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Week - 1 - Consistency of Units

BBhashwanth Venkata Deepak Tummuri7 Apr 2023

1. KG CM MS

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*kg *e-2 m *e-3 s *e+4 N *e+8 pa

*e+2 J

 *e+6 kg/m3 *e-1 Gpa *30.016 kmph *e+4 m/s2
  • For mass 1kg = 1kg (conversion factor =1)
  • for length 1m = 100 cm (conversion factor = 10^-2)
  • Given time 1s = 1000 ms ( conversion factor = 10^-3)
  • Given force 1N = 1 kg.m/s^2 = 1kg. 100cm/ (1000ms)^2=10^-4 kg.cm/ms^2 (conversion factor = 10^4)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1 kg/(100 cm. (1000 ms)^2) = 10^-8 kg/cm.ms^2 (conversion factor = 10^8)
  • Given Energy 1Nm = 10^-4. 100 kg.cm^2/ms^2 = 10^-2 kg.cm^2/ms^2 (conversion factor = 10^2)
  • Given density 1 kg/m3 = 1 kg/ (100 cm)^3 = 10^-6 kg/cm^3 ( conversion factor = 10^6)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-8) kg/cm.ms^2 =2100 kg/cm.ms^2 (conversion factor = 0.1)
  • Given velocity 56.33 kmph = 56.33* 10^5 / (3600*1000) cm/ms= 1.564 cm/ms (conversion factor = 30.016)
  • Given gravity 9.8 m/s2 = 9.8*100/(1000ms)^2 = 9.8*10^-4 cm/ms2 (conversion factor = 10^4)

2. KG CM S

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*kg *e-2 m * s *e-2 N *e+2 pa

*e-4 J

 *e+6 kg/m3 *e-7 Gpa *0.036 kmph *e-2 m/s2
  • For mass 1kg = 1kg (conversion factor =1)
  • for length 1m = 100 cm (conversion factor = 10^-2)
  • Given time 1s = 1s ( conversion factor = 1)
  • Given force 1N = 1 kg.m/s^2 = 1kg. 100cm/ (1s)^2=10^2 kg.cm/s^2 (conversion factor = 10^-2)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1 kg/(100 cm. (s)^2) = 10^-2 kg/cm.s^2 (conversion factor = 10^2)
  • Given Energy 1Nm = 10^2. 100 kg.cm^2/ms^2 = 10^4 kg.cm^2/ms^2 (conversion factor = 10^-4)
  • Given density 1 kg/m3 = 1 kg/ (100 cm)^3 = 10^-6 kg/cm^3 ( conversion factor = 10^6)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-2) kg/cm.s^2 =210*10^7 kg/cm.s^2 (conversion factor = 10^-7)
  • Given velocity 56.33 kmph = 56.33* 10^5 / (3600) cm/ms= 1564.72 cm/s (conversion factor = 0.036)
  • Given gravity 9.8 m/s2 = 9.8*100/(s)^2 = 9.8*10^2 cm/s2 (conversion factor = 10^-2)

3. GM MM MS

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*e-3 kg *e-3 m *e-3 s *N *e+6 pa

*e-3 J

 *e+6 kg/m3 *e-3 Gpa *3.0016 kmph *e+3 m/s2
  • For mass 1kg = 1000 g (conversion factor =10^-3)
  • for length 1m = 1000 mm (conversion factor = 10^-3)
  • Given time 1s = 1000 ms ( conversion factor = 10^-3)
  • Given force 1N = 1 kg.m/s^2 = 1000g. 1000mm/ (1000ms)^2=1 g.mm/ms^2 (conversion factor = 1)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1000g/(1000 mm. (1000 ms)^2) = 10^-6 g/mm.ms^2 (conversion factor = 10^6)
  • Given Energy 1Nm = 1* 1000 g.mm^2/ms^2 = 10^3 g.mm^2/ms^2 (conversion factor = 10^-3)
  • Given density 1 kg/m3 = 1000g/ (1000 mm)^3 = 10^-6 g/mm^3 ( conversion factor = 10^6)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-6) g/mm.ms^2 =210*10^3 g/mm.ms^2 (conversion factor = 10^-3)
  • Given velocity 56.33 kmph = 56.33* 10^6 / (3600*1000) mm/ms= 15.64 mm/ms (conversion factor = 3.0016)
  • Given gravity 9.8 m/s2 = 9.8*1000/(1000ms)^2 = 9.8*10^-3 mm/ms2 (conversion factor = 10^3)

