Explicit physics instruction
Use τ=rF⊥ and Στ=0 in rotational equilibrium. Assign clockwise and counterclockwise torques opposite signs, then solve the balance equation.
A 20 N perpendicular force applied 0.50 m from a hinge produces 10 N·m of torque. The same force at 0.25 m produces only 5 N·m.
Check the physical direction of each torque before substituting numbers.
Core relation: τ=rF⊥ and Στ=0 in rotational equilibrium.
Worked example
A 20 N perpendicular force applied 0.50 m from a hinge produces 10 N·m of torque. The same force at 0.25 m produces only 5 N·m.
Guided question
A 12 N force acts 0.30 m left of a pivot. Where should a 6 N opposing force act to balance it?
Independent work
- Solve three torque or balance cases.
- Draw a pivot/lever-arm diagram.
- State one assumption or uncertainty.
Misconception check
A larger force does not always produce larger torque; lever arm and force direction matter.
Formative check
What two geometric features determine torque besides force magnitude?
Reveal response
Distance from the pivot and the force’s perpendicular component/direction.
Mentor evidence conference
Ask Archaemenes to audit pivot choice, torque signs, lever arms, and equilibrium assumptions.
Teacher guidance
Foundation: Calculate perpendicular torque.
Core: Solve multi-torque equilibrium.
Extended: Analyze stability and uncertainty in a lever model.