Week - 1 - Consistency of Units

Consistency of Units

Objectives: - Write the given measurements of the following different systems of units. Also, mention the conversion factors.

Value of the following measurements are given as follows:

MASS 1kg
LENGTH 1m
TIME 1s
FORCE 1N
STRESS 1Pa
ENERGY 1Nm
DENSITY 1Kg/m3
YOUNG'S Modulus 210GPa
Velocity 56.33KMPH
GRAVITY 9.8m/s2

Now, here are a few systems of units:

Kg cm ms

Kg cm s

gm mm ms

kg m s

g cm s

g cm us

g mm s

ton mm s

slug ft s

kg mm s

g cm ms

kg mm ms

Procedure:-

Mass: -

1 tonne = 1000kg ,

1 kg = 1000 gram = 0.001 tonne = 0.068 slug ,

1 gram = 1000 mg (milligram)

Length: -

1 km = 1000 m ,

1 m = 100 cm = 1000 mm = 3.28 ft ,

1 mm = 100 μm.

Time: -

1 Hour = 3600 s ,

1 s = 1000 ms = 10^6 μs

SI unit to gm mm ms

Mass: -

1 kg = 1000 gram

Length: -

1 m = 1000 mm

Time: -

1 s =1000 ms

Force: -

F = m.a

= 1 kg * m/s2

= (1000 g )*(1000 mm)/ (1000 ms)^2

= 10^6 g mm/ 10^6 ms^2

F=1N = 1 g mm/ms^2

Conversion Factor = 1

Stress: -

1Pa = 1 N/m^2

= (1 g mm/ ms^2) /(1000 mm)^2

= (1 g mm/ ms^2) / (10^6 mm^2)

1Pa = 10^-6 g /mm ms^2

Conversion Factor = 10^-6

Energy: -

Nm = 1 g mm/ ms^2 * 1 m

= 1 g mm/ms^2 * 10^3 mm

Nm = 10^3 g mm^2 / ms^2

Conversion Factor = 10^3

Density: - ρ: -

= kg/m^3

= 10^3 g /( 10^3 mm)^3

= 10^3 g / ( 10^9 mm ^3)

ρ = 10^-6 g /mm^3

Conversion Factor = 10^-6

Young's Modulus = 210 GPa

• 1 Pa (N/m²) = 1x10^-6 N/mm²
• 1 MPa = 10⁶ Pa (N/m²)
• 1 GPa = 10⁹ N/m² = 10⁶ N/cm² = 10³ N/mm²

