Week - 1 - Consistency of Units

Given units are:

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

Force=(MassxLength)/Time^2,Energy=MassxLength^2/Time^2,Young's modulus=Mass/(LengthxTime^2)

Stress=Mass/(LengthxTime^2),Density=Mass/Length^3,Velocity=Length/Time,Gravity=Length/Time^2.

1N=1 kg x m/s^2, 1Pa=1kg/(mxs^2), 1GPa=1E+09 Pa,

SI UNIT to gm/mm/ms:

Mass:1 Kg=1000 gm, Length:1m=1000 mm, 1s=1000 ms,

Force: 1N=1kgXm/s^2=1000gmX1000mm/(1000 ms)^2=1gmXmm/ms^2, so force conversion factor into gmXmm/ms^2=1

Stress:Pa=1 kg/(mXs^2)=1E+03gm/(1E+03mm X 1E+06 ms^2)=1E-06 gm/(mmXms^2),so stress conversion factor into gm/(mmXms^2)=1E-06

Energy:J=1kgX(m/s)^2=1000 gmX(1000mm/1000s)^2=1E+03 gmX(mm/ms)^2 so energy conversion factor into gmX(mm/ms)^2=1E+03

Density:1kg/m^3=1000 gm/(1000 mm)^3=1E-06 gm/mm^3,so density conversion factor into gm/mm^3=1E-06

Young modulus=210 GPa=2.11 E+11Pa=(2.11 E+11)X 1E-06=2.11E+05 gm/(mmXms^2),so Young'Modulus conversion factor into gm/(mmXms^2)=1E-06

Velocity:56.33 km/hr=56.33 X1000m/3600s=15.6472m/s=15.6472 X1000mm/1000 ms=15.6472 mm/ms,so Velocity conversion factor into mm/ms=1

Gravity=9.8 m/s^2=9.8X 1E+03 mm/(1E+03 ms)^2=9.8E-03 mm/ms^2,so gravity conversion factor into mm/ms^2=1E-03.

MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG'S Modulus	Velocity	GRAVITY
kg	1E+02 cm	1E+03 ms	1E-04 kgXcm/ms^2	1E-08 kg/(cmXms^2)	1E-02 kgX(cm/ms)^2	1E-06 kg/cm^3	2.1E+03 kg/(cmXms^2)	15.6472E-1 cm/ms	9.8E-04 cm/ms^2
kg	cm	s	1E+02 kgXcm/s^2	1E-02 kg/(cmXs^2)	1E+04 kgX(cm/s)^2	1E-06 kg/cm^3	2.1E+09 kg/(cmXs^2)	15.6472E+02 cm/s	9.8E+02 cm/s^2
gm	mm	ms	1E-01 gmXmm/ms^2	1E-06 gm/(mmXms^2)	1E+3 gmX(mm/ms)^2	1E-06 gm/mm^3	2.1E+05 gm/(mmXms^2	15.6472E-0 mm/ms	9.8E-3 mm/ms^2
kg	m	s	1N=1E+00 kg x m/s^2	Pa=kg/(mxs^2)	J=kgxm^2/s^2	kg/m^3	2.1E+11 Pa	15.6472 m/s	9 .8 m/s^2
gm	cm	s	1E+05 gmxcm/s^2	1E+01 gm/(cmXs^2)	1E+7 gmXcm^2/s^2	1E-03 gm/cm^3	2.1E+12 gm/(cmXs^2)	15.6472E+02 cm/s	9.8E+02 cm/s^2
gm	cm	us	1E-07 gmXcm/us^2	1E-11 gm/(cmXus^2)	1E-05 gmXcm^2/us^2	1E-03 gm/cm^3	2.1 E+01 gm/(cmXus^2)	15.6472E-04 cm/us	9.8E-10 cm/us^2
gm	mm	s	1E+06 gmxmm/s^2	1E-00 gm/(mmXs^2)	1E+09 gmXmm^2/s^2	1E-06 gm/mm^3	2.1E+11 gm/(mmXs^2)	15.6472E+03 mm/s	9.8E+03 mm/s^2
ton	mm	s	1E+00 tonxmm/s^2	1E-06 ton/(mmXs^2)	1E+03 tonXmm^2/s^2	1E-12 ton/mm^3	2.1E+05 ton/(mmXs^2)	15.6472E+03 mm/s	9.8E+03 mm/s^2
slug	ft	s	6.85E-02 slugxft/s^2	2.25E+0.1 slug/(ftXs^2)	2.05E-02 slugXft^2/s^2	7.216E-1 slug/ft^3	4.305E+09 slug/(ftXs^2)	51.361 ft/s	32.14 ft/s^2
kg	mm	s	1E+03 kgXmm/s^2	1E-03 kg/(mmXs^2)	1E+06 kgX(cm/s)^2	1E-09 kg/mm^3	2.1E+08 kg/(mmXs^2)	15.6472E+03 mm/s	9.8E+03 mm/s^2
gm	cm	ms	1E-01 gmXcm/s^2	1E-05 gm/(cmXms^2)	1E+01 (gmXcm^2/ms^2)	1E-03 gm/cm^3	2.11E+06 gm/(cmXms^2)	15.6472E-01 cm/ms	9.8E-04 cm/ms^2
kg	mm	ms	1E-03 kgxmm/ms^2	1E-09 kg(mmXms^2)	1E+00 (kgXmm^2/ms^2)	1E-09 kg/mm^3	2.11 gm/(cmXms^2)	15.60 mm/ms	9.8E-03 mm/ms^2