4. KG M S

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*kg *m *s *N *pa

*J

 * kg/m3 * Gpa * 3.601 kmph * m/s2
  • For mass 1kg = 1kg (conversion factor =1)
  • for length 1m = 1m (conversion factor = 1)
  • Given time 1s = 1s ( conversion factor = 1)
  • Given force 1N = 1 kg.m/s^2 (conversion factor = 1)
  • Given Stress 1 pa = 1 kg/(m.s^2) (conversion factor = 1)
  • Given Energy 1Nm = 1*1 kg.m^2/s^2 = 1 kg.m^2/s^2 (conversion factor = 1)
  • Given density 1 kg/m3 = 1 kg/m3 ( conversion factor = 1)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa (conversion factor =1)
  • Given velocity 56.33 kmph = 56.33* 10^3/ (3600) m/s= 15.64 m/s (conversion factor = 3.601)
  • Given gravity 9.8 m/s2 (conversion factor = 1)

5. G CM S

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*e-3 kg *e-2 m *s *e-5 N *e-1 pa

*e-7 J

 *e+3 kg/m3 *e-10 Gpa *3.6e-2 kmph *e-2 m/s2
  • For mass 1kg = 1000g (conversion factor =10^-3)
  • for length 1m = 100 cm (conversion factor = 10^-2)
  • Given time 1s = 1s ( conversion factor = 1)
  • Given force 1N = 1 kg.m/s^2 = 1000g. 100cm/ (1s)^2=10^5 g.cm/ms^2 (conversion factor = 10^-5)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1000g/(100 cm. (1s)^2) = 10 g/cm.s^2 (conversion factor = 10^-1)
  • Given Energy 1Nm = 10^5. 100 g.cm^2/s^2 = 10^7 g.cm^2/s^2 (conversion factor = 10^-7)
  • Given density 1 kg/m3 = 1000 g/ (100 cm)^3 = 10^-3 g/cm^3 ( conversion factor = 10^3)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10 g/cm.s^2 =210*10^10 g/cm.s^2 (conversion factor = 10^-10)
  • Given velocity 56.33 kmph = 56.33* 10^5 / (3600) cm/s= 1564.72 cm/s (conversion factor = 3.60*10^-2)
  • Given gravity 9.8 m/s2 = 9.8*100/(1s)^2 = 9.8*10^2 cm/s2 (conversion factor = 10^-2)

6. G CM US

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*e-3 kg *e-2 m *e-6 s *e+7 N *e+11 pa

*e+5 J

 *e+3 kg/m3 *e+2 Gpa *36016 kmph *e+10 m/s2
  • For mass 1kg = 1000g (conversion factor =10^-3)
  • for length 1m = 100 cm (conversion factor = 10^-2)
  • Given time 1s = 10^6 us ( conversion factor = 10^-6)
  • Given force 1N = 1kg.m/s^2 = 1000g. 100cm/ (10^6us)^2=10^-7 g.cm/us^2 (conversion factor = 10^7)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1000g/(100 cm. (10^6 ms)^2) = 10^-11 g/cm.us^2 (conversion factor = 10^11)
  • Given Energy 1Nm = 10^-7. 100 kg.cm^2/us^2 = 10^-5 g.cm^2/ms^2 (conversion factor = 10^5)
  • Given density 1 kg/m3 = 1000g/ (100 cm)^3 = 10^-3 g/cm^3 ( conversion factor = 10^3)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-11) g/cm.us^2 =2.1 g/cm.us^2 (conversion factor = 100)
  • Given velocity 56.33 kmph = 56.33* 10^5 / (3600*10^6) cm/us= 1.564*10^-3 cm/us (conversion factor = 36016)
  • Given gravity 9.8 m/s2 = 9.8*100/(10^6us)^2 = 9.8*10^-10 cm/us2 (conversion factor = 10^10)

