Week - 1 - Consistency of Units
1. Conversion of SI unit to kg cm ms
- Mass = 1 kg
1 kg
- Length = 1m
100 cm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1 kg*100cm)/(1000ms)2
=> 10-4 (kg*cm)/ms2
Conversion factor = 10-4
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-4 (kg cm)/ms2
=> {10-4 (kg cm/ms2)} / (100 cm)2
=> 10-8 kg/cm ms2
Conversion factor = 10-8 kg/cm*ms2
- Energy = 1 Nm
- 1N *1 m
- {10-4 kg cm/ms2} * 100 cm
- 10-2 kg cm2/ms2
Conversion factor = 10-2
- Density = 1Kg/m^3
- 1 kg / (100 cm)3
- 1 kg/1000000 cm3
- 10-6 kg/cm3
Conversion factor = 10-6
- Young’s Modulus = 210 GPa
1 Pa = 10-8 kg/cm*ms2
1 GPa = 109 * 10-8 kg/cm*ms2
210 GPa = 210 * 10 kg/cm*ms2
Conversion factor = 10
- Velocity = 56.33 Kmph
Km/h
1Km = 100000 cm = 105 cm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (105 )/(36*105)
=> 0.0277 cm/ms
Conversion factor = 0.0278
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1000ms)2
= 10 -4 cm/ms2
9.8 m/s2 = 9.8*10-4 cm/ms2
Conversion Factor = 10-4
2. Conversion of SI unit to kg cm s
- Mass = 1 kg
1 kg
- Length = 1m
100 cm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*100cm)/(1s)2
=> 100 kg cm/s2
Conversion factor = 100
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 100 kg cm/s2
=> (100 kg cm/s2 )/ (100 cm)2
=> 10-2 kg/cm s2
Conversion factor = 10-2
- Energy = 1 Nm
- 1N *1 m
- 100 kg cm/s2 * 100 cm
- 104 kg cm2/s2
Conversion factor = 104
- Density = 1Kg/m^3
- 1 kg / (100 cm)3
- 1 kg/10000 cm3
- 10-6 kg/cm3
Conversion factor = 10-6
- Young’s Modulus = 210 GPa
1 Pa = 10-2 kg/cm s2
1 GPa = 109 * 10-2 kg/cm s2
210 GPa = 210 * 107 kg/cm*s2
Conversion factor = 107
- Velocity = 56.33 Kmph
Km/h
1Km = 100000 cm = 105 cm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (105 )/(3600)
=> 27.77 cm/s
Conversion factor = 27.77
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1s)2
= 100 cm/s2
Conversion Factor = 100
3. Conversion of SI unit to gm mm ms
- Mass = 1 kg
1000gm
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1000gm*1000mm)/(1000ms)^2
=> 1 (gm*mm)/ms^2
Conversion Factor = 1
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 1(gm*mm/ms^2)
=> {1 (gm*mm/ms^2)} / (1000mm^2)
=> 1*10^-6 gm/mm*ms^2
Conversion factor = 10-6
- Energy = 1 Nm
- 1N *1 m
- {1 gm*mm/ms^2} * 1000 mm
- 1000 gm*mm^2/ms^2
- 10^3 gm mm^2/ms^2
Conversion factor = 103
- Density = 1Kg/m^3
- 1000 gm / (1000 mm)^3
- 1 gm/1000000 mm^3
- 10^-6 gm/mm^3
Conversion factor = 10-6
- Young’s Modulus = 210 GPa
1 Pa = 10-6 gm/mm ms2
1 GPa = 109 * 10 -6 gm/mm ms2
210 GPa = 210 * 103 gm/mm ms2
Conversion factor = 103
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.277 mm/ms
Conversion factor = 0.278
- Gravity = 9.88 m/s^2
1 m/s2 = 1000mm/(1000ms)2
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion factor = 10-3
4. Conversion of SI unit to kg m s
- Mass = 1 kg
1 kg
- Length = 1m
1 m
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*1m)/(1s)2
=> 1 kg m/s2
Conversion factor = 1
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 1 kg m/s2
=> (1 kg m/s2) / (1 m)2
=> 1 kg/m s2
Conversion factor = 1
- Energy = 1 Nm
