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Lesson_1.1_Printable - Lesson 1.1 1.1 Units and Measurement...

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Lesson 1.1 1.1 Units and Measurement A physical quantity is identified by its unit of measurement. We will use the SI system of units in this course. The unit of length is the meter (m) The unit of mass is the kilogram (kg) The unit of time is the second (s) Units of length, mass and time are called the fundamental units of measurement. The units of all other physical quantities can be obtained by suitably combining these fundamental units. 1
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Meter (m) is the unit of length The following is a summary of units for measuring small and large lengths as part of a meter or combination of a meter. Pico, nano, micro, milli, centi, deci, meter (m) , 10 0 = 1 10 -1 10 -2 10 -3 10 -6 10 -9 10 -12 deka, hecto, kilo, mega, giga, tera 10 1 10 2 10 3 10 6 10 9 10 12 Similar measures are used for measuring small and big masses 2
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Area, volume, speed, density are examples of physical quantities that have units that are derived from the fundamental units. Units of such quantities are called derived units. distance Speed = time The unit of area is m 2 and the unit of volume is m 3 The unit of speed is m s and we write it as: ms -1 mass Density = volume The unit of density is 3 kg m and we write it as: kgm -3 3
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It is important to convert all units to m, kg, s in solving problems in physics. 1 m = 10 3 mm 1 m = 10 2 cm 1 m = 10 6 μ m 1 m 2 = 10 4 cm 2 1 m 3 = 10 6 cm 3 1 mm = 10 -3 m 1 cm = 10 -2 m 1 μ m = 10 -6 m 1 cm 2 = 10 -4 m 2 1 cm 3 = 10 -6 m 3 1 kg = 10 3 g 1 g = 10 -3 kg 1km = 10 3 m 10 6 = Mega (M) 10 3 = kilo (k) 10 -3 = milli (m) 10 -6 = micro ( μ ) 10 -9 = nano (n) 10 -12 = pico (p) 1 h = 3600 s 4
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m Convert 25 to s km hr 25 km h 3 25 10 m × = 3600 s 25 m = 3.6 s -1 = 6.94 m s 3 3 kg Convert 3.5 to g m cm 3 3.5 g cm 6 3 10 m - 3 3.5 10 kg - × = 3 -3 = 3.5 10 kg m × 5
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= 1.26 × 10 21 m 3 3 4 V= 3 r π The radius of the earth is 6700 km. Find the volume of the earth and express it in m 3 Earth is spherical and the volume of a sphere is given by: Here r = 6700 km = 6700 10 3 m = 6.7 × 10 6 m . 6 3 4 V= (6.6 10 ) π × 3 6
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Dimensions Dimension of a physical quantity indicates the nature of the quantity. We will represent the dimension of length by L The dimension of mass is M The dimension of time is T In the equation x = ½ at 2 , x is distance that has the dimension L and t is time that has the dimension T. What is the dimension of a? We replace each quantity by its dimension. L = ½ a T 2 Solving for a gives: 2 2 L a T = Since 2 is a constant, it has no dimension. The dimension of a is: 2 L T 2 LT - = 7
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Some of the physical quantities we use in this course and their dimensions in terms of L, M and Tare given below Quantity Symbol Dimension Area A L 2 Volume V L 3 speed v LT -1 Acceleration a LT -2 Density ρ ML -3 8
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The period of oscillation of a simple pendulum is known to depend on it length and the acceleration due to gravity. Use dimensions of the quantities involved to obtain an equation for the period of a pendulum of length L We start by assuming that the period T is proportional to L x and a y where a is the acceleration caused by gravity We can then write: T = k L x a y where k is a constant.
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