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The balancing point

Gravity and orbits · level 2, lesson 4 of 6

A question to start

Balance a ruler on one finger. Where does your finger have to go? Now tape a coin to one end. Where does your finger go now?

The idea

Gravity pulls on every bit of the ruler. But the ruler behaves as if all its weight pulled at one single spot. That spot is the centre of mass, or balancing point. Hold a thing under its centre of mass and it balances.

For a plain ruler, it is in the middle. Tape a coin to one end and the balancing point moves towards the coin, because that end has more stuff.

middlemoves towards the coin

The centre of mass also tells you whether something will tip over. A thing stays standing as long as its centre of mass is above its base, the patch it stands on. Lean it so far that the centre of mass is past the edge of the base, and over it goes.

That is why tall, narrow things tip easily and low, wide things are steady. Rovers on Mars are built low and wide, with their heavy parts near the bottom, so they can drive across slopes without rolling over. Curiosity can tilt 45° without tipping, though its drivers keep it to much gentler slopes.

Worked examples

1. A broom. Balance a broom across your finger. The balancing point is near the brush, not in the middle, because the brush is the heavy end.

2. Carrying a bag. When you carry a heavy bag in one hand, you lean the other way without thinking. That keeps the centre of mass of you and the bag above your feet.

Try it

  1. Where is the balancing point of a plain pencil?
  2. A hammer is heavy at the head end. Where is its balancing point?
  3. Why is a pile of books harder to knock over if the biggest books are at the bottom?
  4. Why are Mars rovers built low and wide?
Answers
  1. In the middle. If it has a rubber on the end, a little towards the rubber, because the rubber and its metal band add weight there.
  2. Close to the head.
  3. The centre of mass is low, so you have to tilt the pile a long way before it is past the edge of the base.
  4. To keep the centre of mass low and the base wide, so they do not tip over on slopes.

Common mistake

"The balancing point is always in the middle." Only for things that have the same stuff all along. Anything heavier at one end balances closer to that end.

Where it leads