Module 1 Trigonometry

This course assumes Mathematics at the Trigonometry/Pre-calculus level with mastery of prior math courses including algebra, geometry. etc. This module includes a quick refresher of the most important math concepts from trigonometry we will need during this course. A few references are also provided for those students need refreshing on past math courses. A person’s proficiency in Mathematics is one of the major predictors of both future academic success and career earnings. Most academic programs leading to high paying careers have mathematics requirements at Calculus or above and require students who are numerically literate. All physics and engineering programs require incoming freshmen to take multi-course sequences in Calculus and Calculus-based physics during their Freshman year with more advanced course work beyond.  

Module 2 Units

In this module, we review several concepts that many students will have already encountered in previous science and math courses including units, dimensional analysis, scientific and engineering notations, and Fermi estimations. Mastery of these concepts is essential for students interested in careers in Physics, Engineering, Medicine, and other technical fields as well as ensuring the student’s future safety when working in industrial settings.

Module 3 Vector

In this module, we will study scalar and vector math. Solid knowledge of vector math is essential for success in physics at all levels. Vectors behave differently than scalars. For instance, there is no such thing as vector division while there are two different ways to multiply two vectors as well as another way to multiply a vector times a scalar. Vectors also add and subtract differently than scalars. All of these operations have important applications in physics. 

Module 4 1-D Motion

In this module, we will begin Kinematics (the study of the motion of an object) by discussing the basic concepts that physicists use to represent the motion of an object in mathematics. We will then examine one-dimensional motion including the special case of constant acceleration. After completing the module, a student should be able to describe the motion of any object moving in a straight line since you can always rotate your coordinate axis so that the object is moving along the x-axis. In the next module, we will expand our discussion to cover multi-dimensional motion (i.e. motion along a curved path). We will not discuss the cause of acceleration in this module as this is another field of mechanics called Dynamics which will be covered in a later module after we finish Kinematics. 

Module 4 1-D Motion

In this module, we will begin Kinematics (the study of the motion of an object) by discussing the basic concepts that physicists use to represent the motion of an object in mathematics. We will then examine one-dimensional motion including the special case of constant acceleration. After completing the module, a student should be able to describe the motion of any object moving in a straight line since you can always rotate your coordinate axis so that the object is moving along the x-axis. In the next module, we will expand our discussion to cover multi-dimensional motion (i.e. motion along a curved path). We will not discuss the cause of acceleration in this module as this is another field of mechanics called Dynamics which will be covered in a later module after we finish Kinematics. 

Module 4 1-D Motion

In this module, we will begin Kinematics (the study of the motion of an object) by discussing the basic concepts that physicists use to represent the motion of an object in mathematics. We will then examine one-dimensional motion including the special case of constant acceleration. After completing the module, a student should be able to describe the motion of any object moving in a straight line since you can always rotate your coordinate axis so that the object is moving along the x-axis. In the next module, we will expand our discussion to cover multi-dimensional motion (i.e. motion along a curved path). We will not discuss the cause of acceleration in this module as this is another field of mechanics called Dynamics which will be covered in a later module after we finish Kinematics. 

Module 5 2-D Motion

In this module, we will expand our study of Kinematics to multi-dimensional motion. While we could make a linear motion problem that we have studied previously into a multi-dimensional motion problem by rotating our coordinate axis so that the object doesn’t move along any of the coordinate axes, this is not usually done by physicists as it makes the math harder. Motion along a curved path with our present level of math skills requires us to deal with multi-dimensional motion. We will deal in detail with two special cases: projectile motion and circular motion. For those students who decide to go on to more advanced study at a university, you will discover in your advanced physics and math courses that there are additional coordinate systems (curvilinear coordinates) besides just polar coordinates that can simplify more complicated curved motion into simpler one dimensional or multidimensional problems.

Module 5 2-D Motion

In this module, we will expand our study of Kinematics to multi-dimensional motion. While we could make a linear motion problem that we have studied previously into a multi-dimensional motion problem by rotating our coordinate axis so that the object doesn’t move along any of the coordinate axes, this is not usually done by physicists as it makes the math harder. Motion along a curved path with our present level of math skills requires us to deal with multi-dimensional motion. We will deal in detail with two special cases: projectile motion and circular motion. For those students who decide to go on to more advanced study at a university, you will discover in your advanced physics and math courses that there are additional coordinate systems (curvilinear coordinates) besides just polar coordinates that can simplify more complicated curved motion into simpler one dimensional or multidimensional problems.

