Week - 1 - Consistency of units

Measurements

• Conversion from SI to Kg cm ms

i. MASS 1kg

SI Unit system = 1 kg

kg cm ms = 1 kg

conversion factor is 1.

ii. LENGTH 1m

SI Unit system = 1 m

kg cm ms = 100 cm

conversion factor is 100.

iii. TIME 1s

SI Unit system = 1 s

kg cm ms = 1000 ms

conversion factor is 1000.

iv. FORCE 1N

SI Unit system = 1 N

kg cm ms unit system =

1N = 1 kg m/s^2

= 1 kg x `(10^2/10^6)` cm/ms^2`

= 10^-4 kgcm/ms^2

conversion factor is 10^-4.

iv. STRESS 1Pa

SI Unit system = 1Pa

kg cm ms unit system =

1Pa = 1 N/m^2

= `(10^-4/10^4)` (kgcm)/(ms^2cm^2)`

= 10^-8`(kg)/(ms^2cm)`

conversion factor is 10^-8.

v. ENERGY 1Nm

SI Unit system = 1Nm

kg cm ms unit system =

1Nm = 10^-4 x 10^2 (kg(cm)^2/(ms)^2)

= 10^-2 kg (cm)^2/(ms)^2

conversion factor is 10^-2.

vi. DENSITY 1kg/m3

SI Unit system = 1kg/m3

kg cm ms unit system =

1kg/m3 = 1/10^6 kg/(cm)^3

= 10^-6 kg/(cm)^3

conversion factor is 10^-6.

vii. YOUNG'S Modulus 210 GPa

SI Unit system = 210 GP

kg cm ms unit system =

210 GP = 210 x 10^9 N/m^2

= 210 x 10^9 x 10^-8 kg/(ms^2 cm)

= 210 x 10 kg/(ms^2 cm)

conversion factor is 10.

viii. Velocity 56.33KMPH

SI Unit system = 56.33KMPH

kg cm ms unit system =

56.33KMPH = (56.33 x 10^3 x 10^2)/(3600 x 10^3) cm/ms

= 56.33 x (1/36) cm/ms

conversion factor is (1/36).

ix. GRAVITY 9.8 m/s^2

SI Unit system = 9.8 m/s^2

kg cm ms unit system =

9.8 m/s^2 = (9.81 x 10^2)/(10^6) cm/(ms)^2

= 9.81 x (10^-4) cm/(ms)^2

conversion factor is (10^-4).

• Conversion from SI to Kg cm s

i. MASS 1kg

SI Unit system = 1 kg

kg cm s = 1 kg

conversion factor is 1.

ii. LENGTH 1m

SI Unit system = 1 m

kg cm s = 100 cm

conversion factor is 100.

iii. TIME 1s

SI Unit system = 1 s

kg cm s = 1 s

conversion factor is 1.

iv. FORCE 1N

SI Unit system = 1 N

kg cm s unit system =

1N = 1 kg m/s^2

= 1 kg x `(10^2)` cm/s^2`

= 10^2 kg cm/s^2

conversion factor is 10^2.

iv. STRESS 1Pa

SI Unit system = 1Pa

kg cm s unit system =

1Pa = 1 N/m^2

= 10^2/10^4 kgcm/s^2cm^2

`= 10^-2`(kg)/(s^2cm)`

conversion factor is 10^-2.

v. ENERGY 1Nm

SI Unit system = 1Nm

kg cm s unit system =

1Nm = 10^2 x 10^2 (kg(cm)^2/(s)^2)

= 10^4 kg (cm)^2/(s)^2

conversion factor is 10^4.

vi. DENSITY 1kg/m3

SI Unit system = 1kg/m3

kg cm s unit system =

1kg/m3 = 1/10^6 kg/(cm)^3

= 10^-6 kg/(cm)^3

conversion factor is 10^-6.

vii. YOUNG'S Modulus 210 GPa

SI Unit system = 210 GP

kg cm s unit system =

210 GP = 210 x 10^9 N/m^2

= 210 x 10^9 x 10^-2 kg/(s^2 cm)

= 210 x 10^7 kg/(s^2 cm)

conversion factor is 10^7.

viii. Velocity 56.33KMPH

SI Unit system = 56.33KMPH

kg cm s unit system =

56.33KMPH = (56.33 x 10^3 x 10^2)/(3600) cm/s

= 56.33 x (10^3/36) cm/ms

conversion factor is (1000/36).

ix. GRAVITY 9.8 m/s^2

SI Unit system = 9.8 m/s^2

kg cm s unit system =

9.8 m/s^2 = (9.81 x 10^2)/(1) cm/(s)^2

= 9.81 x (10^2) cm/(s)^2

conversion factor is (10^2).

