Week - 1 - Consistency of Units
Objective: To convert the given values in different Unit Systems and write the conversion method
The values of the 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
Solution: For the given values we have scalar and vector quantities,
Convert values to kg cm ms:
- Mass 1kg: 1kg
- Length 1m: 100cm
- Time 1s: 1000ms
- Force 1N:
Force = mass. acceleration
1N =1kg.m/s^2
1N = 1kg. m/ms^2`
1N = 1kg. 100cm/`1000^2`ms
1N = `10^-4kg.cm/ms^2`
Conversion Factor 10^-4 - Stress 1Pa:
Stress = Force/ area
1Pa = 1N/cm^2
as per above
1Pa = 10^-4kg.cm/ms^2/100cm^2
1Pa= 10^-8kg/cm.ms^2
Conversion Factor 10^-8 - Energy 1J:
1J = 1N.m
as per above 1N =1kg.m/s^2
1J =1kg.m/s^2.m
1J =(1kg.100cm.1000ms^2). 100cm
1j - 10^-2 cm^2/ms^2
Conversion Factor 10^-2 - Density: 1Kg/m3
1kg./(100)^3cm
10^-6kg/cm^3
Conversion Factor 10^-6
Young's Modulus = 210GPa
210.10⁹kg.m/s²/m²
210.10⁹kg.100cm/(100cm)².(1000ms)²
2100kg/cm.ms²
Conversion Factor 10
Velocity 56.3kmph
56.33kmph = 56.33(100x1000)/(60x60x1000)
56.33kmph = 1.564cm/ms
Gravity 9.81m/s²
9.81m/s² = 9.81(100)/(1000ms²)
=9.81x10^-4cm/ms²
CONVERSION TO kg cm s
Mass 1kg = 1kg
Lenght 1m = 100cm
Time 1s = 1s
Force 1N=mass.acceleration
1N = 1kg.cm/s²
1kg.100cm/s²
100kg.cm/s²
Conversion Factor 100
Stress 1Pa= Force per unit area
1Pa = 1N/m²
We know 1N = 1kg.cm/s²
= (1kg.100cm/s²)/(100cm²)
=10^-2 kg/cm.s²
Conversion Factor 10^-2
Energy 1J
1J = 1N.m
We know 1N = 1kg.100cm/s²
1J= (1kg.100cm/s²).100cm
1J = 1000kg.cm²/s²
Conversion Factor 1000
Density 1kg/m³
1kg/m³ = 1kg/(100cm)³
1kg/m³ = 10^-6kg/cm³
Conversion Factor 10^-6
Young's Modulus 210GPa
210GPa = 210X10⁹Pa
We know 1Pa= 10^-2 kg/cm.s²
210GPa= 210X10⁹(10^-2 kg/cm.s²)
210GPa = 210X10⁷kg/cm.s²
Velocity 56.33kmph
56.33kmph= 56.33(100X1000cm)/(60x60s)
56.33kmph= 1564.72 cm/s
Conversion Factor 1000
Gravity 9.81m/s²
= 9.81(100cm)/s²
= 9810cm/s²
CONVERSION TO gm mm ms
Mass 1kg = 1000gm
Length 1m = 1000mm
Time 1s = 1000ms
Force 1N= 1kg.m/s²
= (1000gm.1000mm)/(1000ms²)
=1gm.mm/ms²
Conversion Factor 1
Stress 1Pa = 1N/m²
We know that 1N= 1gm.mm/ms
=(1gm.mm/ms)/(1000mm)²
=10^-6gm/mm.ms²
Conversion Factor 10^-6
Energy 1J = 1N.m
1J =( 1gm.mm/ms).1000mm
1J= 1000gm.mm²/ms²
Conversion Factor 1000
Density = 1kg/m³
=1000gm/1000mm³
=10^-6gm/mm³
Conversion Factor 10^-6
Young's Modulus =210Gpa
We know that 1Pa = 10^-6gm/mm.ms²
=210x10⁹(10^-6gm/mm.ms²)
=210x10³gm/mm.ms²
Conversion Factor 10³
Velocity 56.33kmph
= 56.33(1000.1000)/(60x60x1000)
=15.64mm/ms
Conversion Factor 10
Gravity 9.81m/s²
= 9.81(1000mm)/(1000ms)²
= 9.81x10^-3mm/ms²
Conversion Factor 10^-3
Conversion to Kg m s
