Explicit physics instruction
This investigation compares modeled or measured rolling behavior across shapes.
Use a ramp/rolling simulation or safe lightweight objects. Compare arrival times or modeled energy partitions for shapes with different moments of inertia.
Preserve raw time/height data and calculated energy terms before interpreting differences.
Core relations: K_total=½Mv²+½Iω² and v=rω.
Worked example
If two shapes descend the same height, compare mgh with ½Mv²+½Iω² and calculate a residual for each.
Guided question
Which measurements are necessary to test rolling-energy conservation?
Independent work
- Solve three rotational-energy or rolling calculations.
- Draw an energy bar chart.
- State one condition where v=rω fails.
Investigation / Data Lab
Use a ramp/rolling simulation or safe lightweight objects. Compare arrival times or modeled energy partitions for shapes with different moments of inertia.
Evidence record: raw data, energy calculations, residuals, uncertainty, and revision.
Misconception check
Rolling does not mean all kinetic energy is translational; rotation stores part of the total.
Formative check
What extra energy term must be included for a rolling object?
Reveal response
Rotational kinetic energy ½Iω².
Mentor evidence conference
Ask Archaemenes to audit rolling constraints, moment-of-inertia reasoning, and energy accounting.
Teacher guidance
Foundation: Calculate K_rot and v=rω.
Core: Combine translational and rotational energy.
Extended: Compare shapes using I and conservation residuals.