Week - 1 - Consistency of Units

Calculations for conversion from SI unit to gm-mm-ms system:

1. Mass: 1kg = 1000 gm

2. Length 1m = 1000 mm

3. Time 1 s = 1000 ms

4. Force 1 N = 1 kg*m/s2 = 1000 gm * 1000 mm/10^6 ms2 = 1 gm*mm/ms2 conversion factor=1

5. Stress 1 N/m2 = 1 kg/m*s2 = 1000gm/1000mm*10^6 ms2 = 10^-6 gm/mm*ms2 conversion factor = 10^-6

6. Energy 1Nm = 1 kg*m2/s2 = 1000gm*10^6mm2/10^6 ms2 = 1000 gm*mm2/ms2 conversion factor = 1000

7. Density 1 kg/m3 = 1000 gm/10^9 mm3 = 10^-6 gm/mm3 conversion factor = 10^-6

8. Young's modulus = 210 GPa = 210*10^9 kg/m*s2 = 210*10^9*1000 gm/1000mm*10^6ms2 = 210 e^3 conversion factor = 10^-6

9. Velocity 56.33 km/h = 56.33*10^6mm/36* 10^5 ms = 15.6 mm/ms

10. Gravity 9.8 m/s2 = 9.8*1000mm/10^6 ms2 = 9.8*10^-3 mm/ms2 conversion factor = 10^-3

The table below shows the conversion factors for the measurements.

	Mass	Length	Time	Force	Stress	Energy	Density	Young's modulus	Velocity	Gravity
kg-cm-ms	1 kg	100 cm	1000 ms	10^-4	10^-2	10^+4	10^-6	2100	1.564	10^-4
kg-cm-s	1 kg	100 cm	1 s	10^+2	10^-2	10^+4	10^-6	210 e^7	1560	100
gm-mm-ms	1000 gm	1000 mm	1000 ms	1	10^-6	10^+3	10^-6	210 e^3	15.6	10^-3
kg-m-s	1 kg	1 m	1 s	1	1	1	1	210 GPa	15.6	1
g-cm-s	1000 gm	100 cm	1 s	10^+5	10^+1	10^+7	10^-3	210 e^10	1560	100
g-cm-us	1000 gm	100 cm	10^+6 us	10^-7	10^-11	10^+5	10^-3	210 e^-2	1.56 e^-3	10^-10
g-mm-s	1000 gm	1000 mm	1 s	10^+6	1	10^+9	10^-6	210 GPa	15600	1000
ton-mm-s	10^-3 ton	1000 mm	1 s	1	10^-6	10^+3	10^-12	210 e^3	15600	1000
slug-ft-s	0.068 slug	3.28 ft	1 s	0.223	0.005	0.73	2*10^-3	200	5.1168	0.3
kg-mm-s	1 kg	1000 mm	1 s	10^+3	10^-3	10^+6	10^-9	210 e^6	15600	1000
g-cm-ms	1000 gm	100 cm	1000 ms	10	10^-5	10	10^-3	210 e^4	1.56	10^-4
kg-mm-ms	1 kg	1000 mm	1000 ms	10^-3	10^-9	1	10^-9	210	15.65	10^-3