Explicit physics instruction
Objects with the same mass and radius can have different moments of inertia because mass distribution differs.
A larger I allocates more of the same total energy to rotation, which can reduce translational speed after descending the same height.
This explains why shape can affect rolling motion without violating energy conservation.
Core relations: K_total=½Mv²+½Iω² and v=rω.
Worked example
Two objects have equal M and r but different I. The one with larger I generally has more rotational KE at the same ω and may roll down a ramp more slowly under equal energy input.
Guided question
Why can a ring and solid disk of equal mass/radius reach the bottom with different speeds?
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.