- 1N *1 m
- 1 kg m/s2 * 1 m
- 1 kg m2/s2
Conversion factor = 1
- Density = 1Kg/m^3
- 1 kg / (1 m)3
- 1 kg/1 m3
- 1 kg/m3
Conversion factor = 1
- Young’s Modulus = 210 GPa
1 Pa = 1 kg/m s2
1 GPa = 109 * 1 kg/m s2
210 GPa = 210 * 109 kg/m s2
Conversion factor = 109
- Velocity = 56.33 Kmph
Km/h
1Km = 1000 m = 103 m
1 hr = 60min*60sec
= 3600 s
1 kmph
=> (103 )/(3600)
=> 0.277 m/s
Conversion factor = 0.277
- Gravity = 9.88 m/s2
1 m/s2 = 1 m/(1s)2
= 1 m/s2
9.8 m/s2 = 9.8*1 m/s2
Conversion Factor = 1
5. Conversion of SI unit to g cm s
- Mass = 1 kg
1000gm
- Length = 1m
100 cm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*100cm)/(1s)2
=> 105 g cm/s2
Conversion factor = 105
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 105 g cm/s2
=> 105 g cm/s2/ (100 cm)2
=> 10 g/cm s2
Conversion factor = 10
- Energy = 1 Nm
- 1N *1 m
- 105 g cm/s2 * 100 cm
- 107 g cm2/s2
Conversion factor = 107
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa = 10 g/cm s2
1 GPa = 109 * 10 g/cm s2
210 GPa = 210 * 1010 g/cm s2
Conversion factor = 1010
- Velocity = 56.33 Kmph
Km/h
1Km = 100000 cm = 105 cm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (105 )/(3600)
=> 27.77 cm/s
Conversion factor = 27.77
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1s)2
= 100 cm/s2
9.8 m/s2 = 9.8*100 cm/s2
Conversion Factor = 100
6. Conversion of SI unit to g cm us(micro-sec)
- Mass = 1 kg
1000 gm
- Length = 1m
100 cm
- Time = 1 sec
106 us
- Force = 1 N
F => mass* acceleration
=> 1000 g * 100 cm/(106 us)2
=> (1000 g*100 cm)/(106us)2
=> 10-7 g cm/us2
Conversion factor = 10-7
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 10-7 g cm/us2
=> 10-7 g cm/us2/ (100 cm)2
=> 10-11 g/cm us2
Conversion factor = 10-11
- Energy = 1 Nm
- 1N *1 m
- 10-7 g cm/us2 * 100 cm
- 10-5 g cm2/us2
Conversion factor = 10-5
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa =10-11 g/cm us2
1 GPa = 109 * 10-11 g/cm us2
210 GPa = 210 * 10-2 g/cm us2
Conversion factor = 10-2
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 105 cm
1 hr = 60min*60sec*106 us
= 36*108 us
= 36* 108 us
1 kmph
=> (105 )/(36*108)
=> 0.0000278 cm/ us
Conversion factor = 0.0000278
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(106 us)2
= 100 cm/ 1012 us2
9.8 m/s2 = 9.8*10-10 cm/us2
Conversion Factor = 10-10
7. Conversion of SI unit to g mm s
- Mass = 1 kg
1000 gm
- Length = 1m
1000 mm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*1000 mm)/(1s)2
=> 106 g mm/s2
Conversion factor = 106
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 106 g mm/s2
=> (106 g mm/s2 ) /(1000 mm)2
=> 1 g/mm s2
Conversion factor = 1
- Energy = 1 Nm
- 1N *1 m
- 106 g mm/s2 * 1000 mm
- 109 g mm2/s2
Conversion factor = 109
- Density = 1Kg/m^3
- 1000 g / (1000 mm)3
- 1000 g/1000000000 mm3
- 10-6 g/mm3
Conversion factor = 10-6
- Young’s Modulus = 210 GPa
1 Pa = 1 g/mm s2
1 GPa = 109 * 1 g/mm s2
210 GPa = 210 * 109 g/mm s2
Conversion factor = 109
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (106 )/(3600)
=> 277.7 mm/s
Conversion factor = 277.78
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1s)2
= 1000 mm/s2
