Week - 1 - Consistency of units

Entity

Calculation

Conversion Factor from (Kg, m, s) to (gm, mm, ms)

Mass

1kg = 1000 gm

1e+3

Length

1m = 1000 mm

1e+3

Time

1s = 1000 ms

1e+3

Force

1 N = 1 Kg m/s²

= (1 Kg * 1 m)/ (1 s* 1 s)

= (1000 gm * 1000 mm)/ (1000 ms* 1000 ms)

= 1 gm mm/ms²

1

Stress

1 Pa = 1 Kg/ (m s²)

= (1 Kg)/ (1 m* 1 s* 1 s)

= (1000 gm)/ (1000 mm* 1000 ms* 1000 ms)

= 1e-6 gm/ (mm *ms²)

1e-6

Energy

1 Nm = 1 Kg m²/s²

= (1 Kg * 1 m * 1 m)/ (1 s* 1 s)

= (1000 gm * 1000 mm * 1000 mm)/ (1000 ms* 1000 ms)

= 1000 gm mm²/ms²

1e+3

Density

1 Kg/m³

= 1 Kg / (1 m * 1 m * 1 m)

= 1000 gm / (1000 mm * 1000 mm * 1000 mm)

= 1e-6 gm /mm³

1e-6

Youngs Modulus

1 GPa = 1 * 10⁹ * Kg/ (m s²)

=10⁹ * (1 Kg)/ (1 m* 1 s* 1 s)

= 10⁹ * (1000 gm)/ (1000 mm* 1000 ms* 1000 ms)

= 1000 gm/ (mm *ms²)

1e-6

Velocity

1 kmph = 1 km / h

= 1 km /1 h

= 1e+6 mm / 3.6e+6 ms

= (1 / 3.6) mm/ ms

3.6

g

1 m/s²

= 1 m / (1 s * 1 s)

= 1000 mm / (1000 ms * 1000 ms)

= 1e-3 mm / ms²

1e-3

Conversion factor from (Kg, m, s) to another unit system

Units

Force

Stress

Energy

Density

Youngs Modulus

Velocity

g

kg, cm, ms

1E-04

1E-08

1E-02

1E-06

1E-08

1E-01

1E-04

kg, cm, s

1E+02

1E-02

1E+04

1E-06

1E-02

1E+02

1E+02

gm, mm, ms

1

1E-06

1E+03

1E-06

1E-06

1

1E-03

kg, m s

1

1

1

1

1

1

1

g, cm, s

1E+05

1E+01

1E+07

1E-03

1E+01

1E+02

1E+02

g, cm, µs

1E-07

1E-11

1E-05

1E-03

1E-11

1E-04

1E-10

g, mm, s

1E+06

1.00

1E+09

1E-06

1

1E+03

1E+03

ton, mm, s

1

1E-06

1E+03

1E-12

1E-06

1E+03

1E+03

slug, ft, s

2.25E-01

2.09E-02

7.38E-01

1.94E-03

2.09E-02

3.28E+00

3.28E+00

kg, mm, s

1E+03

1E-03

1E+06

1E-09

1E-03

1E+03

1E+03

g, cm, ms

1E-01

1E-05

1E+01

1E-03

1E-05

1E-01

1E-04

kg, mm, ms

1E-03

1E-09

1.00

1E-09

1E-09

1

1E-03