Explicit physics instruction
Angular-position versus time slope is angular velocity; angular-velocity versus time slope is angular acceleration.
A constant angular velocity produces a linear θ(t) graph, while constant angular acceleration produces a changing ω(t).
Same angular speed does not mean same linear speed for points at different radii.
Core relations: s=rθ; v=rω; a_t=rα.
Worked example
If ω rises from 2 to 8 rad/s in 3 s, α=(8−2)/3=2 rad/s².
Guided question
What does the slope of an ω–t graph represent, and what units must it have?
Independent work
- Solve three angular-motion calculations.
- Draw or interpret one rotational graph.
- State one model assumption or limitation.
Misconception check
Same angular speed does not mean same linear speed for points at different radii.
Formative check
What quantity must be known, in addition to ω, to determine a point’s linear speed?
Reveal response
Its distance r from the rotation axis.
Mentor evidence conference
Ask Archaemenes to audit radians, graph interpretation, radius dependence, and unit consistency.
Teacher guidance
Foundation: Identify θ, ω, α and use one-step relations.
Core: Connect angular graphs with linear speed.
Extended: Analyze residuals and compare points at multiple radii.