Title: Theory / Unimportant / Experimental / Physics / Feynman / Mechanics
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Name: Angstrom
Abbreviation: Å
Exponant: -10

Question: The radius of atoms is
Answer: 1 or 2 Angstroms.
Chapter: 1
Section: 2

Name: Almost definition of science
Definition: The test of all knowledge is experiment.
Chapter: 1

Q: How can a law of nature be wrong:
-[...].
-[...].
A: if something is wrong with the apparatus that you did not notice; being innacurate
Chapter: 1

Name: Heat
Definition: (jiggling) motion
Chapter: 1
Section: 2

Q: When [Pression], [temperature]
A: we compress a gas slowly; the temperature of the gas increases
Chapter: 1
Section: 2

Q: Property of [...]: [...].
A: crystal; the position of a few atoms determine the position of the remaining atoms
Chapter: 1
Section: 2

Name: Chemical reaction
Definition: A process in which the rearrangement of the atomic partners occurs.
Chapter: 1
Section: 4

Q: We know [...] because [...].
A: there are atoms; an object greater than the molecules will jiggles, because of the inequalities of the collisions on one side to the other, from one moment to the next
Chapter: 1
Section: 4

Name: Electric field
Definition: Potentiality for producing a force.
Chapter: 2
Section: 1

Q: Two rules of charge:
-[...]
-[...]
A: it make a field; in fields, it have forces on them and it moves
Chapter: 2
Section: 1

Q: [...] can carry [...]
A: The electromagnetic field; electromagnetic waves, e.g. light, radio broadcast
Chapter: 2
Section: 1

Question: Electromagnetic waves are characterized by
Answer: its frequency of oscillation.
Chapter: 2
Section: 1

Kind of electromagnetic waves according to its frequency of oscillation in Hertz:
-Electric currents in the circuits in the walls of a building - 100
-radio broadcast 5-10 \(10^5\)
-FM, TV  \(10^8\)
-Radar \(10^{10}\) 
-Light \(5\times 10^{14}\) to \(10^{15}\)
-X-Rays  \(10^{18}\)
-Gamma rays, nuclear \(10^{21}\)
-Gamma rays, artificial \(10^{24}\)
-Gamma rays, in cosmic rays \(10^{27}\)
Chapter: 2

Question: Diameter of nucleus,
Answer: \(10^{-15}\) m.
Chapter: 2
Section: 3

Question: «Whenever you set up the same conditions, the same thing must happen» is
Answer: false.
Chapter: 2
Section: 3

Name: statistical mechanic
Definition: method of statistics applied in a situation in which there are mechanical laws.
Chapter: 3
Section: 2

Name: conservation of energy
Definition: There is a certain quantity, which we call energy, that does not change in the manifold changes which nature undergoes.
Chapter: 4
Section: 1
Example: 28 black undestructible cubes. Number of seen cubes, plus (the increase in the wheight of the box/weight of a cube), plus (increase in the height of water/eight of the cube normalized) is constant

Name: Perpetual motion for weight-lifting machines
Definition: When we have lifted and lowered a lot of weights and restored the machine to the original condition, we find that the net result is to have lifted a weight. provided the machine which lifted the weight is brought back to its exact original condition, and furthermore that it is completely self-contained—that it has not received the energy to lift that weight from some external source
Chapter: 4
Section: 2

Q: [...] are [...].
A: Action done by reversible machines; an upper bound on what real machine can do
Chapter: 4
Section: 2

Name: gravitational potential energy
Definition: The sum of (the weights times the heights)
Chapter: 4
Section: 2

Name: Potential energy
Definition: Location relative to something else
Chapter: 4
Section: 2

Q: Definition: [...].
Numeric value: [...].
A: Energy of a moving object; \(\frac 12m(\vec v\cdot\vec v)\) with \(m\) the mass and \(\vec v\) its velocity
Chapter: 4, 11
Section: 3, 7
Name: Kinetic energy

Name: Elastic energy
Definition: The energy of the tension of elastic. Energy of stressed strings.
Chapter: 4

Name: Laws of thermodynamics
Definition: Laws governing how much energy is available.
Chapter: 4

Name: study of motion
Definition: Study of Where? and when?
Chapter: 5
Section: 1

