## Unit Conversions

### Basic Units

In mechanics there are only three basic units:  length, mass and time.  US Customary units are based on feet (or inches), pounds, and seconds (or hours).  MKS, or SI units are based on meters (m), kilograms (kg) , and seconds (s).  Pounds are used for both mass (a basic quantity, sometimes written as lbm) and force (a derived quantity, sometimes written as lbf).  Under earth gravity 1 lbm weighs 1 lbf

 Quantity U.S. Customary Units MKS Unit Equivalent Mass 1 lbm 2.204 lbm 0.4536 kg 1 kg Length 1 in. 39.37 in. 1 ft. 3.281 ft. 0.0254 m 1 m 0.3048 m 1 m

### Derived Units

Derived units include force, velocity, stress or pressure, energy, power, volume and others.  Here are just a few that you will need for the torsion lab.  You can find further examples in standard mechanics textbooks.

 Quantity U.S. Customary Units MKS Unit Equivalent Force 1 lbf 0.2248 lbf 4.448 N 1 N Stress or Pressure 1 lb/in2 = 1 psi 0.0001450 psi 1000 lb/in2 = 1 ksi 0.1450 ksi 6895. N/m2 = 6895. Pa 1 Pa 6 895 000 Pa = 6.895 MPa 1 MPa Torque 1 lbf-in 8.850 lbf-in 0.1130 N-m 1 N-m

### Worked Examples

 Elastic Modulus The elastic modulus, E, of 2024 aluminum alloy is approximately .  What is E in MKS units?  Using the basic units and expressing the unit MKS values in terms of their US equivalents: This example could also be done using the derived units, Weight What is the weight, in lbf of a circular PMMA (plexiglass) cylinder, 15 mm diameter and 130 mm long? You need to know the density of PMMA.  It is approximately 1.2 g/cm3.  Mass=volume x density= Mass in US units= Weight in US units equals the mass in US units, so the weight is 0.068 lbf.

### Approximate Conversions to Memorize

You can approximate most unit conversions in your head if you can recall a few basic results.  Here are a few numbers you should know:

1 kg approx.2 lbm

1 kg mass weighs about 10 N, thus 2 lbf approx. 10 N, or 1 lbf approx. 5 N.

1 inch approx. 25 mm

1 m approx. 40 inches

1 ksi approx. 7 MPa

1 N-m approx. 10 lbf-in

 Quantity Value in U.S. Customary Units Value in MKS Units Elastic Modulus of Aluminum  Elastic Modulus of Steel  Elastic Modulus of PMMA 420 ksi 2.9 GPa Yield stress of low strength steel 345 MPa Yield stress of very high strength steel  A pencil diameter 0.3 in 7.6 mm=.0076 m Paper clip diameter .032 in (or 32/1000 in) .8 mm Weight of a small car 2250 lbf 10 000 N = 10 kN