Week - 1 - Consistency of units
CONSISTENCY OF UNITS
OBJECTIVE
Different industries use different system of units as per their convenience. The units for the basic measurement quantities, mass distance and time - dictate how the other derived quantities will be expressed. For example, automotive industries use kg,mm,ms as their standard unit system. Construction industries are likely to use tonne,m,s as their unit system. Similarly, PCB simulation in electronic industry uses gm, micrometer,ms as their system of units.
Value of the following 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
Now, here are a few system of units:
Kg cm ms
Kg cm s
gm mm ms
kg m s
g cm s
g cm us
g mm s
ton mm s
slug ft s
kg mm s
g cm ms
kg mm ms
G LINK : https://drive.google.com/file/d/1RMDS2uq7lwUKhy_jFGk595eNXDGMDu0K/view?usp=sharing
| kg-m-s | kg-cm-ms | kg-cm-s | gm-mm-ms | g-cm-s | g-cm-us | g-mm-s | ton-m-ms | slug-ft-s | kg-mm-s | g-cm-ms | kg-mm-ms |
| mass (1 kg) | 1 kg | 1kg | 1000gm | 1000gm | 1000gm | 1000gm | 0.001 ton | 1/ 14.5939 | 1kg | 1000gm | 1 kg |
| length 1m | 100cm | 100cm | 1000 mm | 100 cm | 100 | 1000 mm | 1000mm | 3.28 feet | 1000 mm | 100 cm | 1000 mm |
| time 1 s | 1s | 1s | 1000ms | 1s | 1000000us | 1s | 1s | 1s | 1s | 1000ms | 1000ms |
| force 1 N | 1x `10^-4`cm`/ms^2` | 1 x`10^2`kg xcm`/s^2`. | 1 N | 1 x `10^5` g x cm`/s^2 | 1 x `10^-7` g x cm`/us ^2` | 1 x `10^6` g x mm`/s^2` | 1 N | 0.2248 slug x ft`/s^2` | 1 x`10^3` kg xmm`/s^2` | 1 x `10^-1` g x cm`/s^2` | 1N |
| stress 1 Pa | 1 x `10^-8` kg /cm x `ms^2` | 1 X `10^-2` kg/cm X `s^2` | 1 X `10^-6` gm/mm x`ms^2` | 1 x10 g/cm x `s^2 | 1 x `10^-13`g/cm x `us^2` | 1 pa | 1mpa | 0.020 slug/ft x`s^2` | 1 x`10^3` kg xmm`/s^2` | 1 x `10^-5`g/cm x `ms^2 | 1mpa |
| energy ( 1N-m) | 1 x `10^-2` kg x `cm^2`/ `ms^2` | 1 x `10^4`kg `cm^2`/ `s^2.` | 1 x `10^3` gm x `mm^2`/`ms ^2`. | 1 x `10^7` g x `cm^2`/ `s^2.` | 1 x `10^-5`g x `cm^2`/`us^2.` | 1 x `10^9`g x `mm^2`/ `s^2`. | 1 x`10^-3`ton x `mm^2`/`s^2.` | 10.7584. | 1 x `10^6` kg x `mm^2`/ `s^2.` | 1 x 10 g x`cm^2`/ `ms^2.` | 1 N-m. |
| density 1 kg/`m^3` | 1 x `10^-6` kg/`cm^3.` | 1 X`10^-6` kg / `cm^3.` | 1 x `10^-6`gm /`mm^3` | 1 x `10^-3`g /`cm^3.` | 1 x `10^3`g / `cm^3.` | 1 x `10^-6`g / `mm^3` | 1 x `10^-6` ton /`mm^3.` | 0.00194 slug / `ft^3.` | 1 x `10^-9` kg / `mm^3.` | 1 x `10^-3` g/`cm^3`. | 1 x `10^ -9.` |
| young's modulus 210 GPa | 210 x 10 kg /cm x `m//s^2` | 210 x `10^7 kg//cm`x `s^2.` | 210 x `10^3 gm //mm(ms)^2.` |
