Week - 1 - Consistency of Units

AIM

Familiar with different Units system and conversion method in Engineering.

OBJECTIVE

Measurements of different quantities need to be converted into different units.

Quantities	Magnitude	Units
Mass	1	Kilogram (Kg)
Length	1	Meter(m)
Time	1	Second
Force	1	Newton(N)
Stress	1	Pascal(pa)
Energy	1	Newton meter (Nm)
Density	1	Kilogram per Meter3(kg/m)
Young’s Modulus	210	Giga Pascal (Gpa)
Velociity	56.33	Kilo meter per Hour (KMPH)
Gravity	9.8	Meter per second2

Theory

Measurement of any physical quantity involves comparison with a certain basic, arbitrarily chosen, internationally accepted reference standard called unit. The result of a measurement of physical quantity is expressed by a magnitude accompanied by unit. Although the magnitude appears to be very large, we need only a limited number of units for expressing all the physical quantities, since they are interrelated with each other. In earlier there are three such units used in the world CGS (Centimeter Gram Second), FPS (Foot pound Second) and MKS (Meter Kilogram Second).

Meter: Length of path travelled by light in vacuum during a time interval of 1/299792458 of a second.

1m = 100cm

1000mm

3 ft 3.37inch

10^-3 km

Kilogram: The mass of international prototype of a Platinum- iridium alloy cylinder kept at international Bureau of weights and measure at serves Paris France.

1 kg = 1000g

10^-3 ton

0.065218 slug

Second: The duration of 9192631770 periods of radiation corresponding to the transition between the two hyperfine levels of the grounds state of the cesium 133 atom.

1 s = 10^-3 milliseconds (ms)

10^-6 microseconds(µs)

Newton: It is derived units of force. The force which gives mass of 1 kg an acceleration 1 m/s² is known as Newton.

1 N = 1 kg m/s²

Pascal (Pa): It is a derived unit of stress. When 1 N of force is applied on the 1 m² area of object then the stress developed is equal to pascal.

1 Pa = 1 N/m²

CONVERSION

	Mass 1 kg	Length 1 m	Time 1 s	Force 1 N	Stress 1 Pa	Energy 1 Nm	Density 1 Kg/m3	Young’s Modulus 210 GPa	Velocity 56.33 Km/H	Gravity 9.8 m/s2
Kg m s	1 kg	1 m	1 s	1 kg m/ s2	1 kg/m s2	1 kg m2/ s2	1 Kg/m3	21 X 1010 kg/m s2	15.6 m/s	9.8 m/s2
Kg cm s	1 kg	102 cm	1 s	102 kg cm/s2	10-2 kg/ cm s2	104 kg cm2/s2	10-6 kg/cm3	21 X 108 kg/cm s2	1560 cm/s	9.8 X 102 cm/s2
Kg cm ms	1 kg	102 cm	10-3 ms	108 kg cm/ ms2	104 kg/cm ms2	1010 kg cm2 /ms2	10-6 kg/cm3	21 X 1014 kg/ cm ms2	15.6 X 102 cm/ms	9.8 X 108 cm/ms2
Kg mm s	1 kg	103 mm	1 s	103 kg mm/s	1 kg/ mm s2	106 kg mm2/s2	10-9 kg/mm3	21 X 106 kg/mm s2	15.6 X 103 mm/s	9.8 X 103 mm/s2
Kg mm ms	1 kg	103 mm	10-3 ms	109 kg mm/ms2	106 kg/mm ms2	1012 kgmm2/s2	10-9 kg/mm3	21 X 1012 kg/mm ms2	15.6 X 106 mm/ms	9.8 X 109 mm/ms2
g mm ms	1000 g	103 mm	10-3 ms	1012 g mm/ms2	109 g/mm ms2	1015 g mm2/s2	10-6 g/mm3	21 X 1015 g/mm ms2	15.6 X 106 mm/ms	9.8 X 109 mm/ms2
g cm s	1000g	102 cm	1 s	105 g cm/s2	10 g/cm s2	107 g cm2/s2	10-3 g/cm3	21 X 1011 g/cm s2	1560 cm/s	9.8 X 102 cm/s2
g cm µs	1000g	102 cm	10-6 µs	1017 g cm/µs2	107 g/ cm µs2	1019gcm2/ µs2	10-3 g/cm3	21 X 1023 g/cm µs2	15.6 X 107 cm/µs	9.8 X 1014 cm/µs2
g mm s	1000g	103 mm	1 s	106 g mm/s2	10-1 g/mm s2	109 g mm2/s2	10-6 g/mm3	21 X 1010 g/mm s2	15.6 X 103 mm/s	9.8 X 103 mm/s2
g cm ms	1000g	102 cm	10-3 ms	1011 g cm/ms2	107 g/cm ms2	1013 g cm2/ms2	10-3 g/cm3	21 X 1017 g/cm ms2	15.6 X 102 cm/ms	9.8 X 108 cm/ms2
Ton mm s	10-3 ton	103 mm	1 s	1 ton mm/s2	10-6 ton/mm s2	103ton mm2/s2	10-6 ton/mm3	21 X 104 ton/mm s2	15.6 X 103 mm/s	9.8 X 103 mm/s2
Slug Ft s	0.065218 slug	3 ft 3.37 inch	1 s	0.2145 slug ft/s2	0.019 slug/ft s2	0.70 slug ft2/s2	2.34 slug / ft2	413.6 X 107 slug/ft s2	51.48 ft/s	32.34 ft/s2

CONCLUSION

Hence all the units is converted into the respective unit system.