Russia 9 класс Physics (advanced)

1. Mechanical phenomena

Describing motion · Vectors in mechanics · Straight-line motion · Projectile and circular motion · Newton's laws · Bernoulli's law · Gravitation · Statics · Momentum · Work and energy

• Motion: Distance, Speed, Velocity, Acceleration and Graphs – An object is in motion when its position changes with time. Distance is the full path length (a scalar); displacement is the straight gap from start to finish with a direction (a vector). Speed = distance ÷ time; velocity = displacement ÷ time. Acceleration = change in velocity ÷ time. The slope of an s–t graph gives velocity, the slope of a v–t graph gives acceleration, and the area under a v–t graph gives the distance. For uniform acceleration: v = u + at, s = ut + ½at², v² = u² + 2as.
• Scalars and Vectors for Motion in a Plane (Class 11) – A scalar has only size; a vector has size and direction. Vectors are equal if their size and direction match. Multiplying by a number changes the length (a negative number flips it). Vectors add tail-to-head (triangle or parallelogram law); A − B = A + (−B). Any vector in a plane is A = Ax î + Ay ĵ with Ax = A cos θ, Ay = A sin θ. A·B = AB cos θ is a scalar; A×B has size AB sin θ and is perpendicular to both.
• Projectile Motion and Uniform Circular Motion (Class 11) – In a plane, r = r₀ + v₀t + ½at² and v = v₀ + at, applied separately along x and y. A projectile has constant horizontal velocity u cos θ and a vertical velocity that changes by g each second, so its path is a parabola: y = x tan θ − gx²/(2u²cos²θ). T = 2u sin θ/g, H = u² sin²θ/2g, R = u² sin 2θ/g (maximum at 45°). In uniform circular motion speed is constant but the velocity turns, giving a centripetal acceleration a = v²/r = ω²r towards the centre.
• Force and Laws of Motion – A force is a push or a pull. Balanced forces (net force zero) do not change motion; an unbalanced force changes speed or direction. Friction opposes sliding. First law: a body keeps its state of rest or uniform motion unless an unbalanced force acts (inertia; heavier bodies have more inertia). Momentum p = mv. Second law: F = ma (rate of change of momentum), 1 N = 1 kg m/s². Third law: forces come in equal and opposite pairs acting on two different bodies. For a system with no outside force, internal forces cancel and total momentum is conserved.
• Viscosity, Stokes' Law and Bernoulli's Theorem – A moving fluid is like a stack of layers sliding over each other. The friction between layers is viscosity: F = ηA(dv/dx). A small ball falling through a fluid feels a drag F = 6πηrv (Stokes' law); when drag plus buoyancy balance the weight, it falls at a steady terminal velocity. Slow flow is streamline; above a critical velocity (Reynolds number about 2000) it becomes turbulent. For steady streamline flow, Av is constant (continuity) and P + ½ρv² + ρgh is constant (Bernoulli). So fast fluid has low pressure. This explains Torricelli's efflux speed √(2gh), the venturimeter, and the lift on wings and spinning balls.
• Newton's Universal Law of Gravitation – Every mass in the universe pulls every other mass. The pull between two point masses m₁ and m₂ a distance r apart is F = G m₁ m₂ / r². It acts along the line joining them. The two bodies pull each other with equal and opposite forces. G = 6.67 × 10⁻¹¹ N m² kg⁻² is the same everywhere, so it is called the universal gravitational constant. When many masses pull one body, the forces add as vectors (superposition).
• Torque, Angular Momentum and Equilibrium of Rigid Bodies – Torque is the turning effect of a force: τ = r × F, size rF sinθ, unit N m. Angular momentum is the turning version of momentum: L = r × p; for a body spinning about a fixed axis L = Iω. Torque changes angular momentum: τ = dL/dt. If the outside torque is zero, L stays constant, so pulling mass in makes a body spin faster. A rigid body is in equilibrium when the total force is zero (no sliding) and the total torque about any point is zero (no turning).
• Third Law, Conservation of Momentum and Equilibrium of Forces – Forces always come in pairs: if A pushes B, B pushes A with an equal and opposite force at the same instant (third law). The pair acts on different bodies. For a system with no net external force, the total linear momentum stays constant, which explains recoil, rockets and collisions. A particle is in equilibrium when all forces on it add to zero; three concurrent forces in equilibrium form a closed triangle.
• Work, Energy and Power – Work is done when a force moves an object: W = F × s, measured in joules (J). Energy is the ability to do work. A moving body has kinetic energy ½mv²; a raised body has potential energy mgh. Energy is never made or destroyed, only changed from one form to another. Power is how fast work is done: P = W ÷ t, in watts. Simple machines like levers and pulleys let a small effort move a big load.