Q: What matters when considering time is not [...] but is [...].
A: how to define it; how to mesure it
Chapter: 5
Section: 2

Name: oscillators
Definition: Electrical pendulum.
Chapter: 5
Section: 2

Name: Time marker, longer than a day, provided by nature
Chapter: 5
Section: 4
Example: tree rings
Example2: river-bottom sediments

Name: Half-life
Definition: The time taken for this substance to lose half of its radioactivity.
Chapter: 5
Section: 4
Variables: \(R\) a radioactive substance

Question: The equation concerning all of those variables is:
Answer: \[\left(\frac 12\right)^{t/T}=\frac BA.\]
Chapter: 5
Section: 4
Variables: \(R\) a radioactive substance
\(T\)bit's half life
\(A\) it's quantity when it was formed
\(B\) it's quantity now.
\(t\) the time since formation.

Q: How to mesure long distances:
-[...]
-[...]
-[...]
A: take a unit stick, count how many time it can be taken in the distance; triangulation, using an already known distance and angles; sending a bouncing message, mesuring the time between emission and reception, dividing by the speed
Chapter: 5
Section: 6

Question: How to mesure the size \(\sigma\) of a small round object:
-
Answer: make a wall of \(N\) objects to mesure in an area \(A\). Send some objects through this wall. Let \(n\) the fraction which do not get through. Then \(\sigma=\frac{An}{N}\).
Chapter: 5
Section: 7

Question: We can speak of
Answer: a repeatable observation.
Chapter: 6
Section: 1

Name: The probability of \(A\)
Definition: When \(N\) events are considered, if we expect \(A\) to happen \(N_A\) times, then it is \(N_A/N\).
Chapter: 6
Section: 1
Variables: \(A\) an event which may or may not occur during many distinct observations
Notation: \(P(A)\)

Question: Assuming head appear with probability 1/2, the number of way to have \(k\) heads appears in \(n\) draw is
Answer: \[{n\choose k}=\frac{n!}{k!(n-k)!}\]
Chapter: 6
Section: 2
Variables: \(0\le k\le n\)
Name: The probability of \(A\)

Question: Assuming head appear with probability \(1/2\), the probability to have \(k\) heads in \(n\) draw is
Answer: \[\frac{ {n\choose k} }{2^n}\]
Chapter: 6
Section: 2
Variables: \(0\le k\le n\)
Name: The probability of \(A\)

Question: Assuming head appear with probability \(p\), the probability to have \(k\) heads in \(n\) draw is
Answer: \[P(k,n)={n\choose k}p^k(1-p)^{n-k}\].
Chapter: 6
Section: 2
Variables: \(0\le k\le n\) and \(0\le p\le 1\)
Name: The probability of \(A\)

Name: The expected value of \(X\)
Definition: The expected average behavior in many repeated sequences.
Chapter: 6
Section: 3
Variables: \(X\) an event taking real values

Question: Let \(D_n\) be the expected maximal distance during a fair random walk of \(n\) steps in 1 dimension. Then \(D^2_n\) is
Answer: \(n\).
Chapter: 6
Section: 3
Variables: \(n\in\mathbb N\).

Q: \[\frac{ [...] }{ [...] } \]
A: e^{\frac{-x^2}{2\sigma^2} }; \sigma\sqrt{2\pi}
Chapter: 6
Section: 4
Name: Normal probability
Name2: Gaussian probability

Name: Standard deviation
Definition: \(\sigma\)
Chapter: 6
Section: 4
Variables: In Gaussian Probability

Name: The probability that the random value is between \(v_1\) and \(v_2\)
Definition: [$]\int_{v_1}^{v_2} p(x)\dd x[/$].
Chapter: 6
Section: 4
Variables: \(p\) a density function
\(v_1<v_2\in\mathbb R\)

Name: The distribution velocity of a gaz
Definition: Let \(p(v)\) a probability density function over velocities such that, given a random molecule, the probability that its velocity is between \(v\) and \(v+\delta(v)\) is \(p(v)\delta(v)\).
Then \(N\,p(v)\).
Chapter: 6
Section: 4

Name: Heisenberg uncertainty principle
Definition: The product of the typical width of the probability distribution of the position and of the velocities is at least \(\hslash /2m\) where \(m\) is the mass of the particul.
Chapter: 6
Section: 4