Module 6 Galilean Transformation

In this module, we will examine how to relate the observations made by an observer in one reference frame for objects moving at speeds much less than the speed of light to those observations made by observers in other reference frames. The equations that relate these measurements are the Galilean Transformations.

Module 5 2-D Motion

In this module, we will expand our study of Kinematics to multi-dimensional motion. While we could make a linear motion problem that we have studied previously into a multi-dimensional motion problem by rotating our coordinate axis so that the object doesn’t move along any of the coordinate axes, this is not usually done by physicists as it makes the math harder. Motion along a curved path with our present level of math skills requires us to deal with multi-dimensional motion. We will deal in detail with two special cases: projectile motion and circular motion. For those students who decide to go on to more advanced study at a university, you will discover in your advanced physics and math courses that there are additional coordinate systems (curvilinear coordinates) besides just polar coordinates that can simplify more complicated curved motion into simpler one dimensional or multidimensional problems.

Module 7 Newton’s Laws

In this module, we will change our perspective from the study of motion to the cause of acceleration. We will discuss two of the most fundamental concepts in physics (force and inertia) and see how Newton’s Three Laws along with a well-drawn free body diagram can enable one to solve problems from the motion of planets to the flight of a baseball.

Module 7 Newton’s Laws

In this module, we will change our perspective from the study of motion to the cause of acceleration. We will discuss two of the most fundamental concepts in physics (force and inertia) and see how Newton’s Three Laws along with a well-drawn free body diagram can enable one to solve problems from the motion of planets to the flight of a baseball.

Module 7 Newton’s Laws

In this module, we will change our perspective from the study of motion to the cause of acceleration. We will discuss two of the most fundamental concepts in physics (force and inertia) and see how Newton’s Three Laws along with a well-drawn free body diagram can enable one to solve problems from the motion of planets to the flight of a baseball.

Module 3 Vector

In this module, we will study scalar and vector math. Solid knowledge of vector math is essential for success in physics at all levels. Vectors behave differently than scalars. For instance, there is no such thing as vector division while there are two different ways to multiply two vectors as well as another way to multiply a vector times a scalar. Vectors also add and subtract differently than scalars. All of these operations have important applications in physics. 

Module 8 Work & Kinetic Energy

In this module, we will examine two of the most important concepts in physics, Work & Kinetic Energy. These two concepts are linked by the Work-Energy Theorem which connects our previous work on Newton’s Laws to an even more general and powerful solution technique for solving physics problems called Energy Analysis. Prior to starting this module, you will need to review the math that we will be using which is called the Dot Product. This material is in the Vector Module.

Module 3 Vector

In this module, we will study scalar and vector math. Solid knowledge of vector math is essential for success in physics at all levels. Vectors behave differently than scalars. For instance, there is no such thing as vector division while there are two different ways to multiply two vectors as well as another way to multiply a vector times a scalar. Vectors also add and subtract differently than scalars. All of these operations have important applications in physics. 

Module 8 Work & Kinetic Energy

In this module, we will examine two of the most important concepts in physics, Work & Kinetic Energy. These two concepts are linked by the Work-Energy Theorem which connects our previous work on Newton’s Laws to an even more general and powerful solution technique for solving physics problems called Energy Analysis. Prior to starting this module, you will need to review the math that we will be using which is called the Dot Product. This material is in the Vector Module.

Module 9 Linear Momentum

In this module, we will examine the concept of linear momentum and its connection to forces. Linear momentum is an extremely useful concept both because of its importance in understanding how the Universe works and in solving collision problems.

Module 9 Linear Momentum

In this module, we will examine the concept of linear momentum and its connection to forces. Linear momentum is an extremely useful concept both because of its importance in understanding how the Universe works and in solving collision problems.

Module 10 Center of Mass

Module 11 Rotation

Module 11 Rotation

In this module, we will examine the rotational motion of objects. Using polar coordinates, we determine angular analogs for many past concepts in mechanics including position, displacement, velocity, acceleration, force, inertia, and momentum. concept of linear momentum and its connection to forces. This will will enable us to use our past experience with motion problems and symbol substitution (The Big Board) to solve a wide range of rotational motion problems including rotational motion graphs and constant angular acceleration problems.

