Calculus › Section H · Applications of integrals › Topic H.6
Moments, centres of mass, and centroids
Balancing a see-saw is moments in disguise: mass times distance, added on both sides until the sums match. This topic turns balancing into calculus — moments for point masses, then for flat plates where the sums become integrals — and delivers the centre of mass, the centroid, and Pappus's volume theorem.
In this topic
- Balancing acts
- Moments along a line
- Worked example: two masses on a beam
- From a line to a plane
- Laminas: from sums to integrals
- Worked example: centroid under a parabola
- The symmetry principle
- Worked example: Pappus and the doughnut
- Centres of mass in the real world
- Common mistakes to avoid
- Key takeaways
This topic is part of Wuanberri Pro. Checking your access…
Standards: Beyond AP