PHYSICAL PENDULUM:

1. Define the physical quantities that describe the rotational motion (kinetic: angle, angular velocity and acceleration; dynamic: angular momentum, rotational inertia, torque).

- angle: $\theta = \frac{s}{r}$ , s – arc, r – radius. It has no unit but number.

- velocity: Angular velocity is the rate of change of angular displacement and can be described by the relationship $\omega = \frac{\Delta\theta}{\Delta t}$. Angular velocity can be considered to be a vector quantity, with direction along the axis of rotation in the right-hand rule sense.

- angular acceleration - is the rate of change of angular velocity. In SI units, it is measured in radians per second squared (rad/s2). $\alpha = \frac{\text{dw}}{\text{dt}} = \frac{d^{2}\theta}{dt^{2}}$

- the angular momentum of a rigid object is defined as the product of the moment of inertia and the angular velocity. It is analogous to linear momentum and is subject to the fundamental constraints of the conservation of angular momentum principle if there is no external torque on the object. Angular momentum is a vector quantity. It is derivable from the expression for the angular momentum of a particle

- moment of inertia is the name given to rotational inertia, the rotational analog of mass for linear motion. It appears in the relationships for the dynamics of rotational motion. The moment of inertia must be specified with respect to a chosen axis of rotation. For a point mass the moment of inertia is just the mass times the square of perpendicular distance to the rotation axis, I = mr2. That point mass relationship becomes the basis for all other moments of inertia since any object can be built up from a collection of point masses.

2. Second law of dynamics for rotation.

Rotational acceleration is directly proportional to net torque and inversely proportional to moment of inertia or ∑τ = I α

3. Calculation of I for a homogeneous rod (length l, mass M) rotating around the axis perpendicular to the rod and passing through its center of mass. Parallel axis theorem (Steiner’s theorem).

Calculating the moment of inertia of a rod about its center of mass is a good example of the need for calculus to deal with the properties of continuous mass distributions. The moment of inertia of a point mass is given by I = mr2, but the rod would have to be considered to be an infinite number of point masses, and each must be multiplied by the square of its distance from the axis. The resulting infinite sum is called an integral. The general form for the moment of inertia is: I = ∫₀^Mr²dm. When the mass element dm is expressed in terms of a length element dr along the rod and the sum taken over the entire length, the integral takes the form:

$I = \int_{- \frac{L}{2}}^{\frac{L}{2}}{r^{2}\frac{M}{L}dr = \frac{M}{L}\frac{r^{3}}{3}\left| \frac{L/2}{L/2} = \frac{M}{3L}\left\lbrack \frac{L^{3}}{8} - \frac{- L^{3}}{8} \right\rbrack dm = \frac{M}{L}\text{dr} \right.\ }$ so we have $I_{\text{cm}} = \frac{1}{12}\text{ML}^{2}$

The moment of inertia of any object about an axis through its center of mass is the minimum moment of inertia for an axis in that direction in space. The moment of inertia about any axis parallel to that axis through the center of mass is given by I_{parallel axis} = I_cm + Md²

4. Harmonic force and harmonic motion. Physical pendulum. Motion of physical pendulum as an example (simplified!) of the harmonic motion.

Simple harmonic motion is typified by the motion of a mass on a spring when it is subject to the linear elastic restoring force given by Hooke's Law. The motion is sinusoidal in time and demonstrates a single resonant frequency. Hanging objects may be made to oscillate in a manner similar to a simple pendulum. The motion can be described by "Newton's 2nd law for rotation": τ = I_supportα, where the torque is τ = −mgL_cmsinθ and the relevant moment of inertia is that about the point of suspension. The resulting equation of motion is: $\alpha \approx \frac{\text{mg}L_{\text{cm}}}{I_{\text{suport}}}\text{θ\ }$for small angles where sinθ ≈ θ This is identical in form to the equation for the simple pendulum and yields a period:$2\pi\sqrt{\frac{I_{\text{suport}}}{\text{mg}L_{\text{cm}}}}$

WHEATSTONE BRIDGE

- Kirchhoff’s current law:

At any node (junction) in an electrical circuit, the sum of currents flowing into that node is equal to the sum of currents flowing out of that node, or:

The algebraic sum of currents in a network of conductors meeting at a point is zero.

- Kirchhoff’s voltage law: This law is also called Kirchhoff's second law, Kirchhoff's loop (or mesh) rule, and Kirchhoff's second rule. Similarly to KCL, it can be stated as: $\sum_{k = 1}^{n}{V_{k} = 0}$ Here, n is the total number of voltages measured. The voltages may also be complex: $\sum_{k = 1}^{n}{{\tilde{V}}_{k} = 0}$

- Serial connection: R = R1 + R2

- Parallel connection: $\frac{1}{R} = \frac{1}{R_{1}} + \frac{1}{R_{2}}$

Detecting zero current with a galvanometer can be done to extremely high accuracy. Therefore, if , and are known to high precision, then can be measured to high precision. Very small changes in disrupt the balance and are readily detected. At the point of balance, the ratio of $\frac{R_{2}}{R_{1}} + \frac{R_{x}}{R_{3}} \Rightarrow R_{x} = \ \frac{R_{2}}{R_{1}} \bullet R_{3}$

