# Mechanics for Scientists and EngineersePrep Course for University Preparation Mechanics for Scientists and Engineers ePrep course is one of the ten ePrep courses specially developed to help NSF, NSmen and others to better prepare themselves for studies in universities in Singapore, or overseas. Poor foundation in mechanics, especially for those without going through A-level physics, has been a big source of difficulties faced by those doing conventional engineering such as mechanical or civil engineering, and physical sciences.

This university preparatory course on mechanics is developed in collaboration with the publishers of the popular physics textbook by Serway and Jewett.  The course comes with the textbook at no additional cost, together with excellent learning materials provided by the publishers and a retired NTU professor as the tutor.

In order to further assist the students in preparing for their university studies, additional learning materials on many other subjects are also provided. These include materials on physics, mathematics (algebra, calculus, and statistics, etc.), business finance, engineering economy, economics, corporate finance, biotechnology, biology (or life science), business ethics, Python Programming, discrete mathematics, etc. Samples of these materials can be found below.

While this university preparatory course on physics was designed to help NSFs, it is now opened to everybody and it is highly recommended, especially for those who do not have a strong foundation in physics but are doing engineering, science or technological courses.

## Mechanics for Scientists and Engineers ePrep Course

### – The Learning Contents

I. Compulsory Chapters

1 Physics and Measurement.

1.1 Standards of Length, Mass, and Time

1.2 Modeling and Alternative Representations

1.3 Dimensional Analysis

1.4 Conversion of Units

1.5 Estimates and Order-of-Magnitude Calculations

1.6 Significant Figures

2 Motion in One Dimension.

2.1 Position, Velocity, and Speed of a Particle

2.2 Instantaneous Velocity and Speed

2.3 Analysis Model: Particle Under Constant Velocity

2.4 The Analysis Model Approach to Problem Solving

2.5 Acceleration

2.6 Motion Diagrams

2.7 Analysis Model: Particle Under Constant Acceleration

2.8 Freely Falling Objects

2.9 Kinematic Equations Derived from Calculu

3 Vectors.

3.1 Coordinate Systems

3.2 Vector and Scalar Quantities

3.3 Basic Vector Arithmetic

3.4 Components of a Vector and Unit Vectors

4 Motion in Two Dimensions.

4.1 The Position, Velocity, and Acceleration Vectors

4.2 Two-Dimensional Motion with Constant Acceleration

4.3 Projectile Motion

4.4 Analysis Model: Particle in Uniform Circular Motion

4.5 Tangential and Radial Acceleration 4.6 Relative Velocity and Relative Acceleration

5 The Laws of Motion.

5.1 The Concept of Force

5.2 Newton’s First Law and Inertial Frames

5.3 Mass

5.4 Newton’s Second Law

5.5 The Gravitational Force and Weight

5.6 Newton’s Third Law

5.7 Analysis Models Using Newton’s Second Law

5.8 Forces of Friction

6 Circular Motion and Other Applications of Newton’s Laws.

6.1 Extending the Particle in Uniform Circular Motion Model

6.2 Nonuniform Circular Motion

6.3 Motion in Accelerated Frames

6.4 Motion in the Presence of Resistive Forces

7 Energy of a System.

7.1 Systems and Environments

7.2 Work Done by a Constant Force

7.3 The Scalar Product of Two Vectors

7.4 Work Done by a Varying Force

7.5 Kinetic Energy and the Work-Kinetic Energy Theorem

7.6 Potential Energy of a System

7.7 Conservative and Nonconservative Forces

7.8 Relationship Between Conservative Forces and Potential Energy

7.9 Energy Diagrams and Equilibrium of a System

8 Conservation of Energy.

8.1 Analysis Model: Nonisolated System (Energy)

8.2 Analysis Model: Isolated System (Energy)

8.3 Situations Involving Kinetic Friction

8.4 Changes in Mechanical Energy for Nonconservative Forces

8.5 Power

9 Linear Momentum and Collisions.

9.1 Linear Momentum

9.2 Analysis Model: Isolated System (Momentum)

9.3 Analysis Model: Nonisolated System (Momentum)

9.4 Collisions in One Dimension

9.5 Collisions in Two Dimensions

9.6 The Center of Mass

9.7 Systems of Many Particles

9.8 Deformable Systems

9.9 Rocket Propulsion

