Unit 5 · Torque and Rotational Dynamics

Angular displacement ● (core concept) — The angle, measured in radians, through which a point on a rigid system rotates about an axis. One rotational direction is taken as positive and the other as negative.

Rigid system ● (core concept) — A system that keeps its shape during rotation. Because different parts move in different directions, a rotating rigid system cannot be modeled as a single point particle.

Average angular velocity ● (core concept) — The rate of change of angular position: ω_avg = Δθ/Δt.

Average angular acceleration ● (core concept) — The rate of change of angular velocity: α_avg = Δω/Δt.

Rotational kinematic equations ● (core concept) — For constant angular acceleration: ω = ω_0 + α·t; θ = θ_0 + ω_0·t + ½·α·t²; ω² = ω_0² + 2·α·(θ − θ_0) — the angular analogs of the linear kinematic equations.

Angular motion graphs ● (core concept) — Angular displacement, angular velocity, and angular acceleration graphs relate by slope and area exactly as their linear counterparts do.

Tangential linear quantities ● (core concept) — For a point at distance r from a fixed axis: distance traveled s = r·θ, tangential speed v = r·ω, tangential acceleration a_t = r·α.

Rigid-body rotation ● (core concept) — Every point in a rigid rotating system shares the same angular velocity and angular acceleration.

Torque ● (core concept) — The rotational effect of a force: τ = r·F·sinθ, where θ is the angle between the position vector and the force. Only the force component perpendicular to the position vector contributes to the torque.

Lever arm ● (core concept) — The perpendicular distance from the axis of rotation to the force's line of action.

Force diagram ○ — A diagram used for rotational analysis that, like a free-body diagram, shows the forces on a system but also indicates where each force is applied relative to the axis of rotation.

Rotational inertia ● (core concept) — A system's resistance to changes in its rotation, determined by its mass and how that mass is distributed about the axis: for a point mass, I = m·r²; for a collection of objects, the individual rotational inertias add. AP Physics 1 expects students to calculate rotational inertia only for systems of five or fewer objects in a two-dimensional arrangement; rotational inertias of extended rigid systems are provided on the exam.

Parallel axis theorem ● (core concept) — Relates rotational inertia about any axis to the rotational inertia about a parallel axis through the center of mass: I = I_cm + M·d².

Rotational equilibrium ● (core concept) — A torque configuration in which the net torque on a system is zero, so its angular velocity stays constant. A system can be in rotational equilibrium without being in translational equilibrium, and vice versa.

Newton's first law (rotational form) ● (core concept) — A system's angular velocity remains constant if and only if the net torque exerted on it is zero.

Newton's second law (rotational form) ● (core concept) — An unbalanced torque changes a system's angular velocity: the angular acceleration is directly proportional to the net torque (in the same rotational direction) and inversely proportional to the rotational inertia (τ_net = I·α).