Week - 1 - Consistency of Units

Consistency of Units

1. General Conversion Factors

2. Detailed Calculation (for gm/mm/ms - system)

Given Values (SI Units):

1. Mass = 1 kg

2. Length = 1 m

3. Time = 1 s

4. Force = 1 N

5. Stress = 1 Pa

6. Energy = 1 Nm

7. Density = 1 kg/m3

8. Young's Modulus = 210 GPa

9. Velocity = 56.33 km/h

10. Gravity = 9.8 m/s2

Conversions:

3. Mass
   1 kg = 1000 g

4. Length
   1 m = 1000 mm

5. Time
   1 s = 1000 ms

6. Force
   Force in SI: 1 N = 1 kg·m/s²
   In gm/mm/ms:
   1 N = (1000 g)⋅(1000 mm)/(1000 ms)2 = 1 g·mm/ms2

7. Stress
   Stress in SI: 1 Pa = 1 N/m2
   In gm/mm/ms:
   1 Pa = (1 g.mm/ms2)/(1000 mm)2 = 10−6 g.mm-1ms-2

8. Energy
   Energy in SI: 1 Nm = 1 kg.m2/s2
   In gm/mm/ms:
   1 Nm = (1000 g)⋅(1000 mm)2/(1000 ms)2 = 106 g.mm2/ms2

9. Density
   Density in SI: 1 kg/m3 = 1 g/cm3
   In gm/mm/ms:
   1 kg/m3 = 10−3 g/mm3

10. Young's Modulus
    210 GPa = 210×109 Pa
    In gm/mm/ms:
    210 GPa = 210×103 g/mm/ms²

11. Velocity
    Velocity in SI: 56.33 km/h = 15.6472 m/s
    In gm/mm/ms:
    56.33 km/h = 15.6472⋅1000/1000 = 15.6472 mm/ms

12. Gravity
    Gravity in SI: 9.8 m/s2
    In gm/mm/ms:
    9.8 m/s2 = 9.8⋅1000/(1000)2 = 0.0098 mm/ms

kindly find the table in the attached doc.