angular displacement

Meaning: Angular displacement is the net change in the angular position of a rotating object, the rotational counterpart of linear displacement. Turning back and forth cancels, so only the net turn counts. One full revolution is 2π rad (360°). Every point on a rigid rotating body has the same Δθ in the same time, but points farther from the axis travel a greater arc length.

Equation: s = rΔθ, where s is arc length traveled by a point (m), r is its distance from the axis (m), and Δθ is angular displacement (rad). Δθ itself is θf − θi (rad).

On the MCAT: Passages describe wheels, gears, pulleys, centrifuges or spinning disks. You may convert revolutions to radians (1 rev = 2π rad), find the arc length a point on the rim travels, or use the rotational kinematics equations, which mirror the linear ones: Δθ = ωt for constant angular velocity ω (rad/s) over time t (s), and Δθ = ω₀t + ½αt² for constant angular acceleration α (rad/s²). Expect to compare two points at different radii: same Δθ and ω, but larger s and linear speed farther out.

Common confusion: Students plug degrees into s = rΔθ. The relation holds only for radians, since a radian is defined as arc length divided by radius. Also, one full turn gives Δθ = 2π rad, not zero, unlike linear displacement for a round trip.