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Contact info: Yiheng.Wang@lonestar.edu What's new in 2015? 1. Closed-caption made by myself! -- not the automatic subtitle anymore. 2. Learning objectives added for each video. 3. Quiz questions added -- including end-of assessment questions and preparatory, exploratory questions. 4. Mistakes fixed and cleaned up. 5. New examples/contents for selective videos. My old videos and playlists will still be left on YouTube. Feel free to watch either one. Personally I think the revised videos are better mainly because of the subtitle.
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Table of Contents:
- 1 - Quantity, Dimension and Units (🎦 video 1)
- 2 - Unit systems, SI unit system (🎦 video 2)
- 3 - Mass and Force in English Unit Systems (USCS &AES) (🎦 video 3)
- 4 - Conversion of units (🎦 video 4)
- 5 - Significant Figure, Scientific And Engineering Notation (🎦 video 5)
- 6 - Bonus: Propagation of Error
- Z) Glossary
1 - Quantity, Dimension and Units (🎦 video 1)
Video
1.1 - Objectives
In engineering problems we deal with many symbols, calculations and units.
Therefore, it is important to understand the difference between:
1.2 - Quantities
Quantities are concepts that are quantifiable *(they can be measured using tools).
Examples: distance, radius, and lenght.
We can use symbols to represent these quantities, for example: d, r, l
These 3 concepts are different, BUT they are measured using the same property or Dimension: Lenght (L).
You may notice that lenght is both a Quantity and a Dimension, this is because lenght (l) is one of the Seven SI base quantities and it is used to DEFINE the dimension of Lenght (L).
Depending on the measuring tool, we will be able to record a value for the quantity that we are interested in.
For Example, with a measuring tape or with a ruler we could get the following values:
- d = 37 ft
- r = 4.8 cm
- l = 26.5 in
Note: Obviously these numbers alone don't mean much without their appropriate units.
More examples!
The quantity time (t), since time is also a SI base quantity, its Dimension is also Time (T).
Another quantity could be volume (V), but it isn't a SI base quantity, therefore its Dimension has to be DERIVED from a SI base dimension. Volume is the measurement of three dimensional space, therefore its Dimension is L^3
Last example,
another physical quantity is velocity (v), which is defined as distance traveled over period of time. It’s dimension is L/T or in exponential notation LT^-1.
The International System of Units (SI) defines the following bases:
1.3 - Derived dimensions
Some times different quantities can have the same Dimension.
Although the dimensions are the same, the meanings of these two quantities are not!
It is also not unusual for a quantity to be dimensionless.
For example, in Fluid mechanics "Reynolds number" is calculated to predict if the flow is laminar or turbulent. All the base dimensions cancel out and we can say that its dimension is a pure number 1. It is a Dimensionless quantity
1.3 - Dimensional Analysis
Dimensional Homogeneity refers to the consistency of dimensions in a physical equation. In simpler terms, it means that the dimensions on both sides of an equation must be the same for the equation to be physically meaningful.
We can apply the rule of Dimensional Homogeneity during our analysis and that is called Dimensional Analysis. This is used to check the correctness of derived equations and formulas.
1.3.1 - EXERCISES (Dimensional Analysis)
2 - Unit systems, SI unit system (🎦 video 2)
Video
2.1 - Objectives
2.2 - Systems of Units
There are 2 main units systems,
2.2.1 - The metric system: The International System of Units (SI)
2.2.1.1 - Coherent SI units
Coherent SI units refer to a system of units in which the units are defined in such a way that there are no conversion factors other than 1 when expressing one unit in terms of the base units.
Example: The SI unit of force is the newton (N), which is defined as:
- Newton (N) = kilogram (kg) × meter per second squared (m/s2)
This is a coherent definition because there's no additional factor other than 1 when expressing the newton in terms of its base units.
Importance: The advantage of having a coherent system is that it simplifies calculations and reduces the potential for errors. There's no need to remember or apply conversion factors when working within the system, making it more intuitive and consistent for scientific and engineering work.
Note: The International System of Units (SI) is designed to be coherent, using its seven base units from which all other units are derived.
More Examples:
3 - Mass and Force in English Unit Systems (USCS &AES) (🎦 video 3)
Video: https://youtu.be/rcLdxdcmOhg
3.1 - Objectives
3.2 - English Unit Systems (USCS & AES)
Let's remember the 2 main units systems
Now, let's review The English system
We will review the United States Customary System (USCS) and the American Engineering System (AES)
Both unit systems are based on foot-pound and second and many of the units are the same.
The mayor difference lies in the units for mass and force.
3.3 - Comparing Mass and Force Units
The International System of Units (SI) and the United States Customary System (USCS) are very similar in their definition of Force.
So how do we determine the weight of an object?
However, according to the American Engineering System (AES), if an object has weight of 1 lbf, then it must have a mass of 1 lbm.
3.3.1 - EXERCISE (Mass and Force Units)
The poundal is a unit of force in the foot-pound-second (fps) system of units, which is a subset of the English Engineering Units. The fps system uses feet for length, pounds for mass, and seconds for time. The poundal is defined in a way that makes Newton's second law of motion particularly simple and coherent in this system.
Definition:
- One poundal is defined as the force required to accelerate a one-pound mass by one foot per second squared.
1 poundal=1 lbm×1 ft/s2
In terms of SI units:
- 1 poundal is approximately equal to 0.138255 Newtons.
1 poundal≈0.138255 N
The poundal was introduced to avoid confusion in physics and engineering calculations that involved pounds-force and pounds-mass, which are units of force and mass respectively in the English Engineering Units system. The poundal provides a distinct unit of force that is not easily confused with a unit of mass, making it easier to work with Newton's second law (F=ma) in the fps system.
In practical terms, the poundal is not widely used today, as the scientific and engineering communities predominantly use The International System of Units (SI). However, it may still be encountered in certain contexts or historical documents.
4 - Conversion of units (🎦 video 4)
Video
4.1 - Objectives
4.2 - Steps for Unit Conversion
5 - Significant Figure, Scientific And Engineering Notation (🎦 video 5)
Video
5.1 Objectives
5.2 - Calculation Rule on Significant Figures (multiplication and division of measurements)
Now, you might me asking yourself...
- Why do we need to follow this rule?
- What is a Significant Figure and how to determine it?
Important Note: This rule only applies to measurements. It doesn't apply to exact quantities.
5.3 - Accuracy of Measurements
Another example with a smaller circle...
It's diameter seems to be exactly 2.9 cm but I still need to guess the last digit, which is a zero.
Although the last digit is an approximation, we still say that the measurement is accurate up to this digit (in this case the second digit after the decimal point), because it provides information on the true value.
In this example, the true value is considered to be somewhere between 2.9 ± half of the smallest unit of this ruler (which is 0.05 cm or 0.5 mm)
The diameter of the circle should not be represented as simply 2.9 cm, because that changes the Accuracy of the measurement and we get different information about the true value. The change in Accuracy would mean that we used another kind of ruler and that would also change the interval in which we could find the true value.
Let's see another example, where we can see how the final answer reported determines the Accuracy of our measurement:
5.4 - Significant and Insignificant Figures
So how do we determine if a figure in the number is a significant figure or not?
Well, it is actually easier to determine the Insignificant Figures in the number.
5.5 - Scientific Notation vs Engineering Notation (using SI prefixes)
5.6 - EXERCISES (S.F. and Engineering Notation)
6 - Bonus: Propagation of Error
http://ipl.physics.harvard.edu/wp-uploads/2013/03/PS3_Error_Propagation_sp13.pdf
Z) Glossary
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