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Chapter 1: Measurement - Physical Quantities, Standards, and Units

This chapter introduces the concept of physical quantities, standards, and units of measurement. It covers the International System of Units, standard of time, length, and mass, as well as dimensional analysis.

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Chapter 1: Measurement - Physical Quantities, Standards, and Units

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  1. Chapter 1 Measurement نظام المقاييس

  2. Units of Chapter 1: Measurement • The Physical Quantities, Standards and Units • The international System of units • The standard of time • The standard of length • The standard of mass • Dimensional Analysis

  3. 1-1 The Physical Quantities, Standards and Units • To describe the physical quantities we need to choose a unit that does not differ from a corresponding quantity physically but has a quite definite dimension. • Every Physical quantity (Y) can be defined as the product of a (unit) multiplied by an abstract number (x): • Y = X (unit) • For example: • Mass = 5 Kg • Physical Quantities • Basic ( Length, Mass, Time) • Derived ( area, speed, density, ….)

  4. 1-2 The International System of Units

  5. Other System of Units • Gaussian System of Units • Length in (cm): 1 cm = 10-2m • Mass in (g) : 1 g = 10-3kg • Time in (s) • British System of Units • Length in feet (ft): 1 foot (ft) = 12 in = 30.48 cm • Mass in Pound (lb): 1 pound (lb) = 453.59 g • Time in second (s)

  6. Prefixes • The standard prefixes are used to designate common multiples in powers of ten. • 1 angstrom=10-10m

  7. 1-3 The Standard of Time • Unit of Time is second (s) • Before 1960, the second was originally defined as of the mean solar day. • Now: the second (s) is defined as the time required for Cesium (Cs-133) atom to undergo 9,192,631,770 vibration .

  8. Typical Time Intervals

  9. 1-4 The Standard of Length • SI Unit of Length: the meter (m) • in October 1983, the meter (m) was redefined as the distance traveled by light in vacuum during a time of 1/299 792 458 second. Converting Units of length • 1 inch (in)= 2.54 cm = 0.0254 m • 1 foot (ft) = 12 in = 30.48 cm = 0.304 m • 1 yard (yd) = 3 feet = 36 in= 0.9144 m • 1 miles (mi) =1760 yards = 5280 feet = 1,609.344 m • 1 m = 3.281 ft

  10. Typical Length

  11. 1-5 Standard Mass • Unit of Mass: kilogram (kg) • The kilogram (kg), is defined as the mass of a specific platinum–iridium alloy cylinder kept at the International Bureau of Weights and Measures at Sèvres, France. • This mass standard was established in 1887 and has not been changed since that time because platinum–iridium is an unusually stable alloy. • Converting Unit of Mass • The atomic mass unit u is 1 u = 1.66110-27 kg 1 pound (lb) = 453.59 g

  12. Typical Mass

  13. Problems • The speed in meters per second equivalent to 66 miles per hour (1 miles (mi) = 1609 m) ؟ • Convert 63 feet to yard ( 1yard=3 feet) is ? • What is the diameter of hydrogen atom has diameter 10nm ? • If the height of a plane in air 35000ft , the height of the unit SI . ( 1m=3.281ft ) ? • A train traveling 100 𝑘𝑚/ℎ .The speed of this train is SI? • A circle with a radius of 5 cm has an area of : (area=πr2) ?

  14. 1-7 Dimensional Analysis • The dimension in physics refer to the type of quantity in question regardless of the unit used in the measurement. • The symbols we use to specify length, mass, and time are L, M, and T, respectively. • We shall often use brackets [ ] to denote the dimensions of a physical quantity. For example, the nature of speed v, is length/time, so the dimension of speed [v]=L/T, and nature of the area is length  length, so the dimension of the area [A]=L2. • Any valid physical formula must be dimensionally consistent- each term of the formula must have the same dimensions. • This type of calculation with dimensions is (dimensional analysis).

  15. 1-7 Dimensional Analysis

  16. Problems • The acceleration a in m/s2 of a car is given by a=bt2, where the t is the time in sec. using the dimensional analysis, the unit of b is ? • If x=kt4 where x is the displacement in m and t is the time in s. The dimension of k ? • Show that the expression v = vo + at is dimensionally correct, where v and vo are the velocities and a is the acceleration, and t is the time. ? • Suppose that the acceleration of a particle moving in circle of radius r with uniform velocity v is proportional to the rn and vm. Use the dimensional analysis to determine the power n and m?

  17. HW • A car is traveling 50 Km/h. The speed of this car in SI units is ? • Using the dimensional analysis check that this equation x = ½ at 2is correct, where x is the distance, a is the acceleration and t is the time?

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