210 x `10^10 g // cm` x `s^2.` |
210 x`10^-12 g //cm` x `us^2.` | 210Gpa | 210 X `10^3 ton //mm`X `S^2.` | 4.38 X `10^9 Slug//ft` x `s^2.` | 210 x `10^6 kg//mm` x `s^2.` | 210 x `10^4 g //cm`x `ms^2.` | 210 Gpa |
| velocity 56.33 KMPH | 1.563 cm/ms | 1563.88 cm/5. | 56.53 KMPH | 1563.88 cm/s | 0.001570cm/us | 15.63 mm/s | 15.63 mm/s | 51.505 ft/s | 15.63 mm/s | 1.5702 cm/ms. | 56.53 KMPH |
| gravity 9.8 m | 9.8 x `10^-4`. | 9.8 x `10^2`cm/`s^2.` | 9.8 x `10^-3` mm /`ms^2.` | 9.81 x `10^2` cm /`s^2` | 9.81 x `10^-10` cm /`us^2` | 9.8 x `10^3` mm / `s^2.` | 9381 x `10^3` mm /`s^2` | 9.81 x 3.28 / `1^2. | 9.8 x `10^3 mm //s^2` | 9.81 x `10^-4 cm//ms^2` | 9.8 x `10^-3 mm //ms^2.` |
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1 force unit = 1 mass unit * 1 acceleration unit
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1 acceleration unit = 1 length unit / (1 time unit)^2
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1 density unit = 1 mass unit / (1 length unit)^3
| MASS | LENGTH | TIME | FORCE | STRESS | ENERGY | DENSITY | YOUNG's | 35MPH 56.33KMPH |
GRAVITY |
|---|---|---|---|---|---|---|---|---|---|
| kg | m | s | N | Pa | J | 7.83e+03 | 2.07e+11 | 15.65 | 9.806 |
| kg | cm | s | 1.0e-02 N | 7.83e-03 | 2.07e+09 | 1.56e+03 | 9.806e+02 | ||
| kg | cm | ms | 1.0e+04 N | 7.83e-03 | 2.07e+03 | 1.56 | 9.806e-04 | ||
| kg | cm | us | 1.0e+10 N | 7.83e-03 | 2.07e-03 | 1.56e-03 | 9.806e-10 | ||
| kg | mm | ms | kN | GPa | kN-mm | 7.83e-06 | 2.07e+02 | 15.65 | 9.806e-03 |
| g | cm | s | dyne | dyne/cm² | erg | 7.83e+00 | 2.07e+12 | 1.56e+03 | 9.806e+02 |
| g | cm | us | 1.0e+07 N | Mbar | 1.0e+07 Ncm | 7.83e+00 | 2.07e+00 | 1.56e-03 | 9.806e-10 |
| g | mm | s | 1.0e-06 N | Pa | 7.83e-03 | 2.07e+11 | 1.56e+04 | 9.806e+03 | |
| g | mm | ms | N | MPa | N-mm | 7.83e-03 | 2.07e+05 | 15.65 | 9.806e-03 |
| ton | mm | s | N | MPa | N-mm | 7.83e-09 | 2.07e+05 | 1.56e+04 | 9.806e+03 |
| lbf-s²/in | in | s | lbf | psi | lbf-in | 7.33e-04 | 3.00e+07 | 6.16e+02 | 386 |
| slug | ft | s | lbf | psf | lbf-ft | 1.52e+01 | 4.32e+09 | 51.33 | 32.17 |
| kgf-s²/mm | mm | s | kgf | kgf/mm² | kgf-mm | 7.98e-10 | 2.11e+04 | 1.56e+04 | 9.806e+03 |
| kg | mm | s | mN | 1.0e+03 Pa | 7.83e-06 | 2.07e+08 | 9.806e+03 | ||
| g | cm | ms | 1.0e+1 N | 1.0e+05 Pa | 7.83e+00 | 2.07e+06 | 9.806e-04 |
FORCE CALCULATION
1. force is derived quantity (1N).
