Investigating Centre of Mass

The centre of mass (often called the centre of gravity for small objects near Earth) is the single point where an object’s weight can be thought to act. If you balance a ruler on a finger, the balance point is close to its centre of mass.

What it means and why it matters

• Weight acts straight down through this point (the line of action of weight). If an object is supported at its centre of mass, it does not turn because the turning effect (moment) is zero: $\text{moment} = F \times d_\perp$. When the line of action passes through the support, $d_\perp = 0$.

• Stability: an object is stable when the line of action of its weight falls within its base. A lower centre of mass and a wider base make it harder to tip.

Experiment: finding the centre of gravity of an irregular lamina

Apparatus: thin irregular card (lamina), hole punch or sharp pencil, pin or nail, cork/retort stand, plumb line (string with a small weight), ruler, pencil.

• 1. Make small holes near the edge of the card at two or three different places.
• 2. Hang the lamina from the first hole on a pin fixed to a stand. Suspend the plumb line from the same pin.
• 3. Draw the line along the plumb line on the card. This is a vertical line through the centre of gravity.
• 4. Repeat steps 2–3 for the other holes.
• 5. Mark the intersection of the drawn lines. This point is the centre of gravity. Check by balancing the card on a pencil tip at that point.

Why this works: When the lamina hangs freely, it settles so its centre of gravity lies directly below the support. The plumb line shows that vertical. Lines from different hanging points cross at the same point—the centre of gravity.

Quick guides for simple shapes

• Rectangle or circle: at the centre.
• Triangle: where the three medians meet (about one-third of the way up from the base).
• Symmetric shapes: at the intersection of lines of symmetry.

Common misconceptions

• The centre of gravity is not always at the geometric centre (it depends on mass distribution).
• It can lie outside the material (e.g., a ring).
• Hanging the object in a different orientation does not move the centre of gravity within the object—it reveals the same point.