Forces and Dynamics covers Newton\'s laws of motion, momentum and its conservation, and the equilibrium of forces — the core mechanics that describe how and why objects move.
First law: body stays at rest or constant velocity unless acted on by resultant force. Second law: F = Δp/Δt = ma (for constant mass). Third law: equal and opposite force pairs (same type, different bodies). Momentum p = mv (kg m/s). Impulse = FΔt = Δp. Conservation of momentum: total momentum before = after (in isolated system). Elastic collision: KE conserved. Inelastic: KE not conserved (some → heat/sound). Perfectly inelastic: objects stick together.
Density ρ = m/V (kg/m³). Pressure p = F/A (Pa). Hydrostatic pressure: p = ρgh (pressure increases with depth). Upthrust (Archimedes): upward force on object in fluid = weight of fluid displaced. Object floats when upthrust ≥ weight. Applications: hydraulic systems (pressure transmitted equally), barometers, manometers.
Translational equilibrium: resultant force = 0. Rotational equilibrium: resultant moment about any point = 0. Moment = force × perpendicular distance from pivot. Couple: two equal opposite parallel forces → torque = Fd (where d is distance between forces). Centre of gravity: point where entire weight acts. For uniform objects: at geometric centre. Triangle of forces: three forces in equilibrium form a closed triangle.
Mass (kg) is the quantity of matter in an object — it is a scalar and does not change with location. Weight (N) is the gravitational force on an object: W = mg, where g is the gravitational field strength. Weight is a vector (directed towards the centre of the gravitational body). An astronaut on the Moon has the same mass as on Earth but less weight (g_Moon ≈ 1.6 N/kg vs g_Earth ≈ 9.81 N/kg). In free fall, an object has weight but appears "weightless" because there is no contact force (normal reaction) — this is why astronauts in the ISS float despite being only ~10% lighter than on Earth\'s surface.
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