## 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