7. G MM S

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*e-3kg *e-3 m *s *e-6 N *pa

*e-9 J

 *e+6 kg/m3 *e-9 Gpa *3.57*10^-3 kmph *e-3 m/s2
  • For mass 1kg = 1000g (conversion factor =10^-3)
  • for length 1m = 1000 mm (conversion factor = 10^-3)
  • Given time 1s = 1s ( conversion factor = 1)
  • Given force 1N = 1 kg.m/s^2 = 1000g. 1000mm/ (1s)^2=10^6 g.mm/s^2 (conversion factor = 10^-6)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1000g/(1000 mm. (1s)^2) = 1 g/mm.s^2 (conversion factor = 1)
  • Given Energy 1Nm = 10^6* 1000 g.mm^2/s^2 = 10^9 g.mm^2/s^2 (conversion factor = 10^-9)
  • Given density 1 kg/m3 = 1000g/ (1000 mm)^3 = 10^-6 g/mm^3 ( conversion factor = 10^6)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9 g/mm.s^2 (conversion factor = 10^-9)
  • Given velocity 56.33 kmph = 56.33* 10^6/ (3600) mm/s= 15647.22 mm/s (conversion factor = 3.57*10^-3)
  • Given gravity 9.8 m/s2 = 9.8*1000/(1s)^2 = 9.8*10^3 mm/s2 (conversion factor = 10^-3)

8. TON MM S

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*e+3 kg *e-3 m *s *N *e+6 pa

*e-3 J

 *e+12 kg/m3 *e-3 Gpa *3.57*10^-3 kmph *e-3 m/s2
  • For mass 1kg = 0.001 Ton (conversion factor =10^3)
  • for length 1m = 1000 mm (conversion factor = 10^-3)
  • Given time 1s = 1s ( conversion factor = 1)
  • Given force 1N = 1 kg.m/s^2 = 0.001ton. 1000mm/ (1s)^2=1 ton.mm/s^2 (conversion factor = 1)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 0.001 ton/(1000 mm. (1s)^2) = 10^-6 ton/mm.s^2 (conversion factor = 10^6)
  • Given Energy 1Nm = 1* 1000 ton.mm^2/s^2 = 10^3 ton.mm^2/s^2 (conversion factor = 10^-3)
  • Given density 1 kg/m3 = 0.001 ton/ (1000 mm)^3 = 10^-12 ton/mm^3 ( conversion factor = 10^12)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-6) ton/mm.s^2 =210*10^3 ton/mm.s^2 (conversion factor = 10^-3)
  • Given velocity 56.33 kmph = 56.33* 10^6 / (3600) mm/s= 15647.22 mm/s (conversion factor = 3.57*10^-3)
  • Given gravity 9.8 m/s2 = 9.8*1000/(1s)^2 = 9.8*10^3 mm/s2 (conversion factor = 10^-3)

9. SLUG FT S

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*14.5939kg *0.3048 m *s *4.448 N *47.880 pa

*1.3558 J

 *515.37 kg/m3 *48.1*10^-9 Gpa *1.091 kmph *0.3048 m/s2
  • For mass 1kg = 0.0685218 slug (conversion factor =14.5939)
  • for length 1m = 3.28084 ft (conversion factor = 0.3048)
  • Given time 1s = 1s (conversion factor = 1)
  • Given force 1N = 1 kg.m/s^2 = 0.0685218 slug*3.28084 ft / (1s)^2=0.22480 slug.ft/s^2 (conversion factor = 10^4)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 0.0685218 slug/(3.28084 ft. (1s)^2) = 2.079*10^-2 slug/ft.s^2 (conversion factor = 47.880)
  • Given Energy 1Nm = 0.22480. 3.28084 slug.ft^2/s^2 = 0.73753 slug.ft^2/s^2 (conversion factor = 1.3558)
  • Given density 1 kg/m3 =0.0685218 slug / (3.28084 ft)^3 = 1.94*10^-3 slug/ft^3 ( conversion factor = 515.37)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*2.079*10^-2 slug/ft.s^2 =436.59*10^7 slug/ft.s^2(conversion factor = 48.1*10^-9)
  • Given velocity 56.33 kmph = 56.33* 3.28084*10^3 / (3600) ft/s= 51.33 ft/s (conversion factor = 1.091)
  • Given gravity 9.8 m/s2 = 9.8*3.28084 ft/(1s)^2 = 32.1522 ft/s2 (conversion factor = 0.3048)

10. KG MM S

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*kg *e-3 m *s *e-3 N *e+3 pa

