Week - 1 - Consistency of Units

Objective:
To write the given measurements in the above different system of units. Also, discuss the conversion factors

Procedure:
In terms of physics, SI units of the quantities are categorized into two types specifically

1. Fundamental quantities (Base)
2. Derived quantities

Assigned units

Mass	1kg
Length	1m
Time	1s
Force	1N
Stress	1Pa
Energy	1Nm
Density	1`(kg)/(m^3)`
Young's Modulus	210GPa
Velocity	56.33KMPH
Gravity	9.8`(m)/(s^2)`

Conversion of given measurements into an above different system of units

Kg, cm, ms

• Mass
  `1kg``rArr``1kg`
• Length
  `1m``rArr``1*10^2cm`
• Time
  `1s``rArr``1*10^3ms`
• Force
  `1N``rarr``1(kg*m)/(s^2)``rarr``1(kg*10^2*cm)/(10^6s^2)``rArr``1(10^-4kg*cm)/(ms^2)`
• Stress
  `1Pa``rarr``1(n)/(m^2)``rarr``1(10^-4*kg*cm)/(ms^2*(cm)^2)``rarr``1(10^-4*kg*cm)/(10^4*ms^2*cm^2)``rArr``1(10^-8kg)/(ms^2cm)`
• Energy
  `1Nm``rarr``1(10^-4*kg*cm*(10^2cm))/(ms^2)``rArr``1(10^-2kg*cm^2)/(ms^2)`
• Density
  1`(kg)/(m^3)``rarr``1(kg)/(10^2cm)^3``rArr``1(10^-6kg)/(cm^3)`
• Young's Modulus
  `210GPa``rarr``210*10^9*Pa``rarr``210.10^9*(n)/m^2``rarr``(210*10^9*10^-8*kg)/((cm*ms^2)``rArr``2100(kg)/(cm*ms^2)`
  
• Velocity
  `56.33KMPH``rarr``56.63*0.277778(m/s)``rarr``15.6472(m/s)``rarr``15.6472*(10^2cm)/(10^3*ms``rArr``15.6472(10^5cm)/(ms)`
  
• Gravity
  `9.81(m)/(s^2)``rarr``9.81(10^2cm)/((10^3ms)^2``rArr``9.81(10^-4cm)/(ms^2)`
  

Gm, mm, ms

• Mass
  `1kg``rArr``1*10^3gm`
• Length
  `1m``rArr``1*10^3mm`
• Time
  `1s``rArr``1*10^3ms`
• Force
  `1N``rarr``1(kg*m)/(s^2)``rarr``1(10^3*gm*10^3*mm)/(10^6ms^2)``rArr``1(gm*mm)/(ms^2)`
• Stress
  `1Pa``rarr``1(n)/(m^2)``rarr``1(gm*mm)/(ms^2(10^6mm)^2)``rArr``1(10^-6gm)/(ms^2*mm)`
• Energy
  `1Nm``rarr``1(gm*mm*(10^3mm))/(ms^2)``rArr``1(10^3gm*mm^2)/(ms^2)`
• Density
  1`(kg)/(m^3)``rarr``1(10^3*gm)/(10^3mm)^3``rArr``1(10^-6gm)/(mm^3)`
• Young's Modulus
  `210GPa``rarr``210*10^9*Pa``rarr``210.10^9(n)/m^2``rarr``(210*10^9*10^-6*gm)/((mm*ms^2)``rArr``210(10^3gm)/(mm*ms^2)`
  
• Velocity
  `56.33KMPH``rarr``56.63*0.277778*(m/s)``rarr``15.6472*(m/s)``rarr``15.6472*((10^3*mm)/(10^3*ms))``rArr``15.6472(mm)/(ms)`
  
• Gravity
  `9.81(m)/(s^2)``rarr``9.81(10^3mm)/((10^3ms)^2``rArr``9.81(10^-3mm)/(ms^2)`

