Title price = 99 $
 Chapter price = 10 $
ALGEBRA 1 Version 2009
Revised and highly enlarged.
Kinematics and dynamics, gravitation, satellites, electric and magnetic fields…
High school 16-18 years


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   1. Circular motion: locating a position using an angle.
  •           1. Definition of circular motion.
  •           2. Angle measurement in degrees.
  •           3. Angle measurement in radians.
  •           4. Radian values of some angles.
  •           5. Conversion of common angles into radians.
   2. Roulette ball throws.
  •           1. Locate the position of the ball.
  •           2. Angle swept by the ball during its motion.
  •           3. Distance (s) covered by the ball.
  •           4. Trying other throws.
   3. Circular motion: velocity, angular velocity, kinetic energy and angular momentum.
  •           1. Algebraic velocity and velocity vector.
  •           2. Algebraic velocity is the derivate of the arc s(t).
  •           3. Angular velocity is the derivative of the angle q(t).
  •           4. Kinetic energy of a particle moving on a circle.
  •           5. Angular momentum of a particle moving on a circle.
   4. Uniform circular motion: period and frequency.
  •           1. Definition of uniform circular motion.
  •           2. Angular period of a circular motion.
  •           3. Period T of a uniform circular motion.
  •           4. Definition of frequency n.
  •           5. Review.
  •           6. Determining the parameters of a circular motion.
  •           7. Relation between period, frequency and angular frequency.
   5. Solid in rotation around an axis. Kinetic energy, angular momentum, moments of inertia.
  •           1. Locate the points of a solid rotating around an axis.
  •           2. Velocity of the solid points during rotation.
  •           3. Rotation velocities of the points of a 33 turns record.
  •           4. A fair wheel.
  •           5. Velocities at the earth surface resulting from its rotation around itself.
  •           6. Kinetic energy and angular momentum of a solid rotating around an axis.
  •           7. Moment of inertia of a cylindrical muff and of a cylinder with respect to their axis.
  •           8. Moment of inertia of a rigid rectangular sheet with respect to an axis, parallel to one of its sides.
  •           9. Moment of inertia of a ball with respect to its diameter.
  •           10. Angular momentum and kinetic energy of earth while it rotates around itself.
   6. Classical harmonic oscillator: position in function of time.
  •           1. Importance of the harmonic oscillator in physics.
  •           2. The harmonic oscillator as a component of a uniform circular motion.
  •           3. Period and frequency of the harmonic oscillator.
  •           4. Graphing the position of the oscillator as a function of time.
  •           5. Effect of the period on the motion of the oscillator.
  •           6. Harmonic oscillator out of phase by an angle j.
  •           7. Harmonic oscillator defined by y = a sin wt.
  •           8. Review.
   7. Recording the motion of an harmonic oscillator and determining its parameters.
  •           1. Recording the oscillator motion.
  •           2. Measuring the amplitude a and the period l of the oscillator.
  •           3. Relation between l, the time period T, the frequency n, and the pulse w.
  •           4. Recording new oscillations.
   8. Velocity and acceleration of the harmonic oscillator. Differential equation of motion.
  •           1. Velocity of the harmonic oscillator.
  •           2. Phase difference between the velocity and position of the oscillator.
  •           3. Comparing the graphs of velocity and displacement.
  •           4. Acceleration of the harmonic oscillator. Differential equation of motion.
  •           5. Deriving the properties of the harmonic oscillator.
  •           6. Velocity and acceleration amplitudes of the harmonic oscillator.
   9. Velocity and acceleration vectors for a uniform circular motion.
  •           1. Position vector r of a material point describing a circle.
  •           2. General definition of velocity vector v of a particle.
  •           3. Working out the velocity vector in a uniform circular motion.
  •           4. General definition of acceleration vector g of a particle.
  •           5. Determination of acceleration g for a uniform circular motion.
  •           6. To recover the relation g = -w2 r using explicit components.
   10. Newton laws. Gravitational field: gravity on earth and projectile motion.
  •           1. Newton first and second laws. Equation of motion.
  •           2. Newton gravitational laws. Action and reaction principle: third law.
  •           3. Center of mass and relative coordinate in the two body problem.
  •           4. Potential j and acceleration field g produced by a planet.
  •           5. Free fall acceleration g and its link with gravitation.
  •           6. Integration of equations of motion in a uniform force field: velocity and position vectors.
  •           7. Projectile motion at the ground: trajectory characteristics.
  •           8. Determination of gravity acceleration g from time measurements of free fall objects.
  •           9. Determination of the universal gravitation constant G form the value of g.
   11. Motion of a projectile at the ground level. Satellite circular orbits.
  •           1. Projectile in a uniform gravitational field.
  •           2. A trapshooting with guarantee to win.
  •           3. Circular orbit in a planet's field.
  •           4. Velocity and period of a satellite as functions of its altitude.
  •           5. Geostationary satellite.
  •           6. The earth, satellite of the sun.
  •           7. Verification of Kepler third law.
   12. Geometrical characterization of the circle. Radius of curvature of a line.
  •           1. Area of a circular sector of radius R and angle q.
  •           2. Limit of sinq/q when q tends to zero.
  •           3. Lengths limit of the arc to the corresponding chord on a circle.
