Week - 1 - Consistency of Units

OBJECTIVE:

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

Converted Measurements:

MASS 1kg = 1000 g
LENGTH 1m = 1000 mm
TIME 1s =1000 ms
FORCE 1N = 1kg * 1m/s^2 = 1000*1000 / (1000^2) = 1g(mm/ms^2)
STRESS 1Pa = 1N/m^2=(1kg*1m/s^2)/m^2=(1000*1000/1000^2)/1000^2=1*10^-6(mm*ms^2)
ENERGY 1Nm = (1kg*1m/s^2)*m=(1000*1000/(1000^2))/1000=1*10^3(g*mm^2/ms)*mm
DENSITY 1Kg/m3 =(1kg*1m/s^2)*m^3=(1000*1000/(1000^2))/1000^3=1*10^-6(g*mm^2/ms)*mm
YOUNG'S Modulus 210GPa=(1kg*1m/s^2)/m^2*10^9=(1000*1000/(1000^2)*10^9=210*10^3 g / (mm/ms^2)
Velocity 56.33KMPH = 56.33*1000*36*10^5 mm*ms =15.64 mm/ms
GRAVITY 9.8m/s2 = 9.80*1000/1000*1000=9.8*10^-3 mm / (ms^2)

Now, here are a few system 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

CONVERTED MEASUREMENTS

	Mass	Length	Time	Force	stress	energy	density	youngs Modulus	Velocity	gravity
kg
cm	1kg	10^2 cm	10^3 ms	10^-4	1*10^-8 kg/(ms^2cm)	1(10^-2kg*cm^2)/(ms^2)	1*10^-6	210*10^1	15.6472*10^-1	9.8*10^-4
ms				(kg*cm)/ms^2			kg/cm^3	(kg)/(cm*ms^2)		cm/ms^2
kg
cm	1kg	10^2 cm	1 s	1(10^2kg)/(s^2)	1(10^2kg)/(s^2 *cm)	1(10^-2kg*cm^2)/(s^2)	1*10^-6	210*10^7	15.6472*10^2	9.8*10^2 cm/s^2
s							kg/(cm^3)	kg/(cm*s^2)	cm/s
gm
mm	10^3g	10^3mm	10^3ms	10^3	1(10^-6gm)/(ms^2mm)	1(10^3gm*mm^2)/(ms^2)1*10^-6		210*10^3	15.6472	9.8*10^-3
ms				(gm*mm)/ms^2			gm/(mm^3)	(gm)/(mm*ms^2)	mm/ms	mm/ms^2
kg
m	1kg	1m	1s	1(kg*m)/s^2	1(kg)/(s^2*m)	1(kg*m^2)/(s^2)	1(kg)/(m^3)	210*10^9	15.64 m/s	9.8 m/s^2
s								(kg)/(m*s^2)
g
cm	10^3g	10^2 cm	1s	10^5(g*cm)/s^2	1(10gm)/(s^2cm)	(1(10^7gm*cm^2)/(s^2)	1(10^-3gm)	210*10^10	15.6472*10^2	9.8*10^2 cm/s^2
s							/(cm^3)	gm/(cm*s^2)	cm/s
g
cm	10^3g	10^2 cm	10^6 us	10^-7	1*10^-11 gm/(us^2cm)	1(10^-5gm*cm^2)/(us^2)	1(10^-3)	210*10^-2	15.6472*10^-4	9.8*10^-10
us				(g*cm)/us^2			gm/(cm^3)	gm/(cm*us^2)	cm/us	cm/us^2
g
mm	10^3g	10^3mm	1s	10^6(g*mm)/s	1(gm)/(s^2)mm	1(10^9gm*mm^2)/(s^2)	1*10^-6	210*10^9	15.6472*10^3	9.8*10^3 mm/s^2
s							gm/(mm^3)	gm/(mm*s^2)	mm/s
ton
mm	0.001t	10^3mm	1s	1(t*mm)/s^2	1*10^-6ton/(s^2mm)	1*(10^3*mm^2)/(s^2)	1*10^-2	210*10^3	15.6472*10^3	9.8*10^3 mm/s^2
s							ton/(mm^3)	ton/(mm*s^2)	mm/ms
slug
ft	0.0685s	3.28ft	1s	0.2246	2.0606*10^-2	74.052*10^-2	0.1892*10^-2	432.726*10^7	51.612 ft/s	32.373/s^2
s				(slug*ft)/s^2	slug/(s^2*ft)	slug*ft^2/(s^2)	slug/(ft^3)	slug/(s^2*ft)
kg
mm	10^3g	10^3mm	1s	10^3	10^-3 kg/(s*mm)	1(10^6kg*mm^2)/(s)	1*10^-9	210*10^6	15.6472*10^3	9.8*10^3 mm/s^2
s				(g*mm)/s^2			kg/(mm^3)	kg/(mm*s)	mm/s
g
cm	10^3g	10^2cm	1000ms	10^-1	1*10^-5gm/(ms^2cm)	1(10gm*cm^2)/(ms^2)	1*10^-3	210*10^4	15.6472*10^-1	9.8*10^-4
ms				(g*cm)/ms^2			gm/(cm^3)	gm/(cm*ms^2)	cm/ms	cm/ms^2
kg
mm	1kg	10^3 mm	1000ms	10^-3	1*10^-9kg/(ms^2mm)	1(10^-9kg*mm^2)/(ms^2)	1*10^-9	210kg/(mm*ms^2)15	15.6472	9.88*10^-3
ms				(kg*mm)/ms^2			kg/(mm^3)		mm/ms	mm/ms^2
g
mm	10^3g	10^3mm	1000ms	1g(mm*ms^2)	10^-6g(mm*ms^2)	1*10^3(g*mm^2/ms^2)	1*10^-6	210*10^3	15.64mm/ms	9.81*10^-3
ms							g/mm^3	(g/mm*ms^2)		mm/ms^2