Center of Mass — Balancing a Multi-Mass Beam

Statics starts with one deceptively simple question: where is the center of mass of a body made of several parts? This simulator makes that question concrete — attach point masses anywhere along a rigid 3D beam, drag them to new positions or masses, and watch the center of mass x̄ = Σmᵢxᵢ / Σmᵢ recompute live. Then move a pivot support under the beam and release it: real rotational dynamics take over, computing the moment of inertia about the pivot and the net gravitational torque every frame, and integrating angular acceleration α = τ/I forward in time. Line the pivot up exactly under the computed center of mass and the beam settles into equilibrium; miss it, even slightly, and the beam swings and tumbles — a live demonstration of why the center of mass is the one point where a composite rigid body can always be balanced.