When analyzing an object undergoing circular motion, traditional linear quantities quickly run into limitations.

Consider displacement, which is defined as the straight-line separation between an object's initial and final positions. If an object completes one full revolution around a circular path:

• Its net linear displacement is zero (because it returns to its starting point).
• Consequently, its average linear velocity over one full turn is also zero.

To describe rotational motion meaningfully, we need a framework that tracks the angle swept out over time rather than linear position alone. This lesson introduces angular displacement (θ) and angular velocity (ω). Watch the video below to explore how these rotational quantities are defined and calculated.

Going Further

We can now extend this framework by examining angular acceleration (α), which is defined as the rate of change of angular velocity over time (α = Δω / Δt).

Important Distinction: Do not confuse angular acceleration with centripetal acceleration:

• Centripetal Acceleration (a_c): Points radially inward toward the center of circular motion (perpendicular to linear velocity), continuously altering the direction of motion.
• Angular Acceleration (α): Acts along the axis of rotation (parallel to angular velocity), changing the rate of spin.

Using these rotational variables (θ, ω, α, and t), we can establish the rotational equations of motion, directly analogous to standard linear kinematics.