Mass 1kg = 1kg
Lenght 1m =1m
Time 1s =1s
Stress 1Pa =1N/m²
=(1kg.m/s²)/m²
=1kg/m.s²
Conversion Factor 1
Energy = 1N.m
=1(kg.m/s²)/m
=1kg.m²/s²
Conversion Factor 1
Density =1kg/m³
=1kg/m³
Conversion Factor 1
Young's Modulus = 210GPa
=210×10⁹Pa
=210×10⁹(kg.m/s²)
=210×10⁹kg/m.s²
Conversion Factor 10⁹
Velocity =56.33km/h
=56.33(1000)/(60×60)
=15.64m/s
Gravity =9.81m/s²
=9.81m/s²
Conversion to gm cm s
Mass =1kg =1000gm
Length = 1m = 100cm
Time =1s =1s
Force= 1N
1N =1kg.m/s²
=1000gm.100cm/s²
=10⁵gm.cm/s²
Conversion Factor 10⁵
Stress = 1Pa
1Pa = 1N/m²
=(1kg.m/s²)/m²
=(1000gm.100cm/s²)/(100)²cm
=10gm/cm.s²
Conversion Factor 10
Energy = 1N.m
1N.m = (10⁵gm.cm/s²).100cm
=10⁷gm.cm²/s²
Conversion Factor 10⁷
Density 1kg/m³
1kg/m³= 1(1000)gm/(100)³cm
=10^-3gm/cm³
Conversion Factor 10^-3
Young's Modulus =210 GPa
=210×10⁹Pa
=210×10⁹(10gm/cm.s²)
=210×10¹⁰gm/cm.s²
Conversion Factor 10¹⁰
Gravity =9.81m/s²
=9.81(100cm)/s²
=9.81×10²cm/s²
Conversion Factor 10²
Conversion to g cm μs
Mass =1kg =1000gm
Length = 1m = 100cm
Time =1s =10⁶μs
Force = 1N
1N = 1kg.m/s²
=1000g.100cm/(10⁶μs)²
=10-⁷g.cm/μs²
Conversion Factor 10-⁷
Stress = 1Pa
1Pa=( 10-⁷g.cm/s²)/(100)cm²
1Pa = 10-¹¹g/cm.μs²
Conversion Factor 10-¹¹
Energy = 1N.m
1N.m =(10-⁷g.cm/μs²).100cm
=10-⁵g.cm²/μs²
Density = 1kg/m³
=1000gm/100cm³
=10-³ g/cm³
Conversion Factor 10-³
Young's Modulus =210Gpa
=210GPa= 210×10⁹Pa
=210×10⁹(10-¹¹g/cm.μs²)
=210×10-²g/cm.μs²
Conversion Factor 10-²
Velocity = 56.33kmph
=56.33(100×1000)/(10⁶×60×60)
=15.64×10-⁴cm/μs
Conversion Factor 10-⁴
Gravity = 9.81m/s²
=9.81×100cm/(10-⁶μs)²
=9.81×10‐¹⁰cm/μs²
Conversion Factor 10-¹⁰
Conversion to g mm s
Mass= 1kg = 1000g
Length =1m =1000mm
Time 1s = 1s
Force 1N = 1kg.m/s²
=1000g.1000mm/s²
=10⁶g.mm/s²
Conversion Factor 10⁶
Stress = 1Pa = 1N/m²
1Pa= (1kg.m/s²)/m²
=(10⁶g.mm/s²)/(1000²)mm
=1g/mm.s²
Conversion Factor 1
Energy = 1N.m
=(10⁶g.mm/s²).1000mm
=10⁹g.mm²/s²
Conversion Factor 10⁹
Density= 1kg/m³
=1000g/1000mm³
=10-⁶g/mm³
Conversion Factor 10-⁶
Young's Modulus = 210Gpa
=210×10⁹Pa
=210×10⁹(g/mm.s²)
=210×10⁹g/mm.s²
Conversion Factor 10⁹
Velocity= 56.33kmph
=56.33(1000×1000)mm/(60×60)s
=15.64×10³mm/s
Conversion Factor 10³
Gravity =9.81m/s²
=9.81×10³mm/s²
Conversion Factor 10³
Convert Ton mm s
Mass 1kg = 10-³ t
Length 1m = 1000mm
Time 1s= 1s
Force 1N= 1kg.m/s²
=10-³t× 1000mm/s²
= 1t.mm/s²
Conversion Factor 1
Stress= 1Pa
1Pa= 1N/m²
=(1t.mm/s²)/(1000)²mm
=10-⁶t/mm.s²
Conversion Factor 10-⁶
Energy = 1N.m
=1(t.mm/s²).1000mm
=10-³t.mm²/s²
Conversion Factor 10-³
Density = 1kg/m³
=10-³t/(1000)mm³
=10-⁹t/mm³
Conversion Factor 10-⁹
Young's Modulus = 210GPa
=210×10⁹×10-⁶t/mm.s²
