Physics Fundamentalized

Capacitance is defined in the context of an arrangement of parallel plates. The electric field energy per unit volume is also derived.

The notion of lines of equipotential is introduced and explored.

The electric potential between two parallel conducting plates of known surface charge density is discussed in detail. This example is of particular interest because it is used to illuminate the relationship between force, field, voltage and energy.

The integral that defines electric potential is evaluated in the context of two uniform, spherically symmetric charge distributions, the first of which results in the electric potential due to a point charge.

The Electrostatic Potential energy is derived from the work-energy theorem which leads, in turn to our definition of electric potential, the energy per unit charge.

The harmonic oscillator is solved with a damping force proportional to the speed of the oscillator.

The principles of harmonic motion are reviewed and then applied to three examples: the simple pendulum, the physical pendulum and a can bobbing in water.

The problem of a mass connected to a spring is analyzed using Newton's 2nd law to reveal the harmonic oscillator differential equation which is then solved for the position, velocity and acceleration of the oscillator as a function of time. Arguments are made that such solutions are approximately true for any system for which there exists a potential energy minimum, provided the oscillation is small. Also, it is demonstrated that identical solutions are obtained for a mass hanging from a vertical spring by applying a thoughtful change in coordinate.

A modern demonstration of the discovery that a one over r squared force law results in planetary motions that are ellipses in agreement with Kepler’s observations.

The gravitational potential energy between two mutually attracting bodies is derived. After, several essential applications of universal gravitation are presented.

The formulation of Newton’s Universal Gravitational Law is explored in its historical context. After advice is given on applying the law, one of its consequences is revealed.

The angular momentum of a point particle is defined and discussed in the context of a classic demonstration.

Rolling is described as a linear superposition of translational and rotational motion. A revelation is made regarding using the point of contact between the rolling object and the surface as the axis of rotation for the motion. The principles are applied to the problem of a sphere rolling down a ramp which is solved with two distinct approaches. After, the motion of a bowling ball skidding before rolling is presented as an essential problem.

The problem of a pulley with a single mass attached is solved two different ways; with Newton's 2nd Law and with Energy. The differences in these two approaches are discussed. Also, the problem of a rigid uniform rod rotating vertically about a hinge point is solved and the forces at the hinge are discussed.

Torque is demonstrated in the context of the classroom door and defined such that a rotational analog on Newton’s second law results. With this new version of the law, the problem of an Atwood’s machine with a massive pulley is solved.

The moment of inertia of a disk is derived and used to compare the dynamics of of a hoop and a disk of equal mass and radius as they roll down identical inclines. The fraction of energy transferred to rotational motion is discussed.

The moments of inertia are calculated for a few simple cases; a point particle, a hoop, a rod about its center of mass and a rod about its end. General observations are made about the properties of the moment of inertia including a derivation of the parallel axis theorem.

The rotational kinetic energy of an arbitrarily shaped mass is investigated, leading to the definition of the moment of inertia.

The kinematic quantities, position, velocity and acceleration, are cast into their rotational analogs.

A special presentation involving the solution of elastic collisions in the center of mass frame of reference.

The center of mass is defined in both its discrete and continuous forms and the observation is made that a system of particles can be generalized as the center of mass motion. Two essentials derivations are performed while finding the center of mass of rods with different linear has density functions.

The nature of elastic collisions is explored and it is pointed out that, by using mass ratios and coordinate systems in relative motion, all elastic collisions may be reduced to the collision of equal masses with one initially at rest.

An example of the application of the conservation of momentum to a classic situation is described in detail. Newton's cradle is explained.

After a brief discussion of the notion of systems as it relates to momentum and its conservation, the velocity of a rocket in deep space as a function of fuel consumption is derived.

Momentum is introduced in the context of what Newton described as the quantity of motion. The second law is then cast into a momentum form, revealing the notion of impulse and the suggestion of momentum as a conserved quantity.

A customized form of the law of conservation of energy is derived and its features described in detail. The relationship between conservative forces and their associated potential energies is revealed and explained. Finally, power is defined and its practical applications are discussed.

The spring potential energy is derived.

The general definition of work is discussed as a practical matter, followed by a derivation of the gravitational potential energy.

In a special lecture of the series the kinetic energy is derived once again, but this time with respect for the variation of the mass with velocity resulting in the famous mass-energy relation. It goes on so long, a classroom door is used for extra space.

In this, the introductory lecture on energy, the kinetic energy is derived using calculus by computing the effect of a force acting in the direction of motion. Energy is also described as a universal symmetry and some practical maters of its application are discussed.

The first of the more informal problem solving sessions in preparation for the exam. A toaster is pulled by its cord and the angle of maximum acceleration is determined. A block slides on a slab which, in turn, rests on a frictionless surface.

The velocity of an object subject to a drag force proportional to the square of the velocity is derived as well as the velocity of an object falling under the influence of gravity while subject to a drag force.

Newton’s second law is used to find the position, velocity and acceleration of an object subject to a viscous drag force that it proportional to the velocity.

The centripetal acceleration is revealed by computing the change in the velocity vector for an object moving around a circular arc at constant speed. To follow up, three essential examples of circular motion are demonstrated; the vertical loop, the graviton ride and the motion of a car along a banked curve.

The nature of the generalized friction force and how to calculate it is presented in detail immediately followed by two essential problems; an object skidding to rest on a surface and the classic inclined plane. Particular focus is given to the inclined plane free body diagram and the system is described as a method for measuring coefficients of friction.

A horse drawn cart is used as a classic example of the application of Newton's Second Law. Free body diagrams are drawn for the system with detailed explanation and advice regarding the technique. With the diagrams complete, the law is applied and the results discussed. Later in the lecture, the classic problem of Atwood's Machine is presented as an essential derivation of classical mechanics.

The 2nd law is stated and its subtleties and limitations are described including the observation of pseudo forces. Strategies are described for the case of compound objects. The 3rd law is described and common examples are discussed, particularly where misconceptions are common.

Newton’s First Law is presented in its traditional form, but strong emphasis is placed on the law as a definition of force. After a short discussion of the history of inertia and the measurement of mass, forces are presented as “a natural constraint or condition that is the cause of alteration of the motion”. The four fundamental forces of nature are described and it is noted that most everyday forces are generalized versions of the electrodynamic force. Physical contact is described as an illusion. A thought experiment is proposed in which the behavior of an object under the influence of multiple forces. Mass is defined as the measurement of inertia and noted to be directly proportional to the weight. Finally, a rough list of forces that one might encounter in physics problems is presented.

The Chain Rule The Power Rule The Power Rule in Kinematics Exponential Functions

Introduction to Vectors Vector Addition Vector Subtraction Component Form Unit Vectors Linear Independence The Principle of Superposition The Scalar (Dot) Product The Vector (Cross) Product

Instantaneous Quantities More on Motion Graphs

Physics as a Description of the Universe Uncertainty in Measurement The Imperfect Notion of Trajectory Kinematic Quantities Defined Units and Dimensional Analysis Graphical Analysis Limitations of Kinematics

Eric Scheidly talks about the lecture series and what he wants listeners to get out of it. He also talks about what drew him to physics and why it is so important.