Module 12 Rotational Dynamics

In this module, we will examine Torque and Moment of Inertia (the rotational analogs of force and mass) and Newton’s Second Law for Rotation. Torque and Rotational Inertia are more complicated than their linear brethren in that their values depend upon the axis of rotation about which they are computed. The torque applied to an object by a force depends not only upon the force, but the point of application through the math of vector cross products. The moment of inertia of an object is different for different axis of rotation even though the object’s mass is the same. Furthermore an object can change it’s moment of inertia by changing how its mass is distributed (like when a skater spreads out their arms) without changing their mass.

Module 13 Angular Momentum

In this module, we will examine the concept of angular momentum and its relationship to torque. We will then discover when the angular momentum of a system is conserved. This powerful conservation law related to rotational symmetry of the Universe is of great importance in many practical situations especially analyzing central force systems.

Module 14 Rolling Without Slipping

In this module, we will examine rolling without slipping and the use of Chassel’s Theorem to analyze the general motion of any body. This will enable us to do energy analysis of a variety of rolling objects.

Module 15 Statics

In this module, we will examine the special case of Statics or Equilibrium as it is called by Physicists. These are problems where there is no translation acceleration or rotational equilibrium. Thus, the sum of the external forces and external torques upon the body must equal zero.

Module 15 Statics

In this module, we will examine the special case of Statics or Equilibrium as it is called by Physicists. These are problems where there is no translation acceleration or rotational equilibrium. Thus, the sum of the external forces and external torques upon the body must equal zero.

Module 16 Fluids

In this module, we will examine fluids using the tools we have developed over the previous chapters. Because fluids can change shape and cannot handle shear stresses, we will find it convenient to rephrase our laws in terms of intensive properties (density and pressure) rather than extensive properties (mass and force). The section begins by handling static fluids and then handles ideal fluids under motion.

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Module 17 Oscillations

In this module, we will examine oscillations using the tools we have developed previously and our knowledge of trigonometry. Oscillatory systems have great historical importance as they helped form the basis of the first accurate time measuring devices. Oscillatory systems have an even greater importance in that they are the natural response to any stable system exposed to small disturbances from crystals in electronic devices to atoms to buildings. Thus, an understanding of oscillators is essential for physics, electrical engineering, civil engineering, mechanical engineering, geology, etc. 

Module 18 Waves

In this module, we will examine waves and their properties. Waves are one of the most important concepts in physics representing half of the physical world. Because a wave has no specific location like a particle, it has no position vector and obeys different rules from particles.

The severe weather has caused us to lose class time. The exam for Monday Dec 9th has been rescheduled for Wed. Dec 11th

Prior to Thanksgiving, you were given a practice test over static fluids and statics to work in class rather than doing the exam for grade. We have now covered moving fluids, and oscillators as well so the next test will cover both the material on the practice test and this new material. Since there is too much material to cover in a single test not all learning objectives in each section will be tested. Approximately 50% will be fluids (both static and moving) and the rest split between oscillations (like the homework) and statics problems similar to the practice test. I have enclosed a copy of the practice test in case you don’t already have one along with a key for you to use in your study prep.

Monday November 25 Practice Test

Practice Test Key 

Module 17 Oscillations

In this module, we will examine oscillations using the tools we have developed previously and our knowledge of trigonometry. Oscillatory systems have great historical importance as they helped form the basis of the first accurate time measuring devices. Oscillatory systems have an even greater importance in that they are the natural response to any stable system exposed to small disturbances from crystals in electronic devices to atoms to buildings. Thus, an understanding of oscillators is essential for physics, electrical engineering, civil engineering, mechanical engineering, geology, etc. 

Module 18 Waves

In this module, we will examine waves and their properties. Waves are one of the most important concepts in physics representing half of the physical world. Because a wave has no specific location like a particle, it has no position vector and obeys different rules from particles.

Because of the different starting times for various campuses as well as various campus holidays, their will not be an exam next week on Monday. As I mentioned prior to the break, we will move quickly through the material in the next couple of chapters due to time constraints so students planning to take the AP Exam in May will need to do additional work outside of class. We will review material from Chapter 11 covered before the break and then move on to consider a special case of waves (Sound) in Chapter 12.

Module 18 Waves

In this module, we will examine waves and their properties. Waves are one of the most important concepts in physics representing half of the physical world. Because a wave has no specific location like a particle, it has no position vector and obeys different rules from particles.

Module 19 Sound

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February to February 14