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Chapter price = 10 $
ALGEBRA 1
Version 2009
Revised and highly enlarged.
ALGEBRA 2
ALGEBRA 3
ALGEBRA 4
GEOMETRY 1
ELECTRICITY 1
ELECTRICITY 2
ELECTRICITY 1&2
OPTICS 1
OPTICS 2
MECHANICS 3
MECHANICS 3
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
w
t.
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
= -
w
^{2}
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 sin
q
/
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.