Explicit physics instruction
Angular position describes orientation; angular velocity ω=Δθ/Δt and angular acceleration α=Δω/Δt describe rotational change.
Points on a rigid body share angular displacement, angular velocity, and angular acceleration, but their linear distance, speed, and tangential acceleration depend on radius.
The bridge between angular and linear motion is s=rθ and v=rω when θ is measured in radians.
Core relations: s=rθ; v=rω; a_t=rα.
Worked example
A wheel turns through 3.0 rad in 0.50 s, so average angular velocity is 6.0 rad/s.
Guided question
A disk rotates 4.0 rad in 2.0 s. Find average angular velocity.
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.