The Average That Outvotes the Middle

You'll learnto locate a system's center of mass as a mass-weighted average of positions.

Three masses on a rail, one balance point that snubs the midpoint. Weight the average, watch internal wiggles fail to move it — then let the sum become an integral, and catch a non-uniform rod pulling the same trick in continuous form.

8 STEPS · 6 QUICK CHECKS · v3

SYSTEMS · COM LAB

Before you start

What you're looking at

Three point masses on a rail — 1 kg at x = 0, 1 kg at 3 m, 4 kg at 9 m — with a hollow diamond at the 4.5 m midpoint.

The question

Where is the single balance point that stands in for the whole system — its center of mass?

Watch for

The midpoint marker losing; the balance point dragged toward the heavy 4 kg, since it holds most of the mass.

What the symbols mean

Teal star = center of mass; hollow diamond = geometric midpoint; the x-axis reads positions in meters.

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