2. Mechanical oscillations and waves

Oscillations · Mechanical waves · Sound

• Oscillations of a Spring and a Simple Pendulum – A block on a spring feels a pull back F = −kx, where k is the force constant (stiffness). It does SHM with T = 2π√(m/k). A simple pendulum, for small swings, feels a pull back mg sinθ ≈ mgθ and does SHM with T = 2π√(L/g). The pendulum’s period does not depend on the bob’s mass or (for small swings) on the amplitude.
• Sound – Sound is made by vibrating objects. It travels through a medium (air, water, solids) as a longitudinal wave: particles move back and forth, making crowded parts (compressions) and spread-out parts (rarefactions). Frequency (Hz) sets the pitch, amplitude sets the loudness, and speed v = f × λ. Sound cannot travel in vacuum. Humans hear 20 Hz to 20,000 Hz; below is infrasound, above is ultrasound. Reflected sound gives echoes, used and controlled in buildings.

3. Electromagnetic field and waves

Electromagnetic waves · Wave properties of light

• The Electromagnetic Spectrum – Electromagnetic (EM) waves are transverse waves of changing electric and magnetic fields. They need no medium and all travel at 3 × 10⁸ m/s in a vacuum. In order of falling wavelength (rising frequency and energy) they are radio, microwaves, infrared, visible light, ultraviolet, X-rays and gamma rays. Speed = frequency × wavelength (c = fλ). Each type has uses; the high-energy ones (UV, X-rays, gamma) are ionising and can harm living cells.
• Interference (Young's Double Slit) and Single Slit Diffraction – Two coherent sources (same frequency, fixed phase difference) make a steady pattern of bright and dark fringes. At a point on the screen the path difference is Δ = yd/D: bright where Δ = nλ, dark where Δ = (n + ½)λ. All fringes have equal width β = λD/d. A single slit of width a gives diffraction: a bright central maximum of width 2λD/a, with first minima where a sin θ = λ, and weaker side maxima.

4. Light phenomena

Reflection and mirrors · Refraction · Thin lens formula · Dispersion

• Reflection of Light: Plane and Spherical Mirrors – Light bounces off a shiny surface so that the angle of incidence equals the angle of reflection. A plane mirror gives a virtual, upright, same-size image as far behind as the object is in front. A concave mirror can give real or virtual images depending on where the object is; a convex mirror always gives a virtual, upright, smaller image. The mirror formula 1/v + 1/u = 1/f and magnification m = −v/u (with the New Cartesian sign convention) let you find the image without drawing.
• Refraction of Light: Laws, Refractive Index and the Glass Slab – Light changes speed when it goes from one transparent medium to another, and so it bends at the boundary (unless it hits along the normal). Going into an optically denser medium it slows down and bends toward the normal; coming out it speeds up and bends away. For a pair of media, sin i / sin r stays constant (Snell's law); this constant is the refractive index, which also equals the ratio of the speeds of light, n = c/v. In a rectangular glass slab the emergent ray is parallel to the incident ray but shifted sideways (lateral displacement).
• Spherical Lenses: Images, Lens Formula and Power – A convex lens is thick in the middle and bends parallel light to meet at its focus; a concave lens is thin in the middle and spreads light out as if from its focus. With two simple rays (one parallel to the axis, one through the optical centre) you can find the image for any object position. A convex lens gives real, inverted images when the object is beyond F₁ and a virtual, erect, enlarged image inside F₁; a concave lens always gives a virtual, erect, diminished image. The lens formula 1/v − 1/u = 1/f, magnification m = v/u and power P = 1/f (in metres, unit dioptre) let you solve lens numericals.
• Refraction Through a Prism, Dispersion of Light and the Rainbow – A glass prism bends light twice, both times towards its base; the total turn is the angle of deviation. Each colour in white light bends by a slightly different amount (violet most, red least), so a prism fans white light out into a spectrum, VIBGYOR. An upside-down second prism joins the colours back into white. Raindrops act like tiny prisms plus a mirror, which gives us the rainbow.

5. Quantum phenomena

Atom models and spectra · Radioactivity and protection · Nuclear reactions and energy

• Structure of the Atom – An atom has a tiny, heavy, positive nucleus made of protons and neutrons. Electrons move around it in fixed shells K, L, M, N. The number of protons (Z) tells the element; protons + neutrons give the mass number (A). Outer electrons decide valency. Isotopes share Z; isobars share A.
• Radioactivity: Alpha, Beta, Gamma and Half-Life – Some atomic nuclei are unstable. They give out radiation at random to become more stable. This is radioactive decay. Alpha (2 protons + 2 neutrons), beta (a fast electron) and gamma (a wave of energy) are the three main kinds. Half-life is the time for half of the unstable nuclei to decay.
• Nuclear Physics: the Nucleus and Radioactivity – The nucleus holds protons (Z) and neutrons (N); mass number A = Z + N. Isotopes have the same Z but different N. Unstable nuclei decay at random: alpha decay removes 2 protons and 2 neutrons (A − 4, Z − 2), beta-minus decay turns a neutron into a proton and an electron (Z + 1), and gamma is energy only. Half-life is the time for half the nuclei in a sample to decay.

6. Review practicum

Problem solving, labs and projects

Coming soon