Week - 1 - Consistency of Units

Aim- To convert the given measurement into different unit system and find their corresponding conversion factor.

Measurement given -

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

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

kg mm ms

Conversion From SI unit to gm/mm/ms unit system.

Mass

1 Kg = 1000 gm Conversion factor - 10^3

Length

1 m = 1000 mm Conversion factor - 10^3

Time

1s = 1000ms Conversion factor - 10^3

Force

1 N = 1Kg*m/s^2

= 1000g*1000mm/(1000ms)^2

=1 gmm/ms^2 Conversion factor - 1

STRESS : 1Pa = 1N/m^2 = {1kg*(1 m/s^2)}/m^2 = 1 kg/ (m* s^2)

= 1000g/{1000mm*(1000ms)^2}

= 10^6 g/ (mm*ms2)

Conversion factor : 10^-6

ENERGY : 1J = 1Nm = (1kg*1 m/s^2) * m = 1 (kg*m^2/s^2)

= {1000g * (1000mm)^2}/(1000ms)^2

= (109 g*mm^2) / (106 ms^2)

= 10^3 (g*mm^2/ ms^2)

Conversion factor : 10^3

DENSITY : 1Kg/m^3 = 1000g/(1000mm)^3

= 10^6 g/mm3

Conversion factor : 10^-6

YOUNGS MODULUS : 210GPa = 210e+9 kg/(m*s^2) = 210e+9 * 10-6 g/ (mm*m s^2)

= 210e+3 g/ (mm*m s^2) = 210*103 g/ (mm*m s^2)

Conversion factor : 10^3

VELOCITY : 56.33 Kmph = 56.33 * {106mm/(3600*1000ms)}

= 15.647 mm/ms

Conversion factor : 5/18

GRAVITY : 9.8m/s2 = 9.8 * 1000mm/(1000ms)^2

= 9.8* 10^-3 mm/ms^2

Conversion factor : 10^-3

Unit table

Unit system	Mass	Length	Time	Force	Stress	Energy
SI Unit kg m s	1kg	1m	1s	1 N = 1 kg*m/s2	1 Pa = 1 kg/(m* s2)	1 J = 1Nm = 1 kg*m2/s2
kg cm ms	1kg	102cm	103ms	10-4 kg*cm/ms2	10-8 kg/(cm*ms2)	10-2 kg*cm2/ms2
kg cm s	1kg	102cm	1s	102 kg*cm/s2	10-2 kg/(cm*s2)	104 kg*cm2/s2
g mm ms	103g	103mm	103ms	1 g*mm/ms2	10-6 g/(mm*ms2)	103 g*mm2/ms2
g cm s	103g	102cm	1s	105 g*cm/s2	10 g/(cm*s2)	107 g*cm2/s2
g cm μs	103g	102cm	106μs	10-7 g*cm/μs2	10-11 g/(cm*μs2)	10-5 g*cm2/μs2
g mm s	103g	103mm	1s	106 g*mm/ s2	1 g/(mm*s2)	109 g*mm2/s2
Ton mm s	10-3ton	103mm	1s	1 ton*mm/s2	10-6 ton/(mm*s2)	103 ton*mm2/s2
slug ft s	0.068slug	3.28 ft	1s	0.2246 slug*ft/ s2	0.0208 slug/(ft*s2)	0.7366 slug*ft2/s2
kg mm s	1kg	103mm	1s	103 kg*mm/s2	10-3 kg/(mm*s2)	106 kg*mm2/s2
g cm ms	103g	102cm	103ms	10-1 g*cm/ms2	10-5 g/(cm*ms2)	10 g*cm2/ms2
kg mm ms	1kg	103mm	103ms	10-3 kg*mm/ms2	10-9 kg/(mm*ms2)	1 kg*mm2/ms2