Centre of Gravity

• The centre of gravity of an object is the point where all the weight of the object may be considered to act.
• It is a model that replaces many small gravitational forces with one equivalent force. It does not mean that gravity acts only on one particle of the object.
• For a uniform, symmetric object (a ruler, a sphere, a plank) the centre of gravity is at the middle.
• For a non-uniform object it sits closer to the heavy end. Its position must be given, measured, or found from moments.

centre of gravity

• The centre of gravity does not have to be inside the object. A high jumper bends backwards over the bar, and at that moment the centre of gravity is outside the body, just below the back.
• While the jumper is in the air, the centre of gravity follows an approximately projectile path when air resistance is negligible. Moving the arms and legs changes the body shape around that path.

For a flat sheet (a lamina), a simple experiment finds the centre of gravity.

1. Make small holes near the edge. Hang the sheet from a pin through one hole, so it can swing freely.
2. Hang a plumb line (a string with a small weight) from the same pin.
3. The sheet comes to rest with its centre of gravity directly below the pin. Draw a line on the sheet along the string.
4. Repeat from a second hole. The centre of gravity is where the two lines cross.

suspend from one holeplumb line shows vertical

• Why it works: a hanging object settles so that its weight acts straight below the support. So the centre of gravity must lie on the vertical line through the pin, every time.

In every force question from now on, draw the weight as one arrow, straight down, from the centre of gravity.

• How the exam uses it: a uniform plank's weight acts at its midpoint. For a non-uniform bar, the question gives the centre of gravity or enough information to find it by taking moments, which is the skill of lesson 4.04.