Q: [...]
[...].
A: -Every object of mass \(m\) acts on every other object of mass \(m'\) at distance \(r\), creating a force \(G\frac{mm'}{r}\) in its direction.; An object responds to a force by accelerating in the direction of the force by an amount that is inversely proportional to the mass of the object
Chapter: 7
Section: 1
Name: Law of gravitation

Name: An ellipse
Definition: The set of points whose sum of distance to \(r_1\) and \(r_2\) is \(d\), for some distance \(d\) and points \(r_1,r_2\) fixed.
Chapter: 7
Section: 2

Name: Principle of inertia
Definition: -If something is moving, with nothing touching it and completely undisturbed, it will go on forever, coasting at a uniform speed in a straight line.
Chapter: 7
Section: 3

Name: A force
Definition: Something which change the motion of a body.
Chapter: 7
Section: 3

Question: How to explain tides:
Answer: Water is pulled by the moon, more near the moon, less far away from the moon. In both case, the water move away from the earth.
Chapter: 7
Section: 3

Name: Cavendish's experiment
Definition: In some place isolated from earth and electrical interaction:
Two fixed big ball of lead. Two small marbles, attached to a very fine fiber, suspended from the floor. Mesure the torsion to the fiber; it is due to the gravitational force of balls to marbles.
Chapter: 7
Section: 6

Question: How to describe such a one-dimensional motion:
Answer: determine the position of the car at different times, we measure its distance from the starting point and record all the observations.
Chapter: 8
Section: 1

Name: Zeno's paradox
Definition: Achilles runs 10 times as fast as a tortoise, nevertheless he can never catch the tortoise. For, suppose that they start in a race where the tortoise is 100 meters ahead of Achilles; then when Achilles has run the 100 meters to the place where the tortoise was, the tortoise has proceeded 10 meters, having run one-tenth as fast. Now, Achilles has to run another 10 meters to catch up with the tortoise, but on arriving at the end of that run, he finds that the tortoise is still 1 meter ahead of him; running another meter, he finds the tortoise 10 centimeters ahead, and so on, ad infinitum. Therefore, at any moment the tortoise is always ahead of Achilles and Achilles can never catch up with the tortoise.
Chapter: 8
Section: 2

Name: Speed's measure
Definition: Measure distance during a short time. Divide distance by time.
Chapter: 8
Section: 2

Name: \(\delta x\)
Definition: An extra part of \(x\).
Chapter: 8
Section: 3
Variables: \(x\) a variable

Definition: \(s(t+\delta t)-s(t)\).
Chapter: 8
Section: 3
Variables: \(s\) a function of a variable \(t\)
Notation: \(\delta s\)

Name: The speed at a moment \(t\)
Definition: \(\frac{\delta s}{\delta t}\).
Chapter: 8
Section: 3
Variables: \(s\) a distance function of a time variable \(t\)

Question: Given a sequence of measure of speed \(v(t_i)\) at regular interval \(\Delta t\), how to measure the distance traveled.
Answer: \(\sum_i v(t_i)\Delta t\).
Chapter: 8
Section: 4

Name: The distance travelled
Definition: [$]\int v(t)\dd t[/$].
Chapter: 8
Section: 4
Variables: \(v\) a function giving speed at a time \(t\)

Name: Accelleration
Definition: Change of speed divided by change of time.
Chapter: 8
Section: 5

Name: Second law of Newton
Definition: Momentum of a quantity is proportional to the force, \(F=\frac d{dt}(mv)\).
Chapter: 9
Section: 1

Name: Inertia of \(O\)
Definition: How hard it is to get \(O\) moving.
Chapter: 9
Section: 1
Variables: \(O\) an object

Name: mass
Definition: Quantitative measure of inertia.
Chapter: 9
Section: 1
Property: constant (for Newton)

Name: Measuring a mass
Chapter: 9
Section: 1
Example: Swinging an object in a circle at a certain speed and measuring how much force we need to keep it in the circle.