9.8 m/s2 = 9.8*1000 mm/s2
Conversion Factor = 103
8. Conversion of SI unit to ton mm s
- Mass = 1 kg
0.001 ton
- Length = 1m
1000 mm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 0.001 ton * 1m/s^2
=> (0.001 ton *1000 mm)/(1s)2
=> 1 ton mm/s2
Conversion factor = 1
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-6 (ton mm)/s2
=> {1 ton mm/s2} / (1000 mm)2
=> 10-6 ton/mm s2
Conversion factor = 10-6
- Energy = 1 Nm
- 1N *1 m
- {1 (ton mm)/s2} * 1000 mm
- 103 ton mm2/s2
Conversion factor = 103
- Density = 1Kg/m^3
- 0.001 ton / (1000 mm)3
- 0.001 ton/1000000000 mm3
- 10-12 ton/mm3
Conversion factor = 10-12
- Young’s Modulus = 210 GPa
1 Pa = 10-6 ton/mm s2
1 GPa = 109 * 10-6 ton/mm s2
210 GPa = 210 * 103 ton/mm s2
Conversion factor = 103
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (106 )/(3600)
=> 277.78 mm/s
Conversion factor = 277.78
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1 s)2
= 10 3 mm/s2
9.8 m/s2 = 9.8*103 mm/s2
Conversion Factor = 103
9. Conversion of SI unit to slug ft s
- Mass = 1 kg
0.068 slug
- Length = 1m
3.28 ft
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (0.068 slug*3.28 ft)/(1s)2
=> 0.223 slug ft/s2
Conversion factor = 0.223
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 0.223 slug ft/s2
=> 0.223 slug ft/s2 / (3.28 ft)2
=> 0.0207 slug/ft s2
Conversion factor = 0.0207
- Energy = 1 Nm
- 1N *1 m
- 0.223 slug ft/s2 * 3.28 ft
- 0.732 slug ft2/s2
Conversion factor = 0.732
- Density = 1Kg/m^3
- 1 kg / (1 m)3
- 0.068 slug/(3.28 ft)3
- 0.068 slug/ 35.29 ft3
- 0.0019 slug/ft3
Conversion factor = 0.0019
- Young’s Modulus = 210 GPa
1 Pa = 0.0207 slug/ft s2
1 GPa = 109 * 0.0207 slug/ft s2
210 GPa = 210 * 109 * 0.0207 slug/ft s2
210 GPa = 207*105 slug/ft s2
Conversion factor = 207*105
- Velocity = 56.33 Kmph
Km/h
1Km = 1000 m = 103 m = 103 * 3.28 ft
1 hr = 60min*60sec
= 3600 s
1 kmph
=> (3.28*103 ft)/(3600 s)
=> 0.911 ft/s
Conversion factor =0.911
- Gravity = 9.88 m/s2
1 m/s2 = 3.28 ft/(1s)2
= 3.28 ft/s2
9.8 m/s2 = 9.8*3.28 ft/s2 = 32.14 ft/s2
Conversion Factor = 3.28
10. Conversion of SI unit to kg mm s
- Mass = 1 kg
1 kg
- Length = 1m
1000 mm
- Time = 1 sec
1 s
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s2
=> (1 kg*1000 mm)/(1s)2
=> 103 kg mm/s2
Conversion factor = 103
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 1000 kg mm/s2
=> (1000 kg mm/s2 )/ (1000 mm)2
=> 10-3 kg/mm s2
Conversion factor = 10-3
- Energy = 1 Nm
- 1N *1 m
- 1000 kg mm/s2 * 1000 mm
- 106 kg mm2/s2
Conversion factor = 106
- Density = 1Kg/m^3
- 1 kg / (1000 mm)3
- 1 kg/1000000000 mm3
- 10-9 kg/mm3
Conversion factor = 10-9
- Young’s Modulus = 210 GPa
1 Pa = 10-3 kg/mm s2
1 GPa = 109 * 10-3 kg/mm s2
210 GPa = 210 * 106 kg/mm s2
Conversion factor = 106
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec
= 3600
= 3600 s
1 kmph
=> (106 )/(3600)
=> 277.78 mm/s
Conversion factor = 277.78
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1s)2
= 1000 mm/s2
9.8 m/s2 = 9.8*1000 mm/s2
Conversion Factor = 103
11. Conversion of SI unit to g cm ms
- Mass = 1 kg
1000gm
- Length = 1m
100 cm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1000 g * 1m/s2