The electrical resistance of a wire would be expected to be greater for a longer wire, less for a wire of larger cross sectional area, and would be expected to depend upon the material out of which the wire is made. Experimentally, the dependence upon these properties is a straightforward one for a wide range of conditions, and the resistance of a wire can be expressed as $R = \frac{\text{ρL}}{A}$, ρ – resistivity, L – length,
A – cross sectional area

The factor in the resistance which takes into account the nature of the material is the resistivity . Although it is temperature dependent, it can be used at a given temperature to calculate the resistance of a wire of given geometry. The inverse of resistivity is called conductivity. There are contexts where the use of conductivity is more convenient.

- Electrical conductivity = σ = 1/ρ

- Resistivity of metals increases as the temperature rises due to reduced mobility of electrons, in varying extent for the different metals.

- Electric current is the rate of charge flow past a given point in an electric circuit, measured in Coulombs/second which is named Amperes. In most DC electric circuits, it can be assumed that the resistance to current flow is a constant so that the current in the circuit is related to voltage and resistance by Ohm's law. The standard abbreviations for the units are 1 A = 1C/s.

- Potential energy can be defined as the capacity for doing work which arises from position or configuration. In the electrical case, a charge will exert a force on any other charge and potential energy arises from any collection of charges. For example, if a positive charge Q is fixed at some point in space, any other positive charge which is brought close to it will experience a repulsive force and will therefore have potential energy. The potential energy of a test charge q in the vicinity of this source charge will be: $U = \frac{\text{kQq}}{r}$ where k is Coulomb's constant. In electricity, it is usually more convenient to use the electric potential energy per unit charge, just called electric potential or voltage.

- Voltage is electric potential energy per unit charge, measured in joules per coulomb ( = volts). It is often referred to as "electric potential", which then must be distinguished from electric potential energy by noting that the "potential" is a "per-unit-charge" quantity. Like mechanical potential energy, the zero of potential can be chosen at any point, so the difference in voltage is the quantity which is physically meaningful. The difference in voltage measured when moving from point A to point B is equal to the work which would have to be done, per unit charge, against the electric field to move the charge from A to B.

INDEX OF REFRACTION FOR SOLIDS

- Refraction is the bending of a wave when it enters a medium where it's speed is different. The refraction of light when it passes from a fast medium to a slow medium bends the light ray toward the normal to the boundary between the two media. The amount of bending depends on the indices of refraction of the two media and is described quantitatively by Snell's Law. Refraction is responsible for image formation by lenses and the eye. As the speed of light is reduced in the slower medium, the wavelength is shortened proportionately. The frequency is unchanged; it is a characteristic of the source of the light and unaffected by medium changes.

- Snell's Law relates the indices of refraction n of the two media to the directions of propagation in terms of the angles to the normal. Snell's law can be derived from Fermat's Principle or from the Fresnel Equations. $\frac{n_{1}}{n_{2}} = \frac{\sin\theta_{2}}{\sin\theta_{1}}$

- In optics the refractive index or index of refraction n of a substance (optical medium) is a dimensionless number that describes how light, or any other radiation, propagates through that medium. It is defined as $n = \frac{c}{v}$ where c is the speed of light in vacuum and v is the speed of light in the substance. For example, the refractive index of water is 1.33, meaning that light travels 1.33 times as fast in vacuum as it does in water. (See typical values for different materials here.)

- When light is incident upon a medium of lesser index of refraction, the ray is bent away from the normal, so the exit angle is greater than the incident angle. Such reflection is commonly called "internal reflection". The exit angle will then approach 90° for some critical incident angle θc , and for incident angles greater than the critical angle there will be total internal reflection.

- The critical angle can be calculated from Snell's law by setting the refraction angle equal to 90°. Total internal reflection is important in fiber optics and is employed in polarizing prisms.

DIELECTRIC CONSTANT

- Electric field is defined as the electric force per unit charge. The direction of the field is taken to be the direction of the force it would exert on a positive test charge.

The electric field of a point charge can be obtained from Coulomb's law: $E = \frac{F}{q} = \frac{kQ_{\text{source}}}{qr^{2}} = \frac{kQ_{\text{source}}}{r^{2}}$

Capacitance is typified by a parallel plate arrangement and is defined in terms of charge storage: $C = \frac{Q}{V}$ [coulomb/volt = farad], where Q = magnitude of charge stored on each plate and V = voltage applied to the plates.

The capacitance of flat, parallel metallic plates of area A and separation d is given by the expression above where: ε₀ = 8.854187817.. × 10⁻¹² F/m is the vacuum permittivity and k = relative permittivity of the dielectric material between the plates. k=1 for free space, k>1 for all media, approximately =1 for air.

If a material contains polar molecules, they will generally be in random orientations when no electric field is applied. An applied electric field will polarize the material by orienting the dipole moments of polar molecules. This decreases the effective electric field between the plates and will increase the capacitance of the parallel plate structure. The dielectric must be a good electric insulator so as to minimize any DC leakage current through a capacitor.