= kg x `m/s^2`(Kg m-s )
2. unit system kg-cm-ms
= 1 x`100/1000^2` = 1x `10^-4`cm`/ms^2`.
unit conversion factor `10^-4`.
3. unit system kg-cm-s.
= 1 x`100/1`= 1 x`10^2`kg xcm`/s^2`.
unit conversion factor `10^2`.
4. unit system gm-mm-ms
=1000 x`1000/(1000)^2` = 1N
5. unit system g-cm-s
= 1000 x `100^1` =1 x `10^5` g x cm`/s^2`
unit conversion factor `10^5`.
6.unit system g-cm-us.
= 1000 x `100/ (1000000)^2` = 1 x `10^-7` g x cm`/us ^2`.
unit conversion factor 10^7.
7. unit system g-mm-s.
=1000 x `1000/1` = 1 x `10^6` g x mm`/s^2`.
unit conversion factor `10^6`.
8. unit system ton -mm -s
=0.001 x`1000/1` = 1N.
9. unit system slug-ft-s.
=`1/14.59` x 3.28 =0.2248 slug x ft`/s^2`.
10. unit system kg-mm-s.
= 1 x`100/1` =1 x`10^3` kg xmm`/s^2`.
11. unit system g-cm-ms
= 1000 x `100/(1000)^2` = 1 x `10^-1` g x cm`/s^2`.
unit conversion factor `10^-1.`
12. Kg-mm-ms.
1N.
STRESS CALCULATION
1. unit system kg-m-s
1pa = kg/m x`s2`.
2. unit system (kg-cm-ms)
=1`/100 X (1000)^2` = 1 x `10^-8` kg /cm x `ms^2`.
unit conversion factor =`10^-8`.
3.unit system kg-cm-s
= 1/100 X `1^2` = 1 X `10^-2` kg/cm X `s^2`.
unit conversion factor =`10^-2.`
4.unit system gm-mm-ms.
= 1000/1000 X `(1000)^2`= 1 X `10^-6` gm/mm x`ms^2`.
unit conversion factor =`10^-6.`.
5. unit system g-cm-s.
= 1000/100 x 1 = 1 x10 g/cm x `s^2.`
unit conversion factor =10.
6.unit system g-cm-us.
1000/100 x`(1000000)^2` = 1 x `10^-13`g/cm x `us^2`.
unit conversion factor = `10^-13.`
7.unit system g-mm-s
1000/1000 x `1^2.` = 1 pa.
8.unit system ton-mm-s.
= 1 x `10^-3`/ 1000 x1 = 1X `10^-6.`
= 1mpa.
9.unit system slug-ft-s.
= 0.2248/`3.28^2.`= 0.020 slug/ft x`s^2`.
unit conversion factor=0.020.
10. unit system kg-mm-s.
= 1000/`1000^2.`
=1 x `10^-3` kg/mm x `s^2.`.
unit conversion factor =`10^-3.`
11. unit system g-cm-ms.
= 0.1/10000.
= 1 x `10^-5`g/cm x `ms^2.`
unit conversion factor =`10^-5.`
12. unit system kg-mm-ms.
=1/`1000^2`
=1 x `10^-6`
=1mpa.
ENERGY CALCULATION
1.unit system kg-m-s
= 1 N-m=kg x`m^2`/`s^2`.
2.unit system kg-cm ms.
= 1 x`100^2`/`1000^2`.
1 x `10^-2` kg x `cm^2`/ `ms^2`.
unit conversion factor = `10^-2`.
3. unit system kg-cm-s
=1 x `100^2 / 1^2`.
1 x `10^4`kg `cm^2`/ `s^2.`
unit conversion factor `10 ^4.`
4.unit system gm-mm-ms
= 1000 x `(1000)^2`/`(1000)^2`.
1 x `10^3` gm x `mm^2`/`ms ^2`.
unit conversion factor = `10^3.`
5. unit system g-cm-s.
= 1000 x `(100)^2`/`1^2`.
= 1 x `10^7` g x `cm^2`/ `s^2.`
unit conversion factor =`10^7.`
6. unit system g-cm-us.
