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 introduces 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...

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