Week - 1 - Consistency of Units

Measurements

Calculation / Units(gm/mm/ms)

Conversion Factor

Mass 1kg

1000 gm

10³

Length 1m

1000 mm

10³

Time 1s

1000 ms

10³

Force 1N

F=mA

1N = 1kg * 1m/s²

= `(kgm)/s^2` = `(1000gm*1000 mm)/(1000ms*1000ms)`

= `(gm*mm)/(ms^2 )`

1

Stress 1Pa

= `N/m^2` = `(kg)/(〖m(s〗^2))`

= `(1000gm)/(1000m*1000ms*1000ms)`

= 10^-6 `(gm)/(mm (m〖s)〗^2 )`

10^-6

Energy 1Nm

= `(kg(m^2))/s^2`

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

= 10³`(gm(〖mm〗^2))/(〖ms〗^2`

10³

Density 1Kg/m3

= `(kg)/m^3`

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

= 10^-6 `(gm)/((m〖m)〗^3 )`

10^-6

Young’s Modulus 210GPa

210 * 10⁹ Pa = 210 * 10⁹ `(kg)/(〖m(s〗^2))`

= 210 * 10⁹ * 10^-6 `(gm)/(mm (m〖s)〗^2 )`

= 210 * 10³ `(gm)/(mm (m〖s)〗^2 )`

10³

Velocity

56.33KMPH

=56.33 * `(1000m)/(60*60 s)`

= 56.33* `(1000000mm)/(60*60*1000 ms)`

= 56.33 * `(5 mm)/(18 ms)`

`(5 )/(18 )`

Gravity

9.8m/s2

= 9.8 `m/s^2` = 9.8 `(1000 mm)/(1000 ms*1000 ms)`

= 9.8 * 10^-3 `(mm)/( (m〖s)〗^2 )`

10^-3

Unit System

Mass

Length

Time

Force

Stress

Energy

Density

Young’s

Modulus

Velocity

Gravity

Kg cm ms

1kg

10²cm

10³ms

10^-4

`(kg*cm)/(ms^2 )`

10^-8 `(kg)/(cm (m〖s)〗^2 )`

10^-2 `(kg(〖cm〗^2))/(〖ms〗^2`

10^-6`(kg)/((c〖m)〗^3 )`

2100 `(kg)/(cm (m〖s)〗^2 )`

1.5647 `( cm)/(ms)`

9.8 *10^-4`(cm)/( (m〖s)〗^2 )`

Kg cm s

1kg

10²cm

1s

10²`(kg*cm)/s^2`

10^-2`(kg)/(cm (〖s)〗^2 )`

10⁴ `(kg(〖cm〗^2))/s^2`

10^-6`(kg)/((c〖m)〗^3 )`

210 *10⁷`(kg)/(cm (〖s)〗^2 )`

1564.7 `( cm)/s`

9.8 *10² `(cm)/( (〖s)〗^2 )`

g mm ms

10³g

10³mm

10³ms

1 `(gm*mm)/(ms^2 )`

10^-6`(gm)/(mm (m〖s)〗^2 )`

10³`(gm(〖mm〗^2))/(〖ms〗^2`

10^-6`(gm)/((m〖m)〗^3 )`

210 *10³ `(gm)/(mm (m〖s)〗^2 )`

15.647 `( mm)/(ms)`

9.8 *10^-3`(mm)/( (m〖s)〗^2 )`

kg m s

1kg

1m

1s

1 `(kg*m)/s^2`

1 `(kg)/(m (〖s)〗^2 )`

1 `(kg(m^2))/s^2`

1 `(kg)/((〖m)〗^3 )`

210 *10⁹`(kg)/(m (〖s)〗^2 )`

15.647 `( m)/(s)`

9.8 `m/( (〖s)〗^2 )`

g cm s

10³g

10²cm

1s

10⁵ `(gm*cm)/s^2`

10 `(gm)/(cm (〖s)〗^2 )`

10⁷`(gm(〖cm〗^2))/s^2`

10^-3`g/((〖cm)〗^3 )`

210 *10¹⁰ `(gm)/(cm (〖s)〗^2 )`

1564.7 `( cm)/s`

9.8 *10² `(cm)/( (〖s)〗^2 )`

g cm µs

10³g

10²cm

10⁶ µs

10^-7 `(gm*cm)/ (〖µs〗^2`

10^-11`(gm)/(cm (〖 µs)〗^2 )`

10^-5`(gm(〖cm〗^2))/(µs^2 )`

10^-3`g/((〖cm)〗^3 )`

2.10 `(gm)/(cm (µs)^2 )`

15.647*10^-4 `( cm)/(µs)`

9.8 *10^-10`(cm)/( (µ〖s)〗^2 )`

g mm s

10³g

10³mm

1s

10⁶ `(g*mm)/s^2`

1 `gm/(mm (〖s)〗^2 )`

10⁹`(gm(〖mm〗^2))/s^2`

10^-6`(gm)/((m〖m)〗^3 )`

210*10¹³ `(gm)/(mm (〖s)〗^2 )`

15647 `( mm)/s`

9.8 *10³ `(mm)/( (〖s)〗^2 )`

ton mm s

10^-3 ton

10³mm

1s

1 `(Ton *mm)/s^2`

10^-6`(Ton)/(mm (〖s)〗^2 )`

10³`(Ton (〖mm〗^2))/s^2`

10^-12`(Ton)/((m〖m)〗^3 )`

210*10¹³ `(Ton)/(mm (〖s)〗^2 )`

15647 `( mm)/s`

9.8 *10³ `(mm)/( (〖s)〗^2 )`

slug ft s

0.068 slug

3.28 ft

1s

0.2246 `(slug*ft)/s^2`

0.0208 `(slug)/(ft (〖s)〗^2 )`

0.7366 `(slug (〖ft〗^2))/s^2`

1.93 * 10^-3 `(slug)/((ft)^3 )`

4.368*10⁹ `(slug)/(ft (〖s)〗^2 )`

51.322 `( ft)/s`

32.144 `(ft)/( (〖s)〗^2 )`

kg mm s

1kg

10³mm

1s

10³ `(kg*mm)/s^2`

10^-3 `(kg)/(mm (〖s)〗^2 )`

10⁶`(kg(〖mm〗^2))/s^2`

10^-9 `g/((〖cm)〗^3 )`

210*10⁶ `(kg)/(mm (〖s)〗^2 )`

15647 `( mm)/s`

9.8 *10³ `(mm)/( (〖s)〗^2 )`

g cm ms

10³g

10²cm

10³ms

10^-1`(g*cm)/(ms^2 )`

10^-5 `(gm)/(cm (m〖s)〗^2 )`

10 `(gm(〖cm〗^2))/ (〖ms〗^2`

10^-3 `g/((〖cm)〗^3 )`

210*10⁴ `(gm)/(cm (m〖s)〗^2 )`

1.5647

9.8 *10^-4`(cm)/( (m〖s)〗^2 )`

kg mm ms

1kg

10³mm

10³ms

10^-3`(kg*mm)/(〖ms〗^2`

10^-9 `(kg)/(mm (m〖s)〗^2 )`

1 `(kg(〖mm〗^2))/(ms^2 )`

10^-9`(kg)/((m〖m)〗^3 )`

210 `(kg)/(mm (m〖s)〗^2 )`

15.647 `( mm)/(ms)`

9.8 *10^-3`(mm)/( (m〖s)〗^2 )`