*e-6 J

 *e+9 kg/m3 *e-6 Gpa *3.57*10^-3 kmph *e-3 m/s2
  • For mass 1kg = 1kg (conversion factor =1)
  • for length 1m = 1000 mm (conversion factor = 10^-3)
  • Given time 1s = 1s ( conversion factor = 1)
  • Given force 1N = 1 kg.m/s^2 = 1kg. 1000mm/ (1s)^2=10^3 kg.mm/s^2 (conversion factor = 10^-3)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1 kg/(1000 mm. (1s)^2) = 10^-3 kg/mm.s^2 (conversion factor = 10^3)
  • Given Energy 1Nm = 10^3* 1000 kg.mm^2/s^2 = 10^6 kg.mm^2/s^2 (conversion factor = 10^-6)
  • Given density 1 kg/m3 = 1 kg/ (1000 mm)^3 = 10^-9 kg/mm^3 ( conversion factor = 10^9)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-3) kg/mm.s^2 =210*10^6 kg/cm.ms^2 (conversion factor = 10^-6)
  • Given velocity 56.33 kmph = 56.33* 10^6 / (3600) mm/s=15647.22 mm/s (conversion factor = 3.57*10^-3)

  • Given gravity 9.8 m/s2 = 9.8*1000/(1s)^2 = 9.8*10^3 mm/s2 (conversion factor = 10^-3)

11. G CM MS

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*e-3 kg *e-2 m *e-3 s *e+1 N *e+5 pa

*e-1 J

 *e+1 kg/m3 *e-4 Gpa *30.016 kmph *e+4 m/s2
  • For mass 1kg = 1000g (conversion factor =10^-3)
  • for length 1m = 100 cm (conversion factor = 10^-2)
  • Given time 1s = 1000 ms ( conversion factor = 10^-3)
  • Given force 1N = 1 kg.m/s^2 = 1000g. 100cm/ (1000ms)^2=10^-1 g.cm/ms^2 (conversion factor = 10^1)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1000 g/(100 cm. (1000 ms)^2) = 10^-5 g/cm.ms^2 (conversion factor = 10^5)
  • Given Energy 1Nm = 10^-1. 100 g.cm^2/ms^2 = 10^1 g.cm^2/ms^2 (conversion factor = 10^-1)
  • Given density 1 kg/m3 = 1000g/ (100 cm)^3 = 10^-1 g/cm^3 ( conversion factor = 10^1)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-5) g/cm.ms^2 =210*10^4 g/cm.ms^2 (conversion factor = 10^-4)
  • Given velocity 56.33 kmph = 56.33* 10^5 / (3600*1000) cm/ms= 1.564 cm/ms (conversion factor = 30.016)
  • Given gravity 9.8 m/s2 = 9.8*100/(1000ms)^2 = 9.8*10^-4 cm/ms2 (conversion factor = 10^4)

12. KG MM MS

Mass length Time Force Stress Energy Density Young's Modulus Velocity Gravity
*kg *e-3 m *e-3 s *e+3 N *e+9 pa

*J

 *e+9 kg/m3 *Gpa *3.0016 kmph *e+3 m/s2
  • For mass 1kg = 1kg (conversion factor =1)
  • for length 1m = 1000 mm (conversion factor = 10^-3)
  • Given time 1s = 1000 ms ( conversion factor = 10^-3)
  • Given force 1N = 1 kg.m/s^2 = 1kg. 1000mm/ (1000ms)^2=10^-3 kg.mm/ms^2 (conversion factor = 10^3)
  • Given Stress 1 pa = 1 kg/(m.s^2) = 1 kg/(1000 mm. (1000 ms)^2) = 10^-9 kg/mm.ms^2 (conversion factor = 10^9)
  • Given Energy 1Nm = 10^-3. 1000 kg.mm^2/ms^2 = 1 kg.mm^2/ms^2 (conversion factor = 1)
  • Given density 1 kg/m3 = 1 kg/ (1000 mm)^3 = 10^-9 kg/mm^3 ( conversion factor = 10^9)
  • Given youngs Modulus = 210 Gpa = 210 * 10^9 pa = 210*10^9*10^(-9) kg/mm.ms^2 =210 kg/mm.ms^2 (conversion factor = 1)
  • Given velocity 56.33 kmph = 56.33* 10^6 / (3600*1000) mm/ms= 15.64 mm/ms (conversion factor = 3.0016)
  • Given gravity 9.8 m/s2 = 9.8*1000/(1000ms)^2 = 9.8*10^-3 mm/ms2 (conversion factor = 10^3)
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