Week - 1 - Consistency of Units

AIM: Convert the given values in the required conversion factor units with detailed calculation.

OBJECTIVE :

• Note down the given data values.
• Detailed calculation for conversion from SI unit to gm/mm/ms unit system.
• Table content of the remaining values of conversion from SI to different unit values as per requirement.

Given data  :

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

conversion from SI unit to gm/mm/ms unit system :

•  MASS         :      1kg = 1000gm

•  LENGTH      :      1m  = 100 cm = 10000 mm

•  TIME          :      1s   =  1000 ms

• Force 1 N in trems of gm/mm/ms

N = kg*(m/s^2)

   = 1000*((1000)/(1000^2))

   = 1 gm mm ms^-2

   = C.F= 1

• Pascal  in terms of gm/mm/ms

Pascal = N/m^2

          = kg*(m/s^2)*(1/m^2)

          = (1000)/((1000*1000^2)

          =1x10^-6 gm/mm/ms   

• Energy in terms of gm/mm/ms       

J = NM   

  = (kg)*(m/s^2)*m

  = (1000)*(1000)^2/(1000)^2

   = 1000

ENERGY 1 NM =  10^3 gm * mm^2 * / ms^2

• Density in terms of gm/mm/ms

1 Kg/m^3 = (1000)/(1000)^3

Density KG/m^3  =  10^-6 g/mm^3 

• YOUNG'S Modulus  210GPa In terms of gm/mm/ms  

GPA = PA = 1*10^9

          = kg*(m/s^2)*(1/m^2) * 1*10^9

          = 210*10^3  gm/mm*ms^2

• Velocity 56.33KMPH in terms of gm/mm/ms 

KM/H = (10^6*1000)/(3600*1000)

         = 15.64 mm / ms

• Gravity in terms of gm/mm/ms 

9.8 m/s^2 = (1000)/(1000)^2

9.8 m/s^2 =  9.8*10^-3 mm/ms^2

Unit	Mass	Length	Time	Force	Stress	Energy	Density	Youngs Modulus	Velocity	Gravity
Kg cm ms	1	100	1000	10^-4 kg*cm/ms^2	10^-8 kg/cm*ms^2	10^−2kg×cm2/ms^2	10^-6 kg/cm^3	2100 kg/cm*ms^2	1.56 cm/ms	9.81 *10^-4cm/ms
Kg cm s	1	100	1	100 kg*cm/s^2	10^-2 kg/cm*s^2	10^-4kg/cm^3	10^-6kg/cm^3	210*10^7kg/cm*s^2	1564.72cm/s	9.8×10^2cm/s^2
gm mm ms	10^3g	10^3mm	10^3ms	1g×mm/ms^2	10^−6g/mm×ms^2	10^3g×mm2/ms^2	10^−6g/mm^3	210×10^3g/mm×ms^2	15.647mm/ms	9.8×10^−3mm/ms^2
kg m s	1	1	1	1kg×m/s^2	1 kg/m*s^2	1kg×m^2/s^2	1kg/m^3	210×10^9kg/m×s^2	15.647m/s	9.8m/s^2
g cm s	10^3g	10^2cm	1	10^5g×cm/s^2	10g/cm×s^2	10^7g×cm^2/s^2	10^−3g/cm^3	210×10^10g/cm×s^2	1564.72cm/s	9.8×10^2cm/s^2
g cm us	10^3g	10^2mm	1	10^−7g×cm/μs^2	10^−11g/cm×μs^2	10^−5g×cm^2/s^2	10^−3g/cm^3	2.10g/cm×μs^2	15.647×10-4cmμs">15.647×10^−4cm/15.647×10-4cmμs">μs	9.8×10^−10cm/μs^2
g mm s	10^3g	10^2mm	1	10^6g×mm/s^2	10^-2 kg/cm*s^2	10^9g×mm^2/s^2	10^−6gm/m^3	210×10^9g/mm×s^2	15647.2mm/s	9.8×10^3mm/s^2
ton mm s	10^−4tonne	10^3mm	1	10^−1tonne×mm/s^2	10^2tonne×mm^2/s^2	10^−13tonne/mm^3	10^−13tonne/mm^3	210×10^2tonne/mm×s^2	15647.2mm/s	9.8×10^3mm/s^2
slug ft s	0.068slug	3.28ft	1	0.223slug×ft/s^2	0.0207slug/ft×s^2	0.7314slug×ft^2/s^2	19×10^−4slug/ft^3	4.347×109slug/ft×s^2	51.34ft/s	32.14ft/s^2
kg mm s	1	1000	1	10^3kg×mm/s^2	10-3kgmm×s2">10^−3kg/mm×s^2	10^6kg×mm^2/s^2	10-9kgmm3">10^−9kg/mm^3	210×10^6kg/mm×s^2	15647.2mm/s	9.8×10^3mm/s^2
g cm ms	1000	100	1000	10^−1g×cmm/s^2	10^−5g/cm×ms^2	10g×cm^2/ms^2	10^−3g/cm^3	210×10^4g/cm×ms^2	1.5647cm/ms	9.8×10^−4cmm/s^2
kg mm ms	1	1000	1000	10-3kg×mmms2">10−3kg×mm/ms^2	10^−9kg/mm×ms^2	1kg×mm^2/ms^2	10^-9kg/mm^3	210kg/mm×ms^2	15.647mm/ms	9.8×10^−3mm/ms^2