=> (1000 g*100cm)/(1000 ms)2
=> 10-1 g cm/ms2
Conversion factor = 10-1
- Stress = 1 Pa
1 Pa => 1N/m2
As from the above derived 1N = 10-1 g cm/ms2
=> 10-1 g cm/ms2 / (100 cm)2
=> 10-5 g/cm ms2
Conversion factor = 10-5
- Energy = 1 Nm
- 1N *1 m
- 10-1 g cm/ms2 * 100 cm
- 10 g cm2/ms2
Conversion factor = 10
- Density = 1Kg/m^3
- 1000 g / (100 cm)3
- 1000 g/1000000 cm3
- 10-3 g/cm3
Conversion factor = 10-3
- Young’s Modulus = 210 GPa
1 Pa = 10-5 g/cm ms2
1 GPa = 109 * 10-5 g/cm ms2
210 GPa = 210 * 104 g/cm ms2
Conversion factor = 104
- Velocity = 56.33 Kmph
Km/h
1Km = 10000 cm = 105 cm
1 hr = 60min*60sec*1000
= 36*105 ms
= 36*105 ms
1 kmph
=> (105 cm)/( 36*105 ms)
=> 0.0278 cm/ms
Conversion factor = 0.0278
- Gravity = 9.88 m/s2
1 m/s2 = 100 cm/(1000 ms)2
= 10-4 cm/ms2
9.8 m/s2 = 9.8*10-4 cm/ms2
Conversion Factor = 10-4
12. Conversion of SI unit to kg mm ms
- Mass = 1 kg
1 kg
- Length = 1m
1000 mm
- Time = 1 sec
1000 ms
- Force = 1 N
F => mass* acceleration
=> 1 kg * 1m/s^2
=> (1 kg*1000 mm)/(1000ms)2
=> 10-3 (kg*mm)/ms2
Conversion factor = 10-3
- Stress = 1 Pa
1 Pa => 1N/m^2
As from the above derived 1N = 10-3 (kg*mm)/ms2
=> {10-3 (kg*mm)/ms2} / (1000 mm)2
=> 10-9 kg/mm ms2
Conversion factor = 10-9
- Energy = 1 Nm
- 1N *1 m
- {10-3 (kg mm)/ms2} * 1000 mm
- 1 kg mm2/ms2
- 1 kg mm2/ms2
Conversion factor = 1
- Density = 1Kg/m^3
- 1 kg / (1000 mm)3
- 1 kg/1000000000 mm3
- 10-9 kg/mm3
Conversion factor = 10-9
- Young’s Modulus = 210 GPa
1 Pa = 10-9 kg/mm ms2
1 GPa = 109 * 10-9 kg/mm ms2
210 GPa = 210 * 1 kg/mm ms2
Conversion factor = 1
- Velocity = 56.33 Kmph
Km/h
1Km = 1000000 mm = 106 mm
1 hr = 60min*60sec*1000
= 3600000
= 36*105 ms
1 kmph
=> (106 )/(36*105)
=> 0.278 mm/ms
Conversion factor = 0.278
- Gravity = 9.88 m/s2
1 m/s2 = 1000 mm/(1000 ms)2
= 10 -3 mm/ms2
9.8 m/s2 = 9.8*10-3 mm/ms2
Conversion Factor = 10-3
|
MASS |
LENGTH |
TIME |
FORCE |
STRESS |
ENERGY |
DENSITY |
YOUNG’S |
VELOCITY |
GRAVITY |
|
Kg |
100cm |
1000ms |
1kg *100cm/(1000)2 = 10e-05 |
10e-10 |
10e-1 |
10e-6 |
210x10e-10 |
1.565 |
9.81 x 10e-04 |
|
Kg |
100cm |
s |
10e+02 |
10e-4 |
10e+5 |
10e-6 |
210x 10e-04 |
1.565 x10e+3 |
9.81 x10e+02 |
|
kg |
1000mm |
s |
10e+03 |
10e-03 |
10e+6 |
10e-9 |
210x10e-03 |
1.5650x10e+4 |
9.81x 10e+03 |
|
gm |
100cm |
s |
10e+05 |
10e-01 |
10e+8 |
10e-3 |
210x10e-01 |
1.565x10e+3 |
9.81 x10e+02 |
|
gm |
100cm |
100000us |
10e-05 |
10e-05 |
10e-2 |
10e-3 |
210x10e-05 |
1.565 x10e-2 |
9.81x10e-08 |
|
gm |
1000mm |
s |
10e+06 |
1 |
10e+9 |
10e-9 |
210 |
1.5650x 10e+4 |
9.81x 10e+03 |
|
Ton=1000kg |
1000mm |
s |
10e+03 |
10e+03 |
10e+12 |
10e-3 |
210x10e+03 |
1.5650x 10e+4 |
9.81x 10e+03 |
|
Slug=14.5kg |
ft=3048mm |
s |
10e+9 |
10e+05 |
1.347 |
0.407 |
210x10e+05 |
47.69 |
2.982 |
|
kg |
1000mm |
s |
10e+03 |
10e-09 |
10e+6 |
10e-09 |
210x10e-09 |
1.5650x 10e+4 |
9.81x 10e+03 |
|
gm |
100cm |
1000ms |
10e-1 |
10e-07 |
10e+3 |
10e-03 |
210x10e-07 |
1.565 |
9.81 x 10e-04 |
|
kg |
1000mm |
1000ms |
10e-3 |
10e-06 |
1 |
10e-09 |
210x10e-06 |
15.659 |
9.81 x 10e |
Conclusion: Unit conversion is done as per the given data.