = Checking dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions. Example: Is this the correct equation for velocity? Check the dimensions:

Example: Is this the correct equation for velocity? Dimensional Analysis = Checking dimensions of all quantities in an equation to ensure that those which are added, subtracted, or equated have the same dimensions. Example: Is this the correct equation for velocity? Check the dimensions: Wrong!

Dimensional Analysis