  •           4. Tangent vector T to the circle at one of its points.
  •           5. Normal vector n to the circle at one of its points.
  •           6. Generalization to a regular curve: radius of curvature.
   13. Curvature radius of a sinuous road.
  •           1. Parameters dimensions of a curve with equation y = a sinkx.
  •           2. Distance ds between two infinitely close points on the curve.
  •           3. Definition and components of tangent vector T.
  •           4. Computing dT/ds components.
  •           5. Definition and computation of the curvature radius r.
  •           6. Physical meaning of the road parameters.
  •           7. Variation of the curvature radius along the curve.
  •           8. Curvature radius minimum.
   14. Velocity and acceleration of a particle with known trajectory and curvilinear coordinate.
  •           1. Vector velocity intrinsic expression: tangent component.
  •           2. Vector acceleration intrinsic expression: tangent and normal components.
  •           3. Motions defined by a given property of acceleration.
  •           4. Circular motion and circular uniform motion.
  •           5. Forces on a car and its acceleration in a turn.
  •           6. Speed limits in a turn.
  •           7. Drawing the velocity limits in function of the curvature radius of a turn.
   15. Kinetic energy, potential energy, energy conservation.
  •           1. Elementary work done by a force. Kinetic energy of a particle.
  •           2. Energy conservation in a force field which derives from a potential.
  •           3. Gravitational energy of a particle near the ground.
  •           4. Potential energy of a charged particle inside a plane capacitor.
  •           5. Gravitation energy of a satellite in the field of a spherical planet.
  •           6. Potential energy of an electron in the electric field of a nucleus.
  •           7. Potential energy and potential.
  •           8. Gravitational potential energy of a solid near the ground.
   16. Applications of energy conservation: free fall, cathode ray tube, satellite, pendulum.
  •           1. Dropping a supplies container from a plane.
  •           2. Electron velocity when coming out of the cathode ray tube.
  •           3. Satellite energy on a circular orbit.
  •           4. Graphing the potential energy of a satellite using reduced variables.
  •           5. Moving a satellite from one circular orbit to another.
  •           6. Escape velocity from a planet.
  •           7. Energy conservation of a solid pendulum.
  •           8. Second order differential equation. Solution for small angles.
  •           9. Deriving and using energy conservation in the pendulum motion.
   17. Vector's cross-product, moment of a vector and of a vector's set. Couple's moment.
  •           1. Definition of the vector cross-product A × B.
  •           2. Cross products of the basis vectors in an orthonormal frame.
  •           3. Cross products vector components in an orthonormal frame.
  •           4. Derivation formula of vector's cross product.
  •           5. Applying the cross product properties to circular uniform motion.
  •           6. Moment, at a given point, of a bound or sliding vector.
  •           7. Resultant and moment of a vector set. Moment of a couple.
  •           8. Set of forces with resultant equal to zero. Couple and its resultant moment.
  •           9. Resultant moment of a vector and of a set of vectors with respect to an oriented axis.
  •           10. Work and power of a couple.
  •           11. Couple and power of an engine.
   18. Angular momentum of a particle and a solid. Pendulum and spinning top.
  •           1. Definition of a particle angular momentum l.
  •           2. Angular momentum fundamental theorem, for a particle.
  •           3. Angular momentum fundamental theorem for a particle set.
  •           4. Motion of a particle with constant angular momentum.
  •           5. Relation between energy and angular momentum of a satellite describing a circular orbit.
  •           6. Equilibrium of a solid free to move around a point or around an axis.
  •           7. Equation of motion of a pendulum. Solution for small amplitudes.
  •           8. To find experimentally the center of gravity of a cardboard triangle.
  •           9. Watching the motion of a spinning top. Rotation about an axis and precession.
  •           10. Precession is explained by angular momentum fundamental theorem.
  •           11. Model for a spinning top: a cone surmounted by a half-ball.
   19. Bohr's model of the hydrogen atom: binding energy and energy quantization.
  •           1. Binding energy of the hydrogen atom in classical mechanics.
  •           2. Angular momentum l of the hydrogen atom in classical mechanics.
  •           3. Problems encountered in the classical model of the atom.
  •           4. Energy quantization in Bohr's Model.
  •           5. Calculation of energy and orbit radius of hydrogen atom in the fundamental state.
  •           6. Uncovering Bohr's model main results.
   20. Recovering Balmer formula from Bohr's model.
  •           1. Recalling hydrogen atom energy levels in Bohr's model.
  •           2. Bohr's model gives Balmer's formula again.
  •           3. Computing and drawing 4 of the spectral lines of Balmer series.
   21. Charged particle motion in a magnetic field.
  •           1. Magnetic phenomena lead to the introduction of magnetic field.
  •           2. Lorentz force acting on a charged particle. Work and power.
  •           3. Charged particle motion in a magnetic field.
  •           4. Equations of motion of a charged particle in a electromagnetic field.
  •           5. Equation of motion of a charged particle in a uniform magnetic field.
  •           6. Solution of equation of motion.
  •           7. Particle motion with velocity is perpendicular to the magnetic field.
  •           8. Particle trajectory parameters in a uniform magnetic field.
  •           9. Description and properties of mass spectrometer.
  •           10. Charged particle trajectory in a uniform magnetic field: general case.