Explicit physics instruction
A complete rotational-kinematics explanation connects angular variables, radius, graph evidence, and model assumptions.
Use the Friday synthesis to select the correct relationship rather than treating angular and linear variables as interchangeable.
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
A point at twice the radius shares the same ω but has twice v; this is the key transfer from angular to linear description.
Guided question
Build a representation chain from θ(t) to ω to v for one rotating point.
Independent work
- Solve three angular-motion calculations.
- Draw or interpret one rotational graph.
- State one model assumption or limitation.
Spiral retrieval bridge
- From Week 17: why can one system be described with several valid models?
- From Week 16: distinguish momentum conservation from kinetic-energy conservation.
- From Week 08: what direction does centripetal acceleration point?
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.