Week - 1 - Consistency of Units

The aim of this challenge is to convert SI unit values of given quantities to required unit system while creating a database table for reference.

Value of the following measurements are given as follows:

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

Conversion to the required unit system:

• 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

Useful conversions:

1 Kg = 1000 gm = 0.068 slug
1 m = 1000 mm = 3.28 ft
1 s = 1000 ms = 10 us

SI Unit to gm/mm/ms

Mass : 1 kg = 1000gm

Length : 1m = 1000 mm

Time : 1 sec = 1000 ms

Force : 1 N = 1 kg * 1m/s^2

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

= 1 (gm*mm)/ms^2

Stress : 1 Pa = 1N/m^2

=1 gm*mm/ms^2 / (1000mm^2)

=1*10^-6 gm/mm*ms^2

Energy : 1 Nm = 1 gm*mm/ms^2 * 1000 mm

= 1000 gm*mm^2/ms^2

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

Density : 1Kg/m^3 = 1000 gm / (1000 mm)^3

= 10^-6 gm/mm^3

Young’s Modulus : 210 GPa

We know that 1 Pa = 10^-6 gm/mm ms
1 GPa = 10 * 10 gm/mm ms

Thus 210 GPa = 210 * 10 gm/mm ms

Velocity : 56.33 Kmph = 56.33 * 1000000 mm / 3600000

= 15.647 mm/ms
Gravity : 9.88 m/s^2 = 9.81 * 1000mm/(1000ms)^2

= 9.81*10-3 mm/ms2

UNIT	Mass	Length	Time	Force	Stress	Energy	Density	Young's Modulus	Velocity	Gravity
Kg m s	1 kg	1 m	1 s	1 N	1 Pa	1 Nm	1 kg/m^3	210 GPa	15.647 m/s	9.8 m/s^2
Kg cm ms	1 kg	100 cm	1000 ms	10^-4 kg cm/ms^2	10^-8 kg/cm ms^2	10^-2 kg cm /ms^2	10^-6 kg/cm^3	2100 Kg/cm ms^2	1.5647 cm/ms	9.8*10^^-4 cm/ms^2
Kg cm s	1 kg	100 cm	1 s	100 kg cm/s^2	10^-2 kg/cm s^2	10^4 kg cm /s^2	10^-6 kg/cm^3	210e7 kg/cm s^2	1564.7 cm/s	9.8*10^2 cm/s^2
Gm mm ms	1000 gm	1000 mm	1000 ms	1 g mm/ms^2	10^-6 gm/mm ms^2	10^3 gm mm /ms^2	10^-6 gm/mm^3	210e3 gm/mm ms^2	15.647 mm/ms	9.8*10^-3 mm/ms^2
G cm s	1000 gm	100 cm	1 s	10^5 gm cm/s^2	10 gm/cm s^2	10^7 gm cm /s^2	10^-3 gm/cm^3	210e10 gm/cm s^2	1564.7 cm/s	9.8*10^2 cm/s^2
G cm us	1000 gm	100 cm	10^6 us	10^-7 gm cm/us^2	10^-11 gm/cm us^2	10^-5 gm cm /us^2	10^-3 gm/cm^3	2.10 gm/cm us^2	15.647*10-4 cm/us	9.8*10^-10 cm/us^2
G mm s	1000 gm	1000 mm	1 s	10^6 gm mm/s^2	1 gm/mm s^2	10^9 gm mm /s^2	10^-6 gm/mm^3	2.10e11 gm/mm s^2	15647 mm/s	9.8*10^3 mm/s^2
Ton mm s	10^-3 ton	1000 mm	1 s	1 ton mm/s^2	10^-6 ton/mm s^2	10^3 ton mm/s^2	10^-12 ton/mm^3	210e3 ton/mm s^2	15647 mm/s	9.8*10^3 mm/s^2
Slug ft s	0.068 slug	3.28 ft	1 s	0.2246 slug ft/s^2	0.0208 slug/ft s^2	0.7366 slug ft/s^2	1.93*10^-3 slug/ft^3	4.368e9 slug/ft s^2	51.322 ft/s	32.144 ft/s^2
Kg mm s	1 kg	1000 mm	1 s	10^3 kg mm/s^2	10^-3 kg/mm s^2	106 kg mm/s^2	10^-9 kg/mm^3	210e6 kg/mm s^2	15647 mm/s	9.8*10^3 mm/s^2
G cm ms	1000 gm	100 mm	1000 ms	10^-1 gm cm/ms^2	10^-5 gm/cm ms^2	10 gm cm/ms^2	10^-3 gm/cm^3	210e4 gm/cm ms^2	1.5647 cm/ms	9.8*10^-4 cm/ms^2
Kg mm ms	1 kg	1000 mm	1000 ms	10^-3 kg mm/ms^2	10^-9 kg/mm ms^2	1 kg mm/ms^2	10^-9 kg/mm^3	210 kg/mm ms^2	15.647 mm/ms	9.8*10^-3 mm/ms^2