Classical Mechanics — 70 Terms Defined

Period Classical Mechanics s The time duration required to complete one full cycle of a recurring motion or oscillation. T = 1 / f = 2π / ω = 2π √(m/k)

Perpendicular Axis Theorem Classical Mechanics kg·m² A theorem stating that for a thin planar lamina, the moment of inertia about an axis perpendicular to the plane equals the sum of moments of inertia about two perpendicular axes in the plane. Iz = Ix + Iy

Potential Energy Classical Mechanics J The stored energy an object possesses due to its relative position in a conservative force field or its structural deformation. PE_grav = m g h, PE_elastic = ½ k x²

Power Classical Mechanics W (J/s) The rate at which work is performed or energy is transferred per unit time. P = dW/dt = F · v

Projectile Motion Classical Mechanics m, m/s The 2D motion of an object launched into a gravitational field under the sole influence of gravity (ignoring air resistance). x(t) = v0 cos θ t, y(t) = v0 sin θ t - ½ g t²

Radius of Gyration Classical Mechanics m The radial distance from a rotation axis at which total mass could be concentrated without altering the moment of inertia. k = √(I / m)

Range Classical Mechanics m The total horizontal distance traveled by a projectile from launch to landing at the same vertical height. R = (v0² sin 2θ) / g

Restoring Force Classical Mechanics N A force that acts to bring a body back toward its stable equilibrium position whenever it is displaced. F = -k x

Reynolds Number Classical Mechanics Dimensionless A dimensionless quantity in fluid mechanics predicting flow patterns, equal to ratio of inertial forces to viscous forces. Re = (ρ v L) / η

Rotational Kinetic Energy Classical Mechanics J The kinetic energy possessed by a body due to its rotation about an axis. KE_rot = ½ I ω²

Simple Harmonic Motion Classical Mechanics m, rad/s Repetitive periodic motion where restoring force is directly proportional to displacement and acts toward the equilibrium position. x(t) = A cos(ω t + φ), ω = √(k/m)

Simple Machine Classical Mechanics Dimensionless A basic mechanical device that changes the direction or magnitude of an applied force. MA = F_out / F_in

Static Equilibrium Classical Mechanics N, N·m The state of a rigid body where both net external force and net external torque are zero, keeping the body completely at rest. ∑ F = 0, ∑ τ = 0

Stokes' Law Classical Mechanics N A mathematical law expressing viscous drag force experienced by small spherical particles moving at low speeds through a viscous fluid. Fd = 6 π η r v

Tension Classical Mechanics N The pulling force transmitted axially through a string, rope, cable, or structural member. T = m g + m a

Terminal Velocity Classical Mechanics m/s The constant maximum speed attained by a falling body when upward aerodynamic drag equals downward gravitational force. v_t = √(2 m g / (ρ A Cd))

Time of Flight Classical Mechanics s The total duration a projectile spends in the air from launch until returning to its landing elevation. T = (2 v0 sin θ) / g

Torque Classical Mechanics N·m The rotational equivalent of linear force, measuring the effectiveness of a force in causing angular acceleration about an axis. τ = r × F = r F sin θ

Velocity Classical Mechanics m/s A vector quantity expressing the time rate of change of position, possessing both speed and direction. v = dr/dt

Viscosity Classical Mechanics Pa·s (kg/(m·s)) A measure of a fluid's internal resistance to gradual deformation by shear or tensile stress. τ = η (dv/dy)

Work Classical Mechanics J (N·m) The scalar energy transferred to or from an object by a force acting through a displacement. W = F · d = |F| |d| cos θ

Work-Energy Theorem Classical Mechanics J The principle stating that net work done by all forces acting on an object equals the net change in its kinetic energy. W_net = ΔKE = ½ m vf² - ½ m vi²