Week - 1 - Consistency of Units

Aim-

The objective is to find out the different conversion factors for different unit systems and give an explanation about a change of SI units to gm/mm/ms units.

System	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity	Gravity	conversion Factor
	kg	m	s	1N	1Pa	1J	1e+3	1e+11	15.65	9.81	10^3
	kg	cm	s	1e-2N	1e2Pa	1e-4J	1e-3	1e+9	1560	981	10^-6
	kg	cm	ms	1e+4N	1e2Pa	1e-4J	1e-3	1e+3	1.56	9.81e-4	10^0
	kg	mm	ms	1KN	Gpa	J	1e-6	210	15.65	9.81e-3	10^-9
	kg	mm	s	1e-3N	kPa	1e-6J	1e-6	2.1e-1	15650	9810	10^0
	gm	cm	s	1dyn	1dyn/cm^2	erg	1J	2.1e+3	1560	981	10^6
	gm	cm	ms	10N	0.1Mpa	0.1J	1J	2.1e-3	1.56	9.81e-4	10^0
	gm	cm	mu s	1e+7N	100Gpa	1e5J	1J	2.1e-9	1.56e-3	9.81e-10	10^0
	gm	mm	s	1e-6N	1Pa	1e-9J	1e-3	2.1e+2	1.56e+4	9810	10^-3
	gm	mm	ms	1N	1MPa	1mJ	1e-3	2.1e-4	15.6	9.81e-3	10^0
	ton	mm	s	1N	1Mpa	1mJ	1e-9	2.1e-4	1.56e+4	9810	10^-6

Explanation:-

As we have been given that in the kg/mm/ms unit system the young's modulus is 210 Gpa in LS Dyna unit system. Taking that as a reference, we can say that in gm/mm/ms system which is grams, millimeters and milliseconds, the value of force will be in Newtons, stress will be in Megapascals which is 10^6Pascals, energy will be in milliJoules(consistent units).

The value of density will change because the value will change from m to millimeter hence it will get divided by 10^3.therefore, it becomes 1e-3. The young's modulus will also change from 210 to 2.1e-4. The velocity will be the same in both cases and the value of gravity will also be the same.