In the equations describing electric and magnetic fields and their propagation, three constants are normally used. One is the speed of light c, and the other two are the electric permittivity of free space ε0 and the magnetic permeability of free space, μ0. The magnetic permeability of free space is taken to have the exact value:

µ₀ = 4π×10⁻⁷ H·m⁻¹≈ 1.2566370614…×10⁻⁶ H·m⁻¹ or N·A⁻²

Experimental measurements of the speed of light have been refined in progressively more accurate experiments since the seventeenth century. Recent experiments give a speed of c = 299,792,458 ± 1.2 m/s

The speed of light in a medium is related to the electric and magnetic properties of the medium, and the speed of light in vacuum can be expressed as $c = \frac{1}{\sqrt{\varepsilon_{0}\mu_{0}}}$ where ε₀= electric permittivity and μ₀ = magnetic permeability.

PHOTOELECTRIC EFFECT

The remarkable aspects of the photoelectric effect when it was first observed were:

1. The electrons were emitted immediately - no time lag!

2. Increasing the intensity of the light increased the number of photoelectrons, but not their maximum kinetic energy!

3. Red light will not cause the ejection of electrons, no matter what the intensity!

4. A weak violet light will eject only a few electrons, but their maximum kinetic energies are greater than those for intense light of longer wavelengths!

The details of the photoelectric effect were in direct contradiction to the expectations of very well developed classical physics. The explanation marked one of the major steps toward quantum theory.

Analysis of data from the photoelectric experiment showed that the energy of the ejected electrons was proportional to the frequency of the illuminating light. This showed that whatever was knocking the electrons out had an energy proportional to light frequency. The remarkable fact that the ejection energy was independent of the total energy of illumination showed that the interaction must be like that of a particle which gave all of its energy to the electron! This fit in well with Planck's hypothesis that light in the blackbody radiation experiment could exist only in discrete bundles with energy E = hν

- The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of action in quantum mechanics. The Planck constant was first described as the proportionality constant between the energy (E) of a photon and the frequency (ν) of its associated electromagnetic wave. This relation between the energy and frequency is called the Planck relation. Since the frequency , wavelength λ, and speed of light c are related by λν = c, the Planck relation for a photon can also be expressed as $E = \frac{\text{hc}}{\lambda}$ and the value of Planck constant is equal about 6.626 069 57 x 10^-34 Js.

- The minimum energy required to eject an electron from the surface is called the photoelectric work function. If the photon's energy is greater than the substance's work function, photoelectric emission occurs and the electron is liberated from the surface. Similar to the thermionic case described above, the liberated electrons can be extracted into a collector and produce a detectable current, if an electric field is applied into the surface of the emitter. Work function depends on the state of the surface of the substance, its impurities. The maximum kinetic energy of the electrons is measured by means of braking power, ie by measuring the voltage at which no liberated electron longer closes the circuit (current stops flowing). The work performed by electrical power, stopping the electron is equal to the kinetic energy that he had when released.

- A phototube or photelectric cell is a type of gas-filled or vacuum tube that is sensitive to light. Such a tube is more correctly called a 'photoemissive cell' to distinguish it from photovoltaic or photoconductive cells. One major application of the phototube was the reading of optical sound tracks for projected films. Phototubes were used in a variety of light-sensing applications until they were superseded by photoresistors and photodiodes. The first photocell was used as a sensor in the mechanism of automatic opening doors in 1931.

SEMICONDUCTOR DIODE current:

Classification of materials due to electric conductivity: Most substances fall into two categories - conductors and insulators.

Conductors are those which electricity can pass through relatively easily. Metals are the usual example, but other substances such as graphite and polar liquids such as water are also good conductors.

Insulators are poor conductors: those that electricity cannot pass through easily. Most plastics are insulators.

Some substances fall in between: these are semiconductors, which allow electricity through in some instances, but not in others. This property makes them very useful in electronics.

Some substances can be such good conductors that, under some circumstances, they can allow electricity to pass through them with no resistance at all. These are called superconductors.

What is a diode? – short definition

A diode is a semiconductor that allows current to flow in one direction only. This makes a diode suitable for changing AC to DC.

PL:

- Przewodnictwo domieszkowe - to rodzaj niesamoistnego przewodnictwa elektrycznego w półprzewodnikach wywołanego wprowadzeniem do sieci krystalicznej atomów obcych pierwiastków.

- Przewodnictwo niesamoistne - to przewodnictwo elektryczne w półprzewodnikach uwarunkowane występowaniem zakłóceń atomowych sieci krystalicznej.

- Donorem nazywamy domieszkę dostarczająca wolnych elektronów, otrzymany poprzez domieszkowanie przewodnik- przewodnikiem typu n (negative - ujemny), gdyż posiada nadmiar swobodnych elektronów. Domieszka mająca za mało elektronów nazywana jest akceptorem, a otrzymany półprzewodnik - półprzewodnikiem typu p (positive - dodatni).