DIMENSIONS AND UNITS
A lesson from:
IOWA STATE UNIVERSITY
Engineering Fundamentals and Multidisciplinary Design
Lecture written by: Dr. James Hilliard
Authored for Presentation by: Mark Sobek and Dana Steffey
Revised by: Lex Jacobson
HTML Documentation by: Lex Jacobson
Last Updated: 8/8/95
Consider the following mechanical system:
Mass Velocity Time Momentum Length Energy Etc.
Dimensions-- The set of physical parameters used to define the state of a system
Units-- A standard quantity that allows one to establish a value for a dimension.
Fundamental Dimension--A dimension that cannot be derived from other dimensions.
Derived Dimension--A dimension that can be defined by some mathematical combination of fundamental dimensions.
Let length(L) and time(T) be fundamental dimensions.
Let velocity(V) be another dimension used to describe a system state.
A relationship exists as follows:
Therefore, velocity is a derived dimension!
Dimensional System--The smallest set of fundamental dimensions that can be used for a complete study of a field of science.
-Fundamental dimensions are length, mass, time.
-Fundamental dimensions are length, force, time.
Note: Force and Mass are related by Newton's Law: F=(M)(A) Where:
Note: Force and Mass are related by Newton's Law: F=(M)(A)
During the past several years, many types of unit systems have been in use. Generally, they were variations of two types:
The new common system being adopted is the SI Metric System!
The density of water at 50 degrees F is about 1.94 slug/ft^3. Determine the volume of a 50.0 ft. diameter cylindrical tank with a height of 35.0 ft. Then, calculate the mass of water contained if the tank is full. Express volume in cubic meters and mass in kilograms.
Types of Errors:
Precision, which is a measure of error, is properly conveyed numerically by using appropriate significant digits.
Significant figures are figures (digits) used in writing a number, except those used to define only the decimal location such as:
Or those zeros which do not have non-zero digits on their left,
Multiplication & Division Rules
Addition & Subtraction Rules
If the first digit discarded is <5, leave the last digit kept unchanged.
If the first digit discarded is > 5 or is = 5 followed by other non-zero digits, increase the last digit kept by 1.
If the first digit discarded is = 5 followed by all zeros, then increase the last digit kept by one if it is odd (not even).
Find the least precise number.
Round all other numbers to one place farther to the right.
Add (Subtract) the numbers.
Round the answer such that the last digit is no farther right than that of the least precise number.
Rules for Addition & Subtraction
The product or quotient shall contain no more significant digits than are contained in the number with the fewest significant digits initially.
Proper Use of Significant Figures