Japan 高校2年 Physics (part 1)
Chapters: 2
1. Various motions
Motion in a plane and rigid-body equilibrium · Momentum · Circular motion and simple harmonic motion · Universal gravitation · Motion of gas molecules
- 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.
- 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.
- Simple Harmonic Motion (SHM) – A motion that repeats after a fixed time is periodic. If the object goes to and fro about a middle point and the force pulling it back is proportional to its distance from the middle (F = −kx), the motion is simple harmonic. Its position is x = A sin(ωt + φ), with ω = 2π/T = 2πf. Speed is largest in the middle, acceleration is largest at the ends, and total energy ½kA² stays constant.
- 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).
- Kinetic Theory of Gases: Pressure, Temperature and rms Speed – Kinetic theory explains gas behaviour by picturing a gas as tiny, fast, randomly moving molecules that bounce elastically and do not pull on each other. Each hit on a wall reverses the molecule's velocity and hands the wall momentum 2mvₓ. Adding the hits of all molecules gives the pressure P = ⅓ n m v̄² = ⅓ ρ v̄². Comparing with PV = N k T shows that the average kinetic energy of a molecule is (3/2) k T: temperature is a measure of the average kinetic energy of the molecules. The root mean square speed is v_rms = √(3RT/M) = √(3kT/m), so lighter gases move faster at the same temperature.
2. Waves
Wave propagation · Sound · Light
- Progressive Waves: Types, Speed and Equation – A wave carries energy from place to place without carrying the matter along. In a transverse wave the particles move at right angles to the wave; in a longitudinal wave they move along it. Speed v = fλ. On a string v = √(T/μ); for sound in a gas v = √(γP/ρ). A wave moving along +x is y = A sin(kx − ωt), with k = 2π/λ and ω = 2πf.
- Superposition, Reflection and Standing Waves – When waves overlap, their displacements add (superposition). A wave reflected from a fixed end comes back upside down; from a free end it comes back upright. A wave and its reflection make a standing wave with nodes (no motion) and antinodes (most motion). A string fixed at both ends allows fₙ = n·v/2L (all harmonics). An open pipe allows fₙ = n·v/2L; a pipe closed at one end allows only odd harmonics, fₙ = n·v/4L (n = 1, 3, 5…).
- 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).