Week - 1 - Consistency of units
1) Mass 1 kg= 1000g
conversation factor: 10^3
2) lenght 1m= 1000mm
conversation factor: 10^3
3) Time 1s = 1000ms
conversation factor: 10^3
4) Force : 1N = 1kg ms^2
=( 1000g*1000mm)/(1000ms)^2 =1gm/ms^2
conversation factor:1
5) Stress : 1pa = 1n/m^2 = (1kg*1m/s^2)/m^2 ==1kg/ms^2
== 10^3gm/10^9mm*ms^2
== 10^-6gm/mm*ms^2
conversation factor : 10^-6
6) Energy : 1J = 1NM =(1kgm/s^2)*m
10^3*(10^3)^2/(10^3ms)^2
= 10^3gm*mm^2/ms^2
conversation factor: 10^3
7 ) Density : 1kg/m^3 = 10^3gm/(10^3mm)^3
= 10^-6gm/mm^3
conversation factor : 10^-6
8) young modulus : 210 GPA = 210*10^9*1N/m^2
210*10^9* 1kg*m/(s^2*m^2)
we know that 1Pa = 10^-6 g/(mm*ms^2)
so 210*10^9*10^-6gm/(mm*ms^2)
210*10^3gm/(mm*ms^2)
conversation factor : 10^3
9) Velocity : 56.33kmphr
= 56.33*1000*1000mm/(3600*1000ms)
=15.647 mm/ms
conversation factor: 5/18
10) gravity: 9.8m/s^2 = 9.8*1000mm/(1000ms)^2
=9.8*10^3mm/10^6ms
= 9.8*10^-3mm/ms
conversation factor : 10^-3
Table system units as rows and measured quantities as column
Unit system mass Lenght Time Force Stress Energy
Kg m s 1kg 1m 1S 1Kg*m/s^2 1kg/(m*s^2) 1kg*m^2/s^2
1 1 1
kg cm s 1Kg 10^2cm 1S Kg*cm/S^2 kg/(cm*s^2) kg*cm^2/s^2
10^2 10^-2 10^4
g mm ms 10^3gm 10^3mm 10^3ms g*mm/ms^2 g/(mm*ms^2) g*mm^2/ms^2
1 10^-6 10^3
kg cm ms 1kg 10^2cm 10^3ms kg*cm/ms^2 kg/(cm*ms^2) kg*cm^2/ms^2
10^-4 10^-8 10^-2
g cm s 10^3g 10^2cm 1s g*cm/s^2 g/(cm*s^2) g*cm^2/s^2
10^5 10 10^7
kg mm ms 1kg 10^3mm 10^3ms kg*mm/ms^2 kg/(mm*ms^2) kg*mm^2/ms^2
10^-3 10^-9 1
kg mm s 1kg 10^3mm 1s kg*mm/s^2 kg/(mm*s^2) kg*mm^2/s^2
10^3 10^-3 10^6
ton mm s 10^-3ton 10^3mm 1s ton*mm/s^2 ton/(mm*s^2) ton *mm^2/s^2
1 10^-6 10^3
Slug ft s 0.068slug 3.28ft 1s slug*ft/s^2 slug/(ft*s^2) slug*ft^2/s^2
0.2246 0.0208 0.7366
g mm s 10^3g 10^3mm 1s g*mm/s^2 g/(mm*s^2) g*mm^2/s^2
10^6 1 10^9
g cm ms 10^3g 10^2cm 10^3ms g*cm/ms^2 g/(cm*ms^2) g*cm^2/ms^2
10^-1 10^-5 10