Name: The momentum of \(o\)
Definition: Product of its mass and of its velocity.
Chapter: 9
Section: 1
Variables: \(o\) an object

Question: The mass of \(o\) and \(o'\) together is
Answer: the sum of their masses.
Chapter: 9
Section: 1
Variables: \(o,o'\) object

Name: Velocity
Definition: A magnitude and a direction.
Chapter: 9
Section: 2

Name: Speed
Definition: A magnitude without a direction.
Chapter: 9
Section: 2

Q: [...] is [...] [...].
A: The direction of the force applied to an object; equal to; the direction of the accelleration of this object
Chapter: 9
Section: 3

Question: Motions in the \(x-\), \(y-\) and \(z-\) directions are
Answer: independant.
Chapter: 9
Section: 3
Assuming: The forces in directions \(x\), \(y\) and \(z\) are not connected

Name: Acceleration of gravity on earth's surface
Abbreviation: \(g\)
Chapter: 9
Represents: \(GM/R^2\) with \(M\) the mass of earth, \(R\) its radius, and \(G\) the gravitational constant.
Section: 4

Question: How to compute numerically, with a time interval \(\epsilon\), more efficiently than calculating position, velocity at each time \(t_0+n\epsilon\):
Answer: \(x(t+\epsilon)=x(t)+\epsilon v(t+\epsilon/2)\),
\(v(t+\epsilon/2)=v(t-\epsilon/2)+\epsilon a(t)\), and \(v(\epsilon/2)=v(0)+(\epsilon/2)a(0)\).
Chapter: 9
Section: 6
Assuming: The forces in directions \(x\), \(y\) and \(z\) are not connected

Name: Three body problem
Definition: Describing (analyticaly) the move of three body, in space.
Chapter: 10
Section: 1

Name: Third law on Newton
Definition: Action equals reaction: each pair of particles has corresponding components of mutual interaction that are equal in magnitude and opposite in direction.
Chapter: 10
Section: 1

Name: The relation between their positions, considering only the action of one on the other
Definition: \(\frac {dp_1}{dt}=-\frac{dp_2}{dt}\).
Chapter: 10
Section: 2
Variables: \(p_1,p_2\) the positions of two particles
Kind: 1

Smaller0: there are no external force
Greater0: the momentum is constant
Chapter: 10
Section: 2
Variables: \(O\) an object
Hide middle: yes

Question: If an explosion occurs between \(b_1\) and \(b_2\),
Answer: both goes in opposite direction with the same speed.
Chapter: 10
Section: 2
Variables: \(b_1,b_2\) two bodies, held together, on a 1-dimension track
Assuming: Both objects have the same mass

Name: One definition of equality of mass of \(b_1\), \(b_2\)
Definition: If an explosion occurs in the middle of \(b_1\), \(b_2\), on a 1-dimension track, both goes in opposite direction with the same speed.
Chapter: 10
Section: 2
Variables: \(b_1,b_2\) two bodies

Question: Both object collide, with same speed and stick together, then their velocity is
Answer: 0
Chapter: 10
Section: 2
Variables: \(b_1,b_2\) two bodies
Assuming: Both objects have the same mass

Question: How to avoid friction:
Answer: air slide.
Chapter: 10
Section: 3

Question: Assume \(b_1\) is still, \(b_2\) goes toward \(b_1\) with speed \(s\) and glue to it. How to figure out what will happen:
Answer: change the referential, choose one with direction of \(b_2\) and speed \(s/2\). It is a case already studied.
Chapter: 10
Section: 3
Variables: \(b_1,b_2\) two bodies, on a 1-dimension track

Question: Assume \(b_1\) is still, \(b_2\) goes toward \(b_1\) with speed \(s\) and glue to it. What happens:
Answer: they move at speed \(s/2\). .
Chapter: 10
Section: 3
Variables: \(b_1,b_2\) two bodies with equal mass, on a 1-dimension track

Name: Testing whether an object moving with velocity \(v\), colliding with an equal one at rest, forms an object moving with velocity \(v/2\)
Chapter: 10
Section: 3
Variables: \(b_1,b_2\) two bodies, on a 1-dimension track

Smaller0: an explosion occurs between bodies \(b_1\) and \(b_2\),
Greater0: they move in opposite direction, and \(b_i\)'s speed is proportional to \(\frac{m_{3-i} }{m_1+m_2}\)
Chapter: 10
Section: 3
Variables: \(b_1,b_2\) two bodies, on a 1-dimension track, with mass \(m_1,m_2\) respectively

