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.