= 1000 x `(100)^2`/`(1000000)^2.`
1 x `10^-5`g x `cm^2`/`us^2.`
unit conversion factor =`10^-5.`
7.unit system g-mms.
= 1000 x `(1000)^2`/ 1. = 1 x `10^9`g x `mm^2`/ `s^2`.
unit conversion factor =`10^9.`
8.unit system ton-mm-s
= 1 x `10^-3` X `(1000)^2`/`1^2`. =1 x`10^-3`ton x `mm^2`/`s^2.`
unit conversion factor =`10^-3.`
9.unit system slug-ft-s.
= 1/14.5939 x `(3.28)^2`/ `1^2.`
= 10.7584 slug x `ft^2`/`s^2.`
unit conversion factor =10.7584.
10.unit system kg-mm-s.
= 1 x `1000^2 / 1^2` = 1 x `10^6` kg x `mm^2`/ `s^2.`
unit conversion factor =`10^6.`
11. unit system g-cm-ms.
= 1000 x `100^2`/ `1000^2.`
= 1 x 10 g x`cm^2`/ `ms^2.`
unit conversion factor = 10.
12.unit system kg-mmms
= 1 x `1000^2 / 1000^2`.
=1 N-m.
DENSITY CALCULATIONS.
1. unit system kg-m-s.
= 1 KG /`m^3`
2. unit system kg-cm-ms.
= 1/ `100^3`= 1 x `10^-6` kg/`cm^3.`
unit conversion factor `10^-6.`
3.unit system kg-cm-s
=1 X`10^-6` kg / `cm^3.`
unit conversion factor = `10^-6.`
4. unit system gm-mm-ms
= 1000 /`(1000)^3` = 1 x `10^-6`gm /`mm^3`
unit conversion factor = `10^-6.`
5.unit system g-cm-s
= 100 / `100^3.` = 1 x `10^-3`g /`cm^3.`
unit conversion factor = `10^-3.`
6.unit system g-cm-us.
= 1 x `10^3`g / `cm^3.`
unit conversion factor =`10^-3.`
7.unit system g-mm-s.
= 1000 / `(1000)^3.`
= 1 x `10^-6`g / `mm^3`.
8.unit system ton-mm-s.
= 1 x `10^-3`/ `(1000)^3` = 1 x `10^-6` ton /`mm^3.`
unit conversion factor =`10^-6`
9.unit system slug-ft-s
= 1 /14.5939 x `(3.28)^2`
= 0.00194 slug / `ft^3.`
10.unit system kg-mm-s
= 1 / (1000)^3.
= 1 x `10^-9` kg / `mm^3.`
unit conversion factor =`10^-9.`
11.unit system g-cm-ms
= 1000 / `(100)^3`.
= 1 x `10^-3` g/`cm^3`.
unit conversion factor = `10^-3.`
12.unit system kg-mm-ms
= 1 /`(1000)^3`
= 1 x `10^-9` kg / `mm^3.`
unit conversion factor = 1 x `10^ -9.`
YOUNG'S MODULUS CALCULATION .
1. unit system kg-m-s
210 Gpa = 210 x `10^9 pa`.
=210 x `10^9 kg`/ m x `s^2.`
2. unit system kg-cm-ms
=210 x `10^9 x 1 /100 x `(1000)^2.`
= 210 x 10 kg /cm x `m//s^2`
unit conversion factor = 10
3.unit system kg-cm-s
=210 x `10^9 x 1 /100 x `1^2.`
=210 x `10^7 kg//cm`x `s^2.`
unit conversion factor = `10^7.`
4. unit system gm-mm-ms
=210 x `10^9 x 1000 / 1000 x `(1000)^2.`
=210 x `10^9 x `10^-6.`
=210 x `10^3 gm //mm(ms)^2.`
unit conversion factor = `10^3.`
5.unit system g-cm-s
=210 x `10^9 x 1000 / 100 x `1^2.`
= 210 x `10^10 g // cm` x `s^2.`
unit conversion factor = `10^10.`
6.unit system g-cm-us
=210 x `10^9 x 1000 /100 x 1000000.