• Conversion from SI to gm mm ms

i. MASS 1kg

SI Unit system = 1 kg

gm mm ms = 1000 gm

conversion factor is 1000.

ii. LENGTH 1m

SI Unit system = 1 m

gm mm ms = 1000 mm

conversion factor is 1000.

iii. TIME 1s

SI Unit system = 1 s

gm mm ms = 1000 ms

conversion factor is 1000.

iv. FORCE 1N

SI Unit system = 1 N

gm mm ms unit system =

1N = 1 kg m/s^2

= 1000 gm x `(10^3/10^6)` mm/ms^2`

`= 1 gm mm/ms^2`

conversion factor is 1.

iv. STRESS 1Pa

SI Unit system = 1Pa

gm mm ms unit system =

1Pa = 1 N/m^2

= 1 x (1/10^6) gm /ms^2 mm

conversion factor is 10^-6.

v. ENERGY 1Nm

SI Unit system = 1Nm

gm mm ms unit system =

1Nm = 1 x 10^3 (gm(mm)^2/(ms)^2)

= 10^3 gm (mm)^2/(ms)^2

conversion factor is 10^3.

vi. DENSITY 1kg/m3

SI Unit system = 1kg/m3

gm mm ms unit system =

1kg/m3 = 1000/10^9 gm/(mm)^3

= 10^-6 gm/(mm)^3

conversion factor is 10^-6.

vii. YOUNG'S Modulus 210 GPa

SI Unit system = 210 GP

gm mm ms unit system =

210 GP = 210 x 10^9 N/m^2

= 210 x 10^9 x 10^-6 gm/(ms^2 mm)

= 210 x 1000 gm/(ms^2 mm)

conversion factor is 1000.

viii. Velocity 56.33KMPH

SI Unit system = 56.33KMPH

gm mm ms unit system =

56.33KMPH = (56.33 x 10^3 x 10^3)/(3600 x 10^3) cm/ms

= 56.33 x (10/36) mm/ms

conversion factor is (10/36).

ix. GRAVITY 9.8 m/s^2

SI Unit system = 9.8 m/s^2

gm mm ms unit system =

9.8 m/s^2 = (9.81 x 10^3)/(10^6) cm/(ms)^2

= 9.81 x (10^-3) cm/(ms)^2

conversion factor is (10^-3).

Unit System	Measurements
	MASS	LENGTH	TIME	FORCE	STRESS	ENERGY	DENSITY	YOUNG'S Modulus	Velocity	GRAVITY
SI	1kg	1m	1s	1N	1Pa	1Nm	1Kg/m3	210GPa	56.33KMPH	9.8m/s2
kg m s	1 kg	1m	1s	1 kg m/s^2	1 kg /m s^2	1 kgm^2/s^2	1Kg/m3	210x10^9 kg /m s^2	56.33x(10/36) m/s	9.8m/s2
g cm s	1000 gm	100 cm	1s	10^5 gm cm/s^2	10 gm /cm s^2	10^7 gmcm^2/s^2	10^-3 gm/cm^3	210x10^10 gm /cm s^2	56.33x(10^3/36) cm/s	980cm/s2
g cm us	1000 gm	100 cm	10^6 us	10^-7 gm cm/us^2	10^-3 gm/cm us^2	10^-5 gmcm^2/us^2	10^-3 gm/cm^3	210x10^6 gm/cm us^2	56.33x(10^-3/36) cm/us	9.8/10^10 cm/us2
g mm s	1000 gm	1000 mm	1s	10^6 gm mm/s^2	1 gm/mm s^2	10^9 gmmm^2/s^2	10^-6 gm/mm^3	210x10^9 gm/mm s^2	56.33x(10^4/36) mm/s	9.8x10^3 mm/s2
ton mm s	0.001 ton	1000 mm	1s	1 ton mm/s^2	10^-6 ton/mm s^2	1000 tonmm^2/s^2	10^-12 ton/mm^3	210x10^3 ton/mm s^2	56.33x(10^4/36) mm/s	9.8x10^3 mm/s2
slug ft s	0.068 slug	3.28 ft	1s	0.2230 slug ft/s^2	0.02 slug/ft s^2	0.7314 slug ft^2/s^2	0.0019 slug/ft^3	0.02x10^9 slug/ft s^2	56.33x(10/36) m/s	3.28 ft/s^2
kg mm s	1kg	1000 mm	1s	10^3 kg mm/s^2	10^-3 kg/mm s^2	10^6 kg mm^2/s^2	10^-9 kg/mm^3	210x10^6 kg/mm s^2	56.33x(10^4/36) mm/s	9.8x10^3 mm/s2
g mm s	1000 gm	1000 mm	1s	10^6 gm mm/s^2	1 gm/mm s^2	10^9 gmmm^2/s^2	10^-6 gm/mm^3	210x10^9 gm/mm s^2	56.33x(10^4/36) mm/s	9.8x10^3 mm/s2
g cm ms	1000 gm	100 cm	10^3 ms	10^-1 gm cm/ms^2	10^-5 gm/cm ms^2	10 gmcm^2/ms^2	10^-3 gm/cm^3	210x10^4 gm/cmms^2	56.33x(1/36) cm/ms	9.8x10^-4 cm/ms2
kg mm ms	1 kg	1000 mm	10^3 ms	10^-3 kg mm/ms^2	10^-9 kg/mm ms^2	1 kgmm^2/ms^2	10^-9 kg/mm^3	210 kg/mmms^2	56.33x(10/36) mm/ms	9.8x10^-3 mm/ms2