Week - 1 - Consistency of Units

UNIT CONVERSION from Kg m ms to g mm ms

Mass

1Kg = 1000gm

Length

1m =1000mm

Time

1 sec =1000 milli seconds

Force

F= mass*acceleration = kg * (m/s^2)
=kg*(m/s^2)
=`10^3`g* (1000mm/1000*10^3 `ms^2`)
1N=1g`(mm)/(ms^2)`

Stress

Stress = Force/ Unit area

1Pa = 1N/m^2
= 1g*`((mm)/(ms^2))/(10^6mm^2)`

1Pa= `10^-6`*`(g)/(mm*ms^2)`

Energy

`Nm= 10^3g``(mm^2)/(ms^2)`

Density

1 kg/`m^3`=`(10^3 g)/(10^9 mm^3)`
=`10^-6`*g/mm^3

Youngs Modulus

210 Gpa= 210*10^9 Pa
=210*10^9 `10^-6`*`(g)/(mm*ms^2)
=210*10^3 g/mm*ms^2

Velocity

56.33km/h=56.33*10^6/3.6*10^6ms
=15.64722mm/ms

Gravity

9.8m/s^2=9.8*`(10^3 mm)/(10^6ms^2)`
=9.8*10^-3 mm/ms^2

Tabular representation:-

Mass	Length	Time	Force	Stress	Energy	Density	Youngs Modulus	Velocity(566.3 km/h)	Acceleration
kg	mm	s	N	Pa	Nm	7.83e+3	2.1e+11	15.65	9.81
kg	cm	s	1e-2N	1e2Pa	1e-4J	7.83e-3	2.1e+9	1560	981.0
kg	cm	ms	1e4 N	1e5GPa	1e-4J	7.83e-3	2.1e+3	1.56	9.81e-4
kg	cm	`mu`s	10GN	GPa	0.1GJ	7.83e-3	2.1e-3	1.56e-3	9.81e-10
kg	mm	ms	10^3N	kPa	J	7.83e-6	2.1e+2	15.65	9.81e-3
kg	mm	s	kN	kpa	1e-6J	7.83e-6	2.1e+8	15650	9810
g	cm	s	dyn	dyn/cm^2	erg	7.83	2.1e+12	1560	981
g	cm	ms	10N	0.1Mpa	0.1J	7.83	2.1e+6	1.56	9.81e-4
g	cm	`mu`s	1e+7N	100GPa	0.1+9J	7.83	2.1	1.56e-3	9.81e-10
g	mm	s	1e-6N	Pa	1e-9J	7.83e-3	2.1e+11	1.56e-4	9810
g	mm	ms	N	Mpa	mJ	7.83e-3	2.1e+5	15.65	9.81e-3
t	mm	s	N	Mpa	mJ	7.83e-9	2.1e+5	1.56e+4	9810