GPa = 10^9 * 10^-6 g/mm ms^2

210 GPa = 210*10^3 g/mm ms^2

Conversion Factor = 10^3

Velocity = 56.33 kmph

km = 10^6 mm

1 Hour = 3600 s = 3600000 ms

kmph = 56.33*10^6 mm / 3.6*10^6 ms

V = 15.60 mm/ms

Conversion Factor = 1

Gravity: - 9.8 m/s^2

= 9.8*10^3 mm/ 10^6 ms^2

= 9.8*10^-3 mm / ms^2

Conversion Factor = 1

SI unit to g mm s

Force N = 10^6 g mm/s^2

Conversion Factor = 10 ^6

Stress: - Pa = 1* g/mm s^2

Conversion Factor = 1

Energy Nm = 10^9 g mm^2/s^2

Conversion Factor = 10^9

Density ρ = 10^-6 g/mm^3

Conversion Factor = 10^-6

Young's Modulus = 210 GPa = 210* 10^9 g/ mm s^2

Conversion Factor = 10^9

Velocity = 56.33 kmph = 15647 mm/s

Conversion Factor = 1

Gravity = 9.8*10^3 mm/s^2

Conversion Factor = 10^3

SI unit to g cm s

Force N = 10^5 g cm /s^2

Conversion Factor = 10^5

Stress: - Pa = 10 g /cm s^2

Conversion Factor = 10

Energy Nm =10^7 g cm^2/s^2

Conversion Factor = 10^7

Density: - ρ = 10^-3 g /cm^3

Conversion Factor = 10^-3

Young's Modulus = 210 GPa = 210*10^10 g/cm s^2

Conversion Factor = 10^10

Velocity = 56.33 kmph = 1564.72 cm/s

Conversion Factor = 1

Gravity = 9.8*10^2 cm/s^2

Conversion Factor = 10^2

SI unit to g cm ms

Force N = 10^-1 g cm /ms^2

Conversion Factor = 10^-1

Stress: - Pa = 10^-5 g /cm ms^2

Conversion Factor = 10^-5

Energy Nm = 10*g cm ^2 / ms^2

Conversion Factor = 10

Density: - ρ = 10^-3 g/cm^3

Conversion Factor = 10^-3

Young's Modulus = 210 GPa = 210*10^4 g/cm ms^2

Conversion Factor = 10^4

Velocity = 56.33 kmph =1.5647 cm/ms

Conversion Factor =1

Gravity = 9.8*10^-4 cm / ms^2

Conversion Factor =10^-4

SI unit to g cm us

Force N = 10^7 g cm /us^2

Conversion Factor = 10^-7

Stress: - Pa = 10^-11 g /cm us^2

Conversion Factor = 10^-11

Energy Nm = 10^-5 g cm^2 / us^2

Conversion Factor = 10^-5

Density: - ρ = 10^-3 g/cm^3

Conversion Factor = 10^-3

Young's Modulus = 210 GPa = 210*10^-2 g / cm us^2

Conversion Factor = 10^-2

Velocity = 56.33 kmph = 1.5647*10^-4 cm/us

Conversion Factor = 10^-4

Gravity = 9.8*10^-10 cm /us^2

Conversion Factor = 10^-10

SI unit to kg m s

Force N = 1 kg m /s^2

Conversion Factor = 1

Stress: - Pa = 1 kg / s^2 m

Conversion Factor = 1

Energy Nm = 1 kg m^2 / s^2

Conversion Factor = 1

Density: - ρ = 1 kg / m^3

Conversion Factor = 1

Young's Modulus = 210 GPa = 210*10^9 kg/s^2 .m

Conversion Factor = 10^9

Velocity = 56.33 kmph = 15.64 m/s

Conversion Factor =1

Gravity = 9.8 m/s^2

Conversion Factor = 1

SI unit to kg cm s

Force N = 10^2 kg cm /s^2

Conversion Factor = 10^2

Stress: - Pa = 10^-2 kg / cm s^2

Conversion Factor = 10^-2

Energy Nm = 10^4 kg cm^2 /s^2

Conversion Factor = 10^4

Density: - ρ = 10^-6 kg / cm^3

Conversion Factor = 10^-6

Young's Modulus = 210 GPa = 210*10^7 kg /cm s^2

Conversion Factor = 10^7

Velocity = 56.33 kmph = 1564.72 cm / s

Conversion Factor = 1

Gravity = 9.8*10^2 cm /s^2

Conversion Factor = 10^2

SI unit to kg cm ms

Force N = 10^-4 kg cm /ms^2

Conversion Factor = 10^-4

Stress: - Pa = 10^-8 kg / cm ms^2

Conversion Factor = 10^-8

Energy Nm = 10^-2 kg cm^2 / ms^2

Conversion Factor = 10^-2

Density: - ρ = 10^-6 kg /cm ^3

Conversion Factor = 10^-6

Young's Modulus = 210 GPa = 210*10^1 kg /cm ms^2

Conversion Factor = 10

Velocity = 56.33 kmph = 1.5647 cm /ms

Conversion Factor =1

Gravity = 9.8*10^-4 cm / ms^2

Conversion Factor = 10^-4

SI unit to kg mm s

Force N = 10^3 kg mm / s^2

Conversion Factor = 10^3

Stress: - Pa = 10^-3 kg / mm s^2

Conversion Factor = 10^-3

Energy Nm = 10^6 kg mm^2 /s^2

Conversion Factor = 10^6

Density: - ρ = 10^-9 kg / mm^3

Conversion Factor = 10^-9