Q: [...].
A: An interaction which conserves kinetic energies. That is, the colliding object gains no internal energy and do not send energy out of the system
Chapter: 10
Section: 4
Name: Elastic interaction
Q: [...]
-[...]
A: Almost perfect: Collision of atoms in a gas; Almost perfect: magnetism

Name: The mass of \(b\) at speed \(v\)
Definition: \(\frac {m_0}{\sqrt{1-\frac{v^2}{c^2} } }\).
Chapter: 10
Section: 5
Variables: \(b\) a body with mass \(m_0\) at rest,
\(v\) a speed
Context: relativity
Index: 7

Name: A symmetry of \(o\)
Definition: An operation such that \(o\) appears exactly the same after the operation.
Chapter: 11
Section: 1
Variables: \(o\) an object

Question: Why can't we find a center of the universe.
Answer: Because, once symmetry laws are applied, other point would be identical, hence also the center.
Chapter: 11
Section: 2

Question: It means
Answer: the laws do not change when we make a translation of our coordinates.
Chapter: 11
Section: 2
Name: The laws of physics are symmetrical for translational displacements

Name: The symmetries of physical laws
Definition: Translation
Chapter: 11
Section: 2,3
Definition2: rotations
Conjdef: All of
Extra: time?

Name: A scalar
Definition: An ordinary/undirected quantity.
Chapter: 11
Section: 4

Name: A vector
Definition: A quantity with a direction.
Chapter: 11
Section: 4

Name: Why do we use vectors ?
Definition: In order to have a symbol which does not depends on the coordinate system.
Chapter: 11
Section: 4

Name: The product of \(\alpha\) and \(\vec a\)
Definition: \((\alpha a_x,\alpha a_y,\alpha a_z)\)
Chapter: 11
Section: 4
Variables: \((a_x,a_y,a_z)\) and \(\alpha\) a scalar
Intuition: the same arrow, scaled by \(\alpha\)

Question: One of the most important characteristics of force is
Answer: that it has a material origin, and this is not just a definition.
Chapter: 12
Section: 1

Name: Example of impossibility of exact definition
Definition: What is a chair? Well, a chair is a certain thing over there … certain?, how certain? The atoms are evaporating from it from time to time—not many atoms, but a few—dirt falls on it and gets dissolved in the paint; so to define a chair precisely, to say exactly which atoms are chair, and which atoms are air, or which atoms are dirt, or which atoms are paint that belongs to the chair is impossible.
Chapter: 12
Section: 1

Name: Difference between the law \(F=ma\) and the law \(F=cv^2\) with \(c\) a constant and \(v\) the velocity of a plane
Definition: this law is the result of an enormous complexity of events and is not, fundamentally, a simple thing. If we continue to study it more and more, measuring more and more accurately, the law will continue to become more complicated, not less. In other words, as we study this law of the drag on an airplane more and more closely, we find out that it is “falser” and “falser,” and the more deeply we study it, and the more accurately we measure, the more complicated the truth becomes.
Chapter: 12
Section: 2

Name: Law of friction
Definition: The force needed to overcome friction and to drag one object over another is \(\mu N\) with \(\mu\) the coefficient of friction and \(N\) the normal force between the two surfaces.
Chapter: 12
Section: 2

Name: A polar molecule
Definition: A molecule where the centers of positive and of negative charges do not coincide.
Chapter: 12
Section: 2

Name: Its dipole moment
Definition: Charge times the separation between centers.
Chapter: 12
Section: 2
Variables: \(m\) a dipole molecule

Name: A nonpolar molecule
Definition: A molecule which is not a dipole.
Chapter: 12
Section: 2

Name: Hooke’s law
Definition: The force in a body which tries to restore the body to its original condition when it is distorted is proportional to the distortion.
Chapter: 12
Section: 2
Context: Mechanics
Name2: Law of elasticity

Name: The charge of an electron
Abbreviation: \(q_{\text{el}}\)
Chapter: 12
Exponant: −19
Section: 4
Typ: coulomb
Significative digit: 1.60

Abbreviation: \(\epsilon_0\)
Chapter: 12
Exponant: -12
Typ: coul^2/newton . m^2
Significative digit: 8.854

Name: Law for static charge
Definition: \(q_1q_2\mathbf{r}/4\pi\epsilon_0r^3\).
Chapter: 12
Variables: \(q_1,q_2\) be electric charge

Name: The electric field generated by \(q_1\)
Definition: \(\frac{q_1\mathbf{r} }{4\pi\epsilon_0r^3}\)
Variables: \(q_1\) a charge
Denoted by: \(\mathbf E\)

Name: The response of \(q_2\) to \(\mathbf E\)
Definition: \(q_2\mathbf E\)
Variables: \(q_1\) a charge
\(\mathbf E\) a field

Name: Field equations
Definition: Laws concerning generating fields and how they apply to objects.

