Rotational & Orbital Mechanics — Core Vocabulary

16 vocabulary flashcards summarizing the essential equations and definitions for rotational motion, torque, angular momentum, and gravitation.

Centripetal Force (F_c)

The inward force required to keep an object moving in a circle; F_c = m v² / r.

Centripetal Acceleration (a_c)

Radial acceleration toward the center of a circular path; a_c = v² / r = r ω².

Tangential Acceleration (a_t)

Linear acceleration due to a change in angular speed; a_t = r α.

Total Linear Acceleration (a)

Combined effect of tangential and centripetal components; a = √(at² + ac²).

Angular Velocity (ω)

Rate of change of angular displacement; measured in rad s⁻¹.

Angular Acceleration (α)

Rate of change of angular velocity; α = dω/dt = Δω/Δt.

Torque (τ)

Rotational equivalent of force; τ = I α = F r sin θ.

Moment of Inertia (I)

Rotational mass; resistance to angular acceleration, depends on mass distribution.

Angular Momentum (L)

Rotational analogue of linear momentum; L = r × p = I ω.

Rotational Kinetic Energy (K_R)

Energy due to rotation; K_R = ½ I ω².

Newton’s Law of Gravitation

Attractive force between masses; F = G m₁ m₂ / r².

Acceleration Due to Gravity (g)

Gravitational field strength; g = G M / r² near a spherical mass.

Orbital Speed (v_orbit)

Velocity needed for circular orbit; v = √(G M / r) = 2πr / T.

Linear Velocity in Rotation (v)

Speed of a point on a rotating body; v = r ω.

Center-of-Mass Velocity (v_cm)

Linear speed of a rolling object’s center; v_cm = r ω for pure rolling without slipping.

Gravitational Constant (G)

Universal constant in Newton’s law; G ≈ 6.674 × 10⁻¹¹ N m² kg⁻².