Objectives:

Conceptualize and analyze numerically, graphically and symbolically the behavior of the various physical systems, generalize your understanding and analysis as much as possible, and solve problems utilizing this knowledge, within the context of the following situations, relations, problems and tasks:

First-semester topics include:

Measurement and Analysis of Uniformly Accelerated Motion; Measurement of Nonuniformly Accelerated Motion 

• From time and position measurements infer linear and angular velocities and accelerations. (University Physics courses: From functions modeling position vs. time obtain functions modeling velocity and acceleration vs. time).
• Analyze  the relationships among initial, average and final linear and angular velocities for situations involving uniform and nonuniform acceleration. (University Physics courses: The relationship between average velocity, average of initial and final velocities, and uniform or nonuniform acceleration functions).
• Analyze the relationships among initial and final linear and angular velocities, acceleration, time intervals and displacements.

Measurement of Restoring Forces on and Motion of a Pendulum including

• Force vs. displacement for a pendulum, as related to pendulum length and mass.
• Work done in displacing a pendulum from equilibrium to a known position (after Activity 8).
• Velocity vs. time and acceleration vs. time of a pendulum as inferred from position vs. time data. (University Physics courses: Relationship to the derivatives of periodic functions).
• The proportionalities relating frequency to pendulum length and period to pendulum length.

Relationship between Force and Acceleration including

• The effects of forces.
• Inference of force vs. acceleration from data for force vs. incline and acceleration vs. incline.
• The process of establishing the relationship among force, mass and acceleration for an object on an incline and for a system accelerated by an unbalanced gravitational force.
• Inference of gravitational acceleration at infinite slope.
• Measurement of gravitational acceleration.

Vectors

• Replacement of a vector by its components in any given rectangular coordinate system.
• Computation of vector components from magnitude and angle and computation of vector magnitude and angle from components.
• The vector nature of forces, displacements, velocities and accelerations.
• (University Physics: Dot and cross products)

Forces

•   Given a situation involving known and unknown forces and constraints, determine the unknown individual forces acting within the system and/or the net force on a given object.

Potential and kinetic energies; energy conservation including

•   Systems involving work and the exchange of kinetic and gravitational or elastic potential energies, and dissipation of energy. (University Physics courses: Determining the work done by a nonconstant force modeled by a function of position).
• The specific relationship between work and kinetic energy change in the absence of potential energy changes or dissipation of energy.
• The specific relationship between work and elastic or gravitational potential energy in the absence of kinetic energy changes or dissipation of energy. Fulfill Activity 3, Objective 2.

Impulse, Momentum, Conservation of Momentum, including:

• The difference between the effects of impulse F dt and work F ds on the motion of an object.
• Relationships among average force, momentum changes and time intervals. (University Physics courses: Net force as the time derivative of momentum).
• The relationship between Newton's Third Law and conservation of momentum.
• Situations involving elastic and inelastic collisions in one or more dimensions. (University Physics courses: coefficients of restitution)

Projectiles and circular motion including:

• Independence of the vertical and horizontal motion of projectiles.
• Motion of a projectile given initial velocity and vertical position relative to landing point.
• Initial velocity inferred from range and other variables.
• Centripetal acceleration
• (University Physics courses: the effects of viscous drag forces)

Torques and rotation; Momentum and Energy in Rotation including:

• Torques and the condition of rotational equilibrium.
• Find the center of mass of a given collection of masses (University Physics courses: includes continuous mass distributions).
• Conversion of gravitational potential energy to rotational kinetic energy.
• Calculate the moment of inertia of a given collection of masses constrained to rotate about a given point (University Physics courses: includes continuous mass distributions).
• Establish the connection between Newton's Second Law and its angular form, and particularly the connection between mass and moment of inertia.
• Explain the connection between Newton's Third Law and conservation of angular momentum, and how conservation of angular momentum is not equivalent to conservation of momentum.

Gravitation  including:

• The idea of gravitational flux, analogous to luminous flux, and the analogical connection to Newton's inverse square law of universal gravitation.
• The mechanics of circular orbits; especially the derivation of the relation between orbital radius and velocity.
• Conservation of angular momentum and Kepler's Laws.
• Potential energy in changing gravitational fields, terminal velocity, total energy of an orbit. (University Physics courses: determining exact values by integration).

Simple Harmonic Motion

• The conditions required for simple harmonic motion.
• Relationships among mass, restoring force constant and angular frequency. (University Physics courses: derivation of these relationships).
• Graphical and circular models of simple harmonic motion and their relationship.
• Energy relationships in simple harmonic motion; derivation of velocity vs. position relation.
• The position, velocity and acceleration functions of time, and their relation to the graphical and circular models. (University Physics courses: derivation of velocity and acceleration functions).

Waves I (Waves II 2d semester)

• Relationships among wave velocity, frequency, wavelength, density of medium, tension of medium, amplitude, energy and period.
• Nature of reflection at boundaries of various types and the formation of standing waves between two points.
• Determining wavelengths of the harmonics of a standing wave given boundary conditions.
• Determining frequencies of harmonics from wavelengths and propagation velocity.

Second-semester topics include:

Waves

• Relationships among wave velocity, frequency, wavelength, density of medium, tension of medium, amplitude, energy and period.
• Superposition of waves
• Nature of reflection at boundaries of various types and the formation of standing waves between two points.
• Determining wavelengths of the harmonics of a standing wave given boundary conditions.
• Determining frequencies of harmonics from wavelengths and propagation velocity.
• Energy in standing and traveling waves

Thermal Energy and Thermodynamics

• Specific heat, calorimetry, latent heat, energy conservation.
• Kinetic theory of gases, ideal gas laws.
• First and second laws of thermodynamics.
• Analysis of multi-cycle heat engines.

Fluids

• Density, pressure, energy relationships and Bernoulli’s Equation.
• Viscosity and surface tension.

Electrostatics

• Coulomb’s Law, electric fields, superposition of fields.
• Gaussian surfaces
• Energy, potential difference, potential functions.

Electrical Circuits

• Ohm’s Law, Series and Parallel Circuits, Kirchoff’s Laws, Energy Relationships

Magnetism

• Magnetic fields.
• Interaction between magnetic fields and moving electric charges.
• Magnetic fields as the result of moving charges.
• Magnetic flux, EMF resulting from changing magnetic flux.

Modern Physics

• Time dilation, length contraction, mass-energy.
• Photoelectric effect, quantization of energy.
• Uncertainty principle.
• Atomic spectra, quantization of angular momentum, atomic structure.
• Modes of nuclear decay, energy conservation.