=210×10³t/mm.s²
Conversion Factor 10³
Velocity = 56.33kmph
=56.33×(1000×1000)mm/(60×60)s
=15.64×10³mm/s
Conversion Factor 10³
Gravity/ 9.81m/s²
=9.81×10³mm/s²
Conversion Factor 10³
Convert to Slug Feet S
Mass 1Kg= 0.0685slug
Length 1m = 3.28 feet
Time 1s =1s
Force 1N= kg.m/s²
=slug.feet/s²
= 0.0685×3.28× /s²
=0.224slug.feet/s²
Conversion Factor 1
Stress = 1Pa
=1N/m²
=0.224slug/feet/s²/(3.28feet)²
=0.020 slug/feet.s²
Conversion Factor 1
Energy 1N.m =
0.224 Slug.ft/s².3.28ft
=0.224 Slug.feet²/s²
Conversion Factor 1
Density = 1kg/m³
=0.0685/(3.28)³ft
=19.41×10‐⁴ slug/ft³
Conversion Factor 10-⁴
Velocity = 56.33kmph
=56.33 (3.28×1000)/(60×60)
=51.32 ft/s
Conversion Factor 1
Gravity =9.81m/s²
= 9.81 (3.28) ft/s²
= 32.17 ft/s²
Conversion Factor 1
Convert to Kg mm s
Mass 1kg = 1Kg
Length 1m = 1000mm
Time = 1s = 1s
Force = 1N
=1kg.1000mm/s²
=1000kg.mm/s²
Conversion Factor 1
Stress = 1Pa
=1N/m²
=1000kg.mm/s²/(1000)² mm²
=10-³kg/mm.s²
Conversion Factor 10-³
Energy 1N.m
=1000kg.mm/s²
=10³kg/mm.s²×1000mm
=10⁶kg.mm²/s²
Conversion Factor 10⁶
Density= 1kg/m³
=1kg/(1000)³mm
=10-⁹kg/mm³
Conversion Factor 10-⁹
Velocity = 56.33kmph
= 56.33(1000×1000)/(60×60)
=15.64×10³mm/s
Conversion Factor 10³
Young's Modulus = 210GPa
=210×10⁹×10-³kg/mm.s²
=210×10⁶kg/mm.s²
Conversion Factor 10⁶
Gravity = 9.81m/s²
= 9.81×(1000)/s²
=9.81×10³mm/s²
Conversion Factor 10³
Convert to g cm ms
Mass = 1kg = 1000gm
Lenght =1m = 100cm
Time=1s = 1000ms
Force = 1N
1N = 1kg.m/s²
= 1000g.100cm/1000ms²
=10-¹g.cm/ms²
Conversion Factor 10-¹
Stress = 1Pa
=1N/m²
=10-¹g.cm/s²/100²cm
=10-³g/cm.s²
Conversion Factor 10-³
Energy 1N.m
=10-¹g.cm/s²× 100cm
= 10g.cm²/s²
Conversion Factor 10
Density = 1kg/m³
= 1000g/100cm³
=10-³g/cm³
Conversion Factor 10-³
Young's Modulus =210GPa
=210×10⁹× 10-¹g/cm.s²
=210×10⁸g/cm.s²
Conversion Factor 10⁸
Velocity = 56.33kmph
= 56.33(1000×100)/(60×60×1000)
= 1.56cm/ms
Conversion Factor 1
Gravity = 9.81m/s²
= 9.81×100cm/1000ms²
=9.81×10-⁴cm/ms²
Conversion Factor 10-⁴
Convert to Kg mm ms
Mass = 1kg = 1kg
Lenght = 1m = 1000mm
Time = 1s = 1000ms
Force = 1N = 1kg.m/s²
=1kg.1000cm/1000ms²
= 10-³kg.mm/ms²
Conversion Factor 10-³
Stress = 1Pa
= 1N/m²
= 10-³kg.mm/ms²/1000mm²
=10-⁹kg/mm.ms²
Conversion Factor 10-⁹
Energy = 1N.m
=10-³kg.mm/ms²×1000mm
=10kg.mm²/ms²
Conversion Factor 1
Density = 1kg/m³
=1kg/1000³mm
=10-⁹kg/mm³
Conversion Factor 10-⁹
Young's Modulus = 210Gpa
=210×10⁹GPa
= 210×10⁹.10-⁹kg/mm.ms²
=210kg/mm.ms²
Conversion Factor 1
Velocity = 56.33kmph
= 56.33×1000×1000/(60×60×1000)
= 15.64mm/ms
Conversion Factor 1
Gravity = 9.81m/s²
= 9.81×1000mm/1000ms²
=9.81×10-³mm/ms²
Conversion Factor 10-³