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Classical Mechanics

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Centripetal Acceleration Classical Mechanics m/s² The inward acceleration of an object moving in a circular path, directed toward the center of curvature. ac = v² / r = ω² r Centripetal Force Classical Mechanics N The net inward force directed toward the center of curvature that keeps an object moving along a curved or circular path. Fc = m v² / r = m ω² r Circular Motion Classical Mechanics m/s, rad/s The movement of an object along the circumference of a circular path or orbit. v = ω r, ac = v² / r Coefficient of Restitution Classical Mechanics Dimensionless (0 to 1) A fractional measure of elasticity in a collision, defined as ratio of relative separation speed to relative approach speed. e = (v2_f - v1_f) / (v1_i - v2_i) Completely Inelastic Collision Classical Mechanics kg·m/s, m/s A collision in which colliding bodies stick together after impact, moving as a single combined mass with maximum kinetic energy loss. m1 v1 + m2 v2 = (m1 + m2) Vf Conservation of Linear Momentum Classical Mechanics kg·m/s The law stating that total linear momentum of an isolated system remains constant if no net external force acts on it. ∑ p_initial = ∑ p_final Conservative Force Classical Mechanics N A force for which total work done in moving an object between two points is independent of the path taken. ∮ F · dr = 0, F = -∇ PE Continuity Equation Classical Mechanics m³/s The equation expressing conservation of mass for fluid flow through a pipe or conduit. A1 v1 = A2 v2 = constant (Volumetric Flow Rate Q) Couple Classical Mechanics N·m A system of two equal, parallel forces acting in opposite directions whose lines of action do not coincide, producing pure torque without net linear force. τ = F d