Young's Modulus = 210 GPa = 210*10^6 kg mm^2 /s^2

Conversion Factor = 10^6

Velocity = 56.33 kmph = 15.64*10^3 mm / s

Conversion Factor = 10^3

Gravity = 9.8*10^3 mm/s^2

Conversion Factor = 10^3

SI unit to kg mm ms

Force N = 10^-3 kg mm /ms^2

Conversion Factor = 10^-3

Stress: - Pa = 10^-9 kg / ms^2 mm

Conversion Factor = 10^-9

Energy Nm = 1 kg mm^2 /ms^2

Conversion Factor = 1

Density: - ρ = 10^-9 kg / mm^3

Conversion Factor = 10^-9

Young's Modulus = 210 GPa = 210 kg / mm ms^2

Conversion Factor = 1

Velocity = 56.33 kmph = 15.64 mm / ms

Conversion Factor = 1

Gravity = 9.8*10^-3 mm/ms^2

Conversion Factor = 10^-3

SI unit to ton mm s

Force N = 1 ton mm /s^2

Conversion Factor = 1

Stress: - Pa = 10^-6 ton/mm s^2

Conversion Factor = 10^-6

Energy Nm = 10^3 ton mm^2 /s^2

Conversion Factor = 10^3

Density: - ρ = 10^-12 ton / mm^3

Conversion Factor = 10^-12

Young's Modulus = 210 GPa = 210*10^3 ton / mm s^2

Conversion Factor = 10^3

Velocity = 56.33 kmph = 15647 mm / s

Conversion Factor = 1

Gravity = 9.8*10^3 mm / s^2

Conversion Factor = 10^3

SI unit to slug ft s

Mass: -

1 slug = 14.5939 kg

Length: -

1 ft = 0.3048 m

Time: -

1 s

Force N = 0.2248 slug ft / s^2

Conversion Factor = 1

Stress: - Pa = 0.02088 slug /ft s^2

Conversion Factor = 1

Energy Nm = 0.7375 slug ft^2 / s^2

Conversion Factor = 1

Density: - ρ = 1.9403*10^-3 slug /ft^3

Conversion Factor = 10^-3

Young's Modulus = 210 GPa = 4.3848*10^9 slug / ft s^2

Conversion Factor = 10^9

Velocity = 56.33 kmph = 51.33 ft / s

Conversion Factor = 1

Gravity = 32.1522 ft /s^2

Conversion Factor = 1

Table : -

S.I Units	Mass	Length	Time	Force (N)	Stress (Pa)	Energy (Nm)	Density (ρ)	Young's Modulus 210 GPa	Velocity 56.33 kmph	Gravity 9.8
Kg m s	1 kg	1 m	1 s	1 kg m /s^2	1 kg / s^2 m	1 kg m^2 / s^2	1 kg / m^3	210*10^9 kg/s^2 .m	15.64 m/s	9.8 m/s^2
kg cm s	1 kg	100 cm	1 s	10^2 kg cm /s^2	10^-2 kg / cm s^2	10^4 kg cm^2 /s^2	10^-6 kg / cm^3	210*10^7 kg/cm s^2	1564.72 cm / s	9.8*10^2 cm /s^2
kg cm ms	1 kg	100 cm	1000 ms	10^-4 kg cm/ms^2	10^-8 kg / cm ms^2	10^-2 kg cm^2 / ms^2	10^-6 kg /cm ^3	210*10^1 kg /cm ms^2	1.5647 cm /ms	9.8*10^-4 cm / ms^2
kg mm ms	1 kg	1000 mm	1000 ms	10^-3 kg mm/ms^2	10^-9 kg / mm. ms^2	1 kg mm^2/ms^2	10^-9 kg / mm^3	210 kg / mm. ms^2	15.64 mm / ms	9.8*10^-3 mm /ms^2
kg mm s	1 kg	1000 mm	1 s	10^3 kg mm / s^2	10^-3 kg / mm s^2	10^6 kg mm^2 /s^2	10^-9 kg / mm^3	210*10^6 kg mm^2 /s^2	15.64*10^3 mm / s	9.8*10^3 mm/s^2
g cm s	1000 g	100 cm	1 s	10^5 g cm /s^2	10 g /cm s^2	10^7 g cm^2/s^2	10^-3 g /cm^3	210*10^10 g/cm s^2	1564.72 cm/s	9.8*10^2 cm/s^2
g cm us	1000 g	100 cm	10e6 s	10^7 g cm /us^2	10^-11 g /cm us^2	10^-5 g cm^2 / us^2	10^-3 g/cm^3	210*10^-2 g / cm us^2	1.5647*10^-4 cm/us	9.8*10^-10 cm /us^2
g mm s	1000 g	1000 mm	1 s	10^6 g mm/s^2	1* g/mm s^2	10^9 g mm^2/s^2	10^-6 g/mm^3	210* 10^9 g/ mm s^2	15647 mm/s	9.8*10^3 mm/s^2
g mm ms	1000 g	1000 mm	1000 ms	1 g mm/ms^2	10^-6 g /mm ms^2	10^3 g mm^2 /ms^2	10^-6 g /mm^3	210*10^3 g/mm ms^2	15.60 mm/ms	9.8*10^-3 mm / ms^2
g cm ms	1000 g	100 cm	1000 ms	10^-1 g cm /ms^2	10^-5 g /cm ms^2	10* g cm ^2 / ms^2	10^-3 g/cm^3	210*10^4 g/cm ms^2	1.5647 cm/ms	9.8*10^-4 cm / ms^2
ton mm s	0.001 tonne	1000 mm	1 s	1 ton mm /s^2	10^-6 ton/mm s^2	10^3 ton mm^2 /s^2	10^-12 ton / mm^3	210*10^3 ton / mm s^2	15647 mm / s	9.8*10^3 mm / s^2
slug ft s	0.068 slug	3.28 ft	1 s	0.2248 slug ft / s^2	0.02088 slug /ft.s^2	0.7375 slug ft^2 / s^2	1.9403*10^-3 slug /ft^3	4.3848*10^9 slug /ft s^2	51.33 ft / s	32.1522 ft /s^2

Conclusion: -

In this challenge, we convert the S.I. unit to other different units with a conversion factor.