Explicit physics instruction
A rolling object can have translational kinetic energy ½Mv² and rotational kinetic energy ½Iω² at the same time.
For rolling without slipping, v=rω links translation and rotation. The moment of inertia determines how much energy is stored in rotation for a given mass and speed.
Energy conservation can compare gravitational potential energy with translational and rotational kinetic energy when losses are negligible.
Core relations: K_total=½Mv²+½Iω² and v=rω.
Worked example
For a rolling body with M=2 kg, v=3 m/s, I=0.50 kg·m², and ω=6 rad/s, K_trans=9 J and K_rot=9 J, so total KE=18 J.
Guided question
Calculate rotational KE for I=0.8 kg·m² and ω=5 rad/s.
Independent work
- Solve three rotational-energy or rolling calculations.
- Draw an energy bar chart.
- State one condition where v=rω fails.
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.