Basic
Units
Derived Units
Worked Examples
Approximate Conversions to Memorize
Getting the Feel of Conversions
Online Conversion Calculator
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 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/in^{2} = 1 psi 0.0001450 psi 1000 lb/in^{2} = 1 ksi 0.1450 ksi |
6895. N/m^{2} = 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 |
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/cm^{3}. 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. |
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
Knowing the approximate value of important engineering constants and material properties will also help you become more comfortable with working with both US and MKS units. Here are some commonly used quantities:
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} |