Converted tabulations

Unit systems	Mass `1kg`	Length `1m`	Time `1s`	Force `1n`	Stress `1Pa`	Energy `1Nm`	Density `1(kg)/(m^3)`	Young's Modulus `210GPa`	Velocity `56.33KMPH`	Gravity `9.8(m)/(s^2)`
kg, cm, ms	`1kg`	`10^2cm`	`10^3ms`	`(10^-4*kg*cm)/(ms^2)`	`1(10^-8kg)/(ms^2cm)`	`1(10^-2kg*cm^2)/(ms^2)`	`1(10^-6kg)/(cm^3)`	`210*10^1(kg)/(cm*ms^2)`	`15.6472(10^-1cm)/(ms)`	`9.8(10^-4cm)/(ms^2)`
kg, cm, s	`1kg`	`10^2cm`	`1s`	`(10^2*kg*cm)/(s^2)`	`1(10^2kg)/(s^2cm)`	`1(10^-2kg*cm^2)/(s^2)`	`1(10^-6kg)/(cm^3)`	`210*10^7(kg)/(cm*s^2)`	`15.6472(10^2cm)/(s)`	`9.8(10^2cm)/(s^2)`
gm, mm, ms	`10^3gm`	`10^3mm`	`10^3ms`	`(1*gm*mm)/(ms^2)`	`1(10^-6gm)/(ms^2mm)`	`1(10^3gm*mm^2)/(ms^2)`	`1(10^-6gm)/(mm^3)`	`210*10^3(gm)/(mm*ms^2)`	`15.6472(mm)/(ms)`	`9.8(10^-3mm)/(ms^2)`
kg, m, s	`1kg`	`1m`	`1s`	`(kg*m)/(s^2)`	`(kg)/(s^2*m)`	`(kg*m^2)/(s^2)`	`(kg)/(m^3)`	`210*10^9(kg)/(m*s^2)`	`15.64(m)/(s)`	`9.8(m)/(s^2)`
gm, cm, s	`10^3gm`	`10^2cm`	`1s`	`(10^5gm*cm)/(s^2)`	`1(10gm)/(s^2cm)`	`1(10^7gm*cm^2)/(s^2)`	`1(10^-3gm)/(cm^3)`	`210*10^10(gm)/(cm*s^2)`	`15.6472(10^2cm)/(s)`	`9.8(10^2cm)/(s^2)`
gm, cm, us	`10^3gm`	`10^2cm`	`10^6mus`	`(10^-7*gm*cm)/(mus^2)`	`1(10^-11gm)/(mus^2cm)`	`1(10^-5gm*cm^2)/(mus^2)`	`1(10^-3gm)/(cm^3)`	`210*10^-2(gm)/(cm*mus^2)`	`15.6472(10^-4cm)/(mus)`	`9.8(10^-10cm)/(mus^2)`
gm, mm, s	`10^3gm`	`10^3mm`	`1s`	`(10^6*gm*mm)/(s^2)`	`1(gm)/(s^2mm)`	`1(10^9gm*mm^2)/(s^2)`	`1(10^-6gm)/(mm^3)`	`210*10^9(gm)/(mm*s^2)`	`15.6472(10^3mm)/(s)`	`9.8(10^3mm)/(s^2)`
ton, mm, s	`10^-3Ton`	`10^3mm`	`1s`	`(Ton*mm)/(s^2)`	`(10^-6 Ton)/(s^2mm)`	`1(10^3Ton*mm^2)/(s^2)`	`1(10^-12Ton)/(mm^3)`	`210*10^3(Ton)/(mm*s^2)`	`15.6472(10^3mm)/(s)`	`9.8(10^3mm)/(s^2)`
slug, ft, s	`6.8*10^-2slug`	`3.3ft`	`1s`	`(22.44*10^-2*slug*ft)/(s^2)`	`(2.0606*10^-2*slug)/(s^2*ft)`	`(74.052*10^-2*slug*ft^2)/(s^2)`	`(0.1892*10^-2*slug)/(ft^3)`	`(432.726*10^7*slug)/(s^2*ft)`	`(51.612ft)/(s)`	`(32.373)/(s^2)`
kg, mm, s	`1kg`	`10^3mm`	`1s`	`(10^3*kg*mm)/(s)`	`10^-3(kg)/(s*mm)`	`1(10^6kg*mm^2)/(s)`	`1(10^-9kg)/(mm^3)`	`210*10^6(kg)/(mm*s)`	`15.6472(10^3mm)/(s)`	`9.8(10^3mm)/(s^2)`
gm, cm, ms	`10^3gm`	`10^2cm`	`10^3ms`	`(10^-1*gm*cm)/(ms^2)`	`1(10^-5gm)/(ms^2cm)`	`1(10gm*cm^2)/(ms^2)`	`1(10^-3gm)/(cm^3)`	`210*10^4(gm)/(cm*ms^2)`	`15.6472(10^-1cm)/(ms)`	`9.8(10^-4cm)/(ms^2)`
kg, mm, ms	`1kg`	`10^3mm`	`10^3ms`	`(10^-3*kg*mm)/(ms^2)`	`1(10^-9kg)/(ms^2mm)`	`1(10^-9kg*mm^2)/(ms^2)`	`1(10^-9kg)/(mm^3)`	`210(kg)/(mm*ms^2)`	`15.6472(mm)/(ms)`	`9.8(10^-3mm)/(ms^2)`

Conclusion:
The given measurements are converted to the above different system of units respectively