Physics Fundamentalized

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 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.