Smaller0: the total electric field produced by a number of sources
Greater0: the vector sum of the electric fields produced by every sources
Smaller to greater: equals
Name: principle of superposition of fields

Name: Electric field
Definition: The forces, proportional to the charge when an object is still
Chapter: 12
Section: 4

Name: The force applied to \(q\)
Definition: \(F_=q(E_x+v_yB_z-v_zB_y)\),
\(F_=q(E_y+v_zB_x-v_xB_z)\) and
\(F_=q(E_z+v_xB_y-v_yB_x)\).
Chapter: 12
Section: 4
Variables: \((E_x,E_y,E_z)\) an electric field
\((B_x,B_y,B_z)\) a magnetic induction
\((v_x,v_y,v_z)\) a velocity of a moving charge \(q\)

Name: Nuclear forces
Definition: Forces between the nuclei of atoms.
Chapter: 12
Section: 6

Question: Simplest example of conservation of energy ?
Answer: Let O an object on which the only external force is gravity.
The sum of its kinetic energy and of its potential energy is constant.
Chapter: 13
Section: 1

Name: The power of \(\mathbf F\) acting on \(\mathbf v\)
Definition: \(\mathbf F\cdot\mathbf v\)
Page: http://www.feynmanlectures.caltech.edu/I_13.html
Chapter: 13
Section: 1
Variables: \(\mathbf F\) a force,
\(\mathbf v\) a vector

Smaller0: the rate of change of kinetic energy of \(o\)
Greater0: the power expended by the forces acting on \(o\)
Page: http://www.feynmanlectures.caltech.edu/I_13.html
Chapter: 13
Section: 1
Variables: \(\mathbf F\) a force,
\(o\) an object
Smaller to greater: is equal to

Name: Keplers' laws
Definition: Each planet moves around the sun in an ellipse, with the sun at one focus.
Chapter: 7
Section: 2
Definition2: The radius vector from the sun to the planet sweeps out equal areas in equal intervals of time.
Definition3: The squares of the periods of any two planets are proportional to the cubes of the semimajor axes(Distance from center to the more distant point) of their respective orbits: \(T\equiv a^{3/2}\).

Name: Pseudo force
Chapter: 12
Section: 5
Example: Forces generated by the fact that a system rotates,
Example2: Forces generated by the fact that a system which accelerates.

Question: Pseudo force is
Answer: Proportional to the mass
Variables: 12
Extra: 5

Name: Their sum
Definition: \((a_x+b_x,a_y+b_y,a_z+b_z)\).
Chapter: 11
Section: 5
Variables: \((a_x,a_y,a_z)\) and \((b_x,b_y,b_z)\) two vectors
Intuition: the two arrows, with the tail of \(\vec b\) on the head of \(\vec a\).
Assuming: Both vectors are expressed in the same coordinate system

Section: 5
Chapter: 11
Name: The scalar product
Definition: \((a_x,a_y,a_z),(b_x,b_y,b_z)\mapsto(a_xb_x + a_yb_y+a_zb_z)\)
Commutative: Yes
Intuition: the product of the length of the vectors, time the cosinus of their angle
Extra: Distributive over sum
Assuming: Both vectors are expressed in the same coordinate system

Name: Gravitational constant
Abbreviation: G
Chapter: 7
Exponant: -11
Section: 6
Typ: \(\frac{Nm^2}{kg^2}\)
s: -2
m: 3
kg: -1
Significative digit: 6.670
Other fields (not shown on cards):
SI types: \(\frac{m^3}{kg.s^2}\)

Question: Why does things turn around a star/planet ?
Answer: It falls toward the planet. The sum of the falling and of the intertia describe an ellipse
Chapter: 7
Section: 3
Answer2: Its direction is parallel to the floor of the planet, and its fall is similar to the curvature of the planet, hence never come closer to the floor