10 Rotation of a Rigid Object About a Fixed Axis

10.1 Angular Position, Velocity, and Acceleration

10.2 Analysis Model: Rigid Object Under Constant Angular Acceleration

10.3 Angular and Translational Quantities

10.4 Torque

10.5 Analysis Model: Rigid Object Under a Net Torque

10.6 Calculation of Moments of Inertia

10.7 Rotational Kinetic Energy

10.8 Energy Considerations in Rotational Motion

10.9 Rolling Motion of a Rigid Object

11 Angular Momentum

11.1 The Vector Product and Torque

11.2 Analysis Model: Nonisolated System (Angular Momentum)

11.3 Angular Momentum of a Rotating Rigid Object

11.4 Analysis Model: Isolated System (Angular Momentum)

11.5 The Motion of Gyroscopes and Tops.

12 Static Equilibrium and Elasticity.

12.1 Analysis Model: Rigid Object in Equilibrium

12.2 More on the Center of Gravity

12.3 Examples of Rigid Objects in Static Equilibrium

12.4 Elastic Properties of Solids

13 Universal Gravitation.13.1 Newton’s Law of Universal Gravitation

13.2 Free-Fall Acceleration and the Gravitational Force

13.3 Analysis Model: Particle in a Field (Gravitational)

13.4 Kepler’s Laws and the Motion of Planets

13.5 Gravitational Potential Energy

13.6 Energy Considerations in Planetary and Satellite Motion

14 Fluid Mechanics.

14.1 Pressure

14.2 Variation of Pressure with Depth

14.3 Pressure Measurements

14.4 Buoyant Forces and Archimedes’s Principle

14.5 Fluid Dynamics

14.6 Bernoulli’s Equation

14.7 Flow of Viscous Fluids in Pipes

14.8 Other Applications of Fluid Dynamics

II. Optional Chapters

1. Oscillatory Motion.
2. Wave Motion.
3. Superposition and Standing Waves.
4. Temperature.
5. Heat and the First Law of Thermodynamics.
6. The Kinetic Theory of Gases.
7. Heat Engines, Entropy, and the Second Law of Thermodynamics.
8. Electric Fields
9. …… see complete topics

### 1. Video Lesson (Position and Velocity Vectors)

##### 2. Problem and Solution (Motion of Satellite)

Question: An artificial satellite circles the Earth in a circular motion at a location where the acceleration is 9.00 m/s2.  Determine the orbital period of the satellite.

Solution: ### Samples of Bonus Materials

##### 3. Cross-Word Puzzle on Biotechnology (Genetically Modified Organisms) ##### 4. Worked Example on Engineering Economy (Cost Concepts and Design Economics)

Question: A lash adjuster keeps the pressure constant on engine valves, thereby increasing fuel efficiency in automobile engines. The relationship between price (p) and monthly demand (D) for lash adjusters made by the Wicks Company is given by this equation: D = (2,000 − p)/0.10. What is the demand (Dˆ ) when total revenue is maximized? What important data are needed if maximum profit is desired? ##### 5. Python Programming (Plotting a Sine Curve)
`Code:import matplotlibimport matplotlib.pyplot as pltimport numpy as np# Data for plottingpi = 22/7theta = np.arange(0.0, 2*pi, 0.05) #uniformly from 0 to 2 pi in step of 0.05sine = 1 + np.sin(theta)plt.plot(theta, sine)plt.show()Output: Plot for y = 1 + sin (theta)` #### 6. Economics (Analyzing Changes in Equilibriums)

Three Steps to Analyzing Changes in equilibrium:

Step 1. Decide whether the event shifts the supply or demand curve (or perhaps both).

Step 2. Decide in which direction the curve shifts.

Step 3. Use the supply-and-demand diagram to see how the shift changes the equilibrium price and quantity.

Three steps explained using the market for milk.

1 Example: A Change in Demand — the effect of hot weather on the market for Change in tastes and increase in demand at any given price. 2 Example: A Change in Supply – drought drives up the price of animal feed for dairy cattle. Higher costs reduce supply at any given price. 3 Example: A Change in Both Supply and Demand – 1. Suppose that the hot weather and the rise in animal feed occur during the same time period. 4 Example: A Change in Both Supply and Demand – 2. Forecasters predict a heat wave for some weeks. Hot weather is likely to increase demand for milk and so the demand curve will shift to the right. However, sellers’ expectations that sales of milk will increase as a result of the forecasts mean that they take steps to expand the production of milk. #### 7. Discrete Mathematics (Converse and Contraposition of Statements)

Question: Solution: 