Unit 5 · 5.1 — Rotational Kinematics

15 learning items · ~2% exam weight (unit share)

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Concept: Rotational kinematics mirrors linear kinematics; displacement, velocity, and acceleration are replaced by their angular counterparts.
Concept: All points on a rigid system share the exact same angular displacement, angular velocity, and angular acceleration, regardless of their radial distance from the axis.
Equation: $Δ θ = \frac{s}{r} (Angular Displacement in radians)$
Equation: $o m e g a_{a v g} = Δ θ /Δ t (Average Angular Velocity)$
Equation: $a l p h a_{a v g} = Δ ω /Δ t (Average Angular Acceleration)$
Equation: $ω = o m e g a 0 + α \cdot t (Rotational Kinematic Equation 1)$
Equation: $θ = t h e t a 0 + o m e g a 0 \cdot t + 0.5 \cdot α \cdot t^{2} (Rotational Kinematic Equation 2)$
Equation: $ω^{2} = o m e g a 0^{2} + 2 \cdot α \cdot Δ θ (Rotational Kinematic Equation 3)$
Vocabulary: Rigid System — An object that holds its shape, allowing all points to rotate around an axis simultaneously with identical angular speeds.
Vocabulary: Angular Velocity (omega) — The rate of change of angular position, strictly measured in radians per second (rad/s).
Vocabulary: Angular Acceleration (alpha) — The rate of change of angular velocity, measured in rad/s^2.
Skill: Mathematical Routines — Converting revolution or degree measurements into radians prior to applying rotational kinematic equations to prevent scaling errors.
Skill: Translation Between Representations — Matching a graph of angular position (theta) vs. time to its corresponding angular velocity (omega) vs. time graph by evaluating slopes.
Skill: Use angular displacement, velocity, and acceleration to describe the clockwise or counterclockwise rotation of a system over time.
Vocabulary: Vocabulary: Angular displacement — The angle in radians through which a point on a rigid system rotates about a specified axis.

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