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Classical Mechanics

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Classical Mechanics

Period

The time duration required to complete one full cycle of a recurring motion or oscillation.

T = 1 / f = 2π / ω = 2π √(m/k) s
Classical Mechanics

Perpendicular Axis Theorem

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…

Iz = Ix + Iy kg·m²
Classical Mechanics

Potential Energy

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 J
Classical Mechanics

Power

The rate at which work is performed or energy is transferred per unit time.

P = dW/dt = F · v W (J/s)
Classical Mechanics

Projectile Motion

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 m, m/s
Classical Mechanics

Radius of Gyration

The radial distance from a rotation axis at which total mass could be concentrated without altering the moment of inertia.

k = √(I / m) m
Classical Mechanics

Range

The total horizontal distance traveled by a projectile from launch to landing at the same vertical height.

R = (v0² sin 2θ) / g m
Classical Mechanics

Restoring Force

A force that acts to bring a body back toward its stable equilibrium position whenever it is displaced.

F = -k x N
Classical Mechanics

Reynolds Number

A dimensionless quantity in fluid mechanics predicting flow patterns, equal to ratio of inertial forces to viscous forces.

Re = (ρ v L) / η Dimensionless
Classical Mechanics

Rotational Kinetic Energy

The kinetic energy possessed by a body due to its rotation about an axis.

KE_rot = ½ I ω² J
Classical Mechanics

Simple Harmonic Motion

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) m, rad/s
Classical Mechanics

Simple Machine

A basic mechanical device that changes the direction or magnitude of an applied force.

MA = F_out / F_in Dimensionless
Classical Mechanics

Static Equilibrium

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 N, N·m
Classical Mechanics

Stokes' Law

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 N
Classical Mechanics

Tension

The pulling force transmitted axially through a string, rope, cable, or structural member.

T = m g + m a N
Classical Mechanics

Terminal Velocity

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)) m/s
Classical Mechanics

Time of Flight

The total duration a projectile spends in the air from launch until returning to its landing elevation.

T = (2 v0 sin θ) / g s
Classical Mechanics

Torque

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 N·m
Classical Mechanics

Velocity

A vector quantity expressing the time rate of change of position, possessing both speed and direction.

v = dr/dt m/s
Classical Mechanics

Viscosity

A measure of a fluid's internal resistance to gradual deformation by shear or tensile stress.

τ = η (dv/dy) Pa·s (kg/(m·s))
Classical Mechanics

Work

The scalar energy transferred to or from an object by a force acting through a displacement.

W = F · d = |F| |d| cos θ J (N·m)
Classical Mechanics

Work-Energy Theorem

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 J