Topic 6 connects mechanics to circular and gravitational motion. Students learn to analyse objects moving in circles and apply Newton\'s law of universal gravitation to orbital problems.
Speed is constant but direction changes continuously → velocity is changing → there is acceleration. Centripetal (centre-seeking) acceleration: a = v²/r = ω²r. Centripetal force: F = mv²/r = mω²r. The centripetal force is not a new force — it is provided by tension, gravity, friction, normal force, etc. Period T = 2πr/v = 2π/ω.
F = GMm/r² where G = 6.67 × 10⁻¹¹ N·m²·kg⁻². The force is attractive, acts along the line joining the centres, and follows an inverse-square law. Gravitational field strength: g = F/m = GM/r² (N/kg or m/s²). At Earth\'s surface: g ≈ 9.81 m/s². g decreases with altitude.
For a satellite in circular orbit, gravity provides the centripetal force: GMm/r² = mv²/r → v = √(GM/r). Orbital period: T = 2πr/v. Kepler\'s third law: T² ∝ r³. Geostationary orbit: T = 24 hours, r ≈ 42,200 km, equatorial plane. Weightlessness in orbit: the satellite and occupants are in free fall together.
Astronauts appear weightless not because gravity is zero (at 400 km altitude, g ≈ 8.7 m/s² — only about 11% less than on Earth). They float because the ISS and everything inside it are in free fall — all falling towards Earth at the same rate. This creates apparent weightlessness, similar to the feeling in a free-falling lift. The ISS doesn\'t crash because its horizontal velocity keeps it continually falling around the curvature of Earth.
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