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Classical Mechanics

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Classical Mechanics

Acceleration

The vector rate of change of velocity with respect to time.

a = dv/dt = d²r/dt² m/s²
Classical Mechanics

Amplitude

The maximum magnitude of displacement from the equilibrium position in an oscillating or wave system.

A = x_max m
Classical Mechanics

Angular Acceleration

The rate of change of angular velocity with respect to time.

α = dω/dt = τ / I rad/s²
Classical Mechanics

Angular Displacement

The angle through which a point or line rotates about a specified axis in a specified direction.

θ = s / r rad (radians)
Classical Mechanics

Angular Momentum

The rotational analog of linear momentum, defined as the product of moment of inertia and angular velocity.

L = I ω = r × p kg·m²/s (J·s)
Classical Mechanics

Angular Velocity

The vector rate of change of angular displacement with respect to time.

ω = dθ/dt rad/s
Classical Mechanics

Apparent Weight

The effective weight of a body, equal to the normal contact force supporting it in an accelerating frame.

W_app = m (g + a) N
Classical Mechanics

Archimedes' Principle

The principle stating that any object fully or partially submerged in a fluid experiences an upward buoyant force equal to the weight of…

Fb = m_fluid g = ρ_fluid V_displaced g N
Classical Mechanics

Bernoulli's Principle

The principle in fluid dynamics stating that an increase in fluid speed occurs simultaneously with a decrease in static pressure or…

P + ½ ρ v² + ρ g h = constant Pa
Classical Mechanics

Buoyancy

The net upward fluid force exerted on an object immersed in a fluid due to pressure difference between top and bottom.

Fb = ρ_fluid V_submerged g N
Classical Mechanics

Centripetal Acceleration

The inward acceleration of an object moving in a circular path, directed toward the center of curvature.

ac = v² / r = ω² r m/s²
Classical Mechanics

Centripetal Force

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 N
Classical Mechanics

Circular Motion

The movement of an object along the circumference of a circular path or orbit.

v = ω r, ac = v² / r m/s, rad/s
Classical Mechanics

Coefficient of Restitution

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) Dimensionless (0 to 1)
Classical Mechanics

Completely Inelastic Collision

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 kg·m/s, m/s
Classical Mechanics

Conservation of Linear Momentum

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 kg·m/s
Classical Mechanics

Conservative Force

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 N
Classical Mechanics

Continuity Equation

The equation expressing conservation of mass for fluid flow through a pipe or conduit.

A1 v1 = A2 v2 = constant (Volumetric Flow Rate Q) m³/s
Classical Mechanics

Couple

A system of two equal, parallel forces acting in opposite directions whose lines of action do not coincide, producing pure torque without…

τ = F d N·m
Classical Mechanics

Drag Force

The fluid resistance force opposing the motion of an object moving through a liquid or gas.

Fd = ½ ρ v² Cd A N
Classical Mechanics

Dynamic Equilibrium

The state of a physical system moving at constant linear velocity and constant angular velocity with zero net force and zero net torque.

∑ F = 0 (v = const ≠ 0), ∑ τ = 0 (ω = const) N, N·m
Classical Mechanics

Efficiency

The ratio of useful work output to total energy input for a machine or system.

η = (W_output / E_input) × 100% %
Classical Mechanics

Elastic Collision

A collision between bodies in which both total linear momentum and total kinetic energy are conserved.

∑ p_i = ∑ p_f, ∑ KE_i = ∑ KE_f kg·m/s, J
Classical Mechanics

Elasticity

The mechanical property of a material to deform under applied stress and return to its original shape when stress is removed.

Stress / Strain = Elastic Modulus (E) Pa (N/m²)