Week - 1 - Consistency of Units

unit systems

mass 1 kg length1m time1s force1N stress1pa energy1nm Density 1 kg/m3 young"s modulus velocity 56.33kmph gravity 9.8m/s
kg cm ms
1 kg

100cm 1000ms 10^4kg(cm^2mm^2) 10^3kg (cm^2 mm^2) 10^2(kg^2cm^2ms^2)

kg cm s 1 kg 100cm 1s 10^2kg(cm^2s^2) 10^2kgcm^2s^2) 10^4(kg^2cm^2 ms^2

gm mm ms 1000g 1000mm 1000ms 1(gmm^2 ms^2 10^6g(mm^2 ms^2) 10^3g (mm^2 ms^2)

kg m s 1 kg 1m 1s 1 kg^2 m^2 s^2 1kg (m^2s^2) 1kg m^2 s^2

g cm s 1000g 100 cm 1s 10^5 g^2 cm 1g (cm^2 s^2) 10^7 g^2 cm^2 s^2

g cm us 1000g 100cm 1000000us 10^7 s^2 cm s^2
10^5 g^2 mm^2 us^2

Unit conversion

1m=1000mm

1 sec =1000ms

1N force, F=mass*acceleration

1kg*1m/s^2

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

Stress, 1 pa =1 N/m^2

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

1 NM energy,

= 1N*1m

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

=1000(gm*mm)

1 kg Density,

= 1000gm / (1000mm)^3

1gm/1000000mm^3

=10^6 gm/mm^3

210 GPA Youngs modulus

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

1GPA 10^9*10^-6gm/mm*ms^2

210 GPA = 210*10^3gm/mm*ms^2

= 10^3gm/mm*ms