Moments, Couples & Metre Rule
Principle of Moments, torque of a couple, centre of gravity, equilibrium of rigid bodies, and determining mass of a metre rule on a knife-edge.
Marking a lesson complete represents finishing your study of the topic; it does not denote tested mastery.
Learning Objectives
- State and apply the Principle of Moments to rigid levers, beams, and knife-edge balances.
- Determine the mass and centre of gravity of a metre rule experimentally using unknown and known counterweights.
Core Theory & Concepts
For an extended rigid body to remain in equilibrium, not only must linear forces sum to zero, but the rotational turning effects (moments) about any axis must also completely cancel out.
Principle of Moments
In rotational equilibrium, the sum of clockwise moments about any pivot equals the sum of anti-clockwise moments about that same pivot: Στ = 0.
Metre Rule Mass Determination
Balancing a uniform metre rule off-center on a fulcrum at x_f with mass m_1 at x_1: m_1 · (x_f - x_1) = M_rule · (x_G - x_f) where x_G ≈ 50.0 cm.
Common Misconceptions
Forgetting that the weight of the metre rule itself exerts a moment when the fulcrum is not at 50 cm.
Syllabus Topic Outline
- 1Moment of a force: τ = F × perpendicular distance d
- 2Torque of a couple: τ = F × arm distance
- 3Principle of Moments: Στ_clockwise = Στ_anticlockwise
- 4Laboratory practical: determination of metre rule mass