=210 x`10^-12 g //cm` x `us^2.`
unit conversio factor = `10^-12.`
7.unit system g-mm-s
=210 x `10^9 x 1000 / `1000 X 1^2`
=210 x `10^9 g /mm x `s^2.`
=210Gpa
8.unit system ton-mm-s
= 210 x `10^9 x `10^-3` / 1000 x `1^3.`
= 210 X `10^3 ton //mm`X `S^2.`
UNIT CONVERSION FACTOR =`10^3`.
9.unit system slug-ft-s
=210 x `10^9 X 1 /14.5939 X (3.28) X `1^2`.
= 4.38 X `10^9 Slug//ft` x `s^2.`
10.unit system kg-mm-s
=210 x `10^9 x 1 / 1000 x 1.
=210 x `10^6 kg//mm` x `s^2.`
11.unit system g-cm-ms
=210 x `10^9 x 1000 /1000 x `(1000)^2.`
=210 x `10^4 g //cm`x `ms^2.`
12.unit system kg-mm-ms
= 210 x `10^9 x 1 /1000 x `(1000)^2.`
=210 Gpa
VELOCITY CALCULATIONS.
1. unit system kg-m-s
= 56.53 KMPH
= 56.53 x 1000/3600 = 56.53 x 5 /18 m/s
2. unit system kg-cm-ms.
= 56.53 x 1000/3600 x 100/1000
= 1.563 cm/ms
3.unit system kg-cm-s
= 56.53 x 1000/3600 x 100/1.
= 1563.88 cm/5.
4. unit system gm-mm-ms
=56.53 x 1000/36000 x 1000/1000
=56.53 KMPH
5.unit system g-cm-s
=56.53 x 1000/3600 x 100/1
= 1563.88 cm/s
6.unit system g-cm-us
= 56.53 x 1000/3600 x 100/1000000
=0.001570cm/us
7.unit system g-mm-s
=56.53 x1000/3600 x 1000/1
=15.63 mm/s
8.unit system ton-mm-s
=56.53 x1000/3600 x 1000/1
=15.63 mm/s
9.unit system slug-ft-s
= 56.53 x 1000/3600 x 3.28/1
= 51.505 ft/s
10.unit system kg-mm-s
= 15.63 mm/s
11.unit system g-cm-ms
=56.53 x 1000/ 3600 x 100/1000
=1.5702 cm/ms.
12.unit system kg-mm-ms
=56.53 KMPH
GRAVITY CALCULATION
1. unit system kg-m-s
= 9.8 m /`s^2.`
2. unit system kg-cm-ms
= 9.8 x 100 / `1000^2`.
=9.8 x `10^-4`.
unit conversion factor = `10^-4.`
3.unit system kg-cm-s
= 9.8 x 100 / `1 ^2.`
=9.8 x `10^2`cm/`s^2.`
4. unit system gm-mm-ms
= 9.8 x 1000 / `(1000)^3.`
=9.8 x `10^-3` mm /`ms^2.`
unit conversion factor =`10^-3.`
5.unit system g-cm-s
=9.81 x 100/1
=9.81 x `10^2` cm /`s^2`
6.unit system g-cm-us.
=9.81 x 100/`(1000000)^2`
=9.81 x `10^-10` cm /`us^2`
7.unit system g-mm-s
=9.8 x 1000 /`1^2`
=9.8 x `10^3` mm / `s^2.`
8.unit system ton-mm-s
=9381 x `10^3` mm /`s^2`
9.unit system slug-ft-s.
= 9.81 x 3.28 / `1^2.`
=32.17 ft/`s^2.`
10.unit system kg-mm-s
=9.8 x `10^3 mm //s^2`
11.unit system g-cm-ms
= 9.81 x 100/ `(1000)^2.`
=9.81 x `10^-4 cm//ms^2`
12.unit system kg-mm-ms
= 9.8 x `10^-3 mm //ms^2.`