Commonly Covered Areas of Classical Mechanics


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Kinematics

This is where practically everyone's journey into physics starts, regardless of how far one takes their physics education. Everyone understands what it means for something to be in motion in that it is not standing still, it is moving in some manner. However, what is not so intuitive is how we describe this act of being in motion through the language in which the universe speaks, mathematics. This mathematical description of motion is generally referred to as kinematics. In this section we discuss the basic concepts of motion, vectors & coordinates, and kinematics in 1 & 2 dimensions. Also, we provide thoroughly worked examples, as well as calculators you can use to help you quickly calculate equations with your values.


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Dynamics

Once one has a grasp on kinematics the next step is to understand the phenomena that drives the motion that is discussed in kinematics. These phenomena are referred to as forces and are the causes that drive the motion, the effects. Here we discuss Newton's Laws, give a brief overview of various forces, dive more in depth into motion, and work through setting up 'free-body' diagrams which can be extremely helpful when tackling physics problems.


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Conservation Laws

Conservation is the notion that a certain property does not change throughout an interaction. This is a very import concept in physics because it provides information about a property within the system that is repeatedly measurable over time, and remains consistent with each measurement. Taking this deeper there is something called Noether's Theorem which states that every differentiable symmetry of the action of a physical system has a corresponding conservation law. We will not dive into Noether's Theorem or symmetries in this section but it is a good concept to keep in mind while you make your way through this material. Here we discuss Work, Interactions, Kinetic & Potential Energy, Impulse, and Momentum. There are worked examples, and equation calculators to help you more efficiently work through your calculations.


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Applications of Classical Mechanics

Here we apply kinematics, dynamics, and conservation laws into progressively more complex systems. We discuss rotation of a rigid body, Newton's theory of gravity, fluids, and elasticity. It is not enough however to simply work out problems with no explanation or reason as to why certain steps are taken or why certain items are assumed so we shall attempt to thoroughly explain what is done, and why. Also, we take an introductory look at what it means to be in an inertial reference frame compared to non-intertial and the effects this has on the equations.


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