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8.6 Centre of Mass

GCSE Physics · AQA · Chapter 8: Forces in Balance

A free GCSE Physics lesson for AQA (8463) from OBA School: where the weight of an object acts, finding the centre of mass, suspended objects and toppling. Watch the video, read the explanation and worked examples, then try the revision questions. You can work through the full lesson, with every video, practice quizzes and printable worksheets with mark schemes, in our free online course.

What you will learn

  • Define the centre of mass of an object
  • Locate the centre of mass of a uniform ruler and of symmetrical objects
  • Explain why a freely suspended object comes to rest with its centre of mass directly below the point of suspension
  • Describe how to find the centre of mass of an irregular flat card using a plumb line
  • Use the centre of mass to explain why objects topple

Key words

  • Centre of mass: The point at which the mass of an object can be thought of as being concentrated; its weight acts at this point.
  • Centre of gravity: Another name for the centre of mass (used when talking about weight).
  • Uniform: Having the same thickness and density all the way through.
  • Lamina: A thin, flat sheet of material, such as a piece of card.
  • Freely suspended: Hung from a point so that it can swing without friction stopping it.
  • Plumb line: A string with a small weight on the end; it hangs vertically.
  • Equilibrium: A state in which an object is at rest because the forces and their moments are balanced.

The centre of mass

Every particle of an object has weight. We can replace all these tiny forces by one force – the weight of the object – acting at a single point called the centre of mass. On force diagrams, draw the weight arrow starting from the centre of mass.

Key fact: The centre of mass of a uniform object is at its geometric centre. If one end is heavier (like a hammer), the centre of mass moves towards the heavy end.

Symmetrical objects

For a symmetrical flat object, the centre of mass lies on the axis of symmetry. If the object has two or more axes of symmetry, the centre of mass is where they cross.

Freely suspended objects

If you hang an object from a point and let it swing, it always comes to rest with its centre of mass directly below the point of suspension. In this position the line of action of the weight passes through the pivot, so the weight has no moment and the object is in equilibrium.

A child on a swing, a picture on a nail and a hanging basket all settle in this position. Once friction has stopped the swinging, the object stays there.

Finding the centre of mass of an irregular card

1. Make three small holes near the edge of the card, well apart.

2. Hang the card from a pin through one hole, held in a clamp stand. Check that it swings freely, then let it come to rest.

3. Hang a plumb line from the same pin. When it is still, mark two points on the card under the string and join them with a ruler and a sharp pencil.

4. Repeat using a second hole. The centre of mass is where the two lines cross.

5. Use the third hole as a check: its line should pass through the same point.

Evaluating the method: the card should balance on the flat end of a pencil placed under the point you found. Thin lines, holes far apart and making sure the card hangs freely (not rubbing on the stand) all improve accuracy.

Stability and toppling

When an object is tilted, it turns about the edge of its base. If the line of action of its weight still falls inside the base, the weight’s moment turns it back. If the line of action falls outside the base, the moment turns it further over and it topples.

Objects are more stable (harder to topple) if they have a low centre of mass and a wide base. Racing cars, desk lamps with heavy bases and wide-legged high chairs use this idea.

Common mistakes

  • Thinking the centre of mass must be inside the material. For a ring or a horseshoe it is in the empty space.
  • Saying a suspended object stops “because the weight is balanced”. Explain with moments: the weight acts through the pivot, so it has no turning effect.
  • Drawing only one plumb line. You need at least two lines to find where they cross.
  • Forgetting that a heavy part of an object moves the centre of mass towards it.

Revision questions

Try these, then check your answers below each one.

Question 1. What is meant by the centre of mass of an object? (Choose from: the point where its mass can be thought of as being concentrated, the point halfway between its top and bottom, the heaviest part of the object, the point where it touches the ground.)

Answer: the point where its mass can be thought of as being concentrated

Working: The centre of mass is the point at which the mass (and so the weight) of the object can be thought of as acting.

Question 2. Where is the centre of mass of a uniform metre ruler? (give the cm mark)

Answer: 50 cm mark

Working: At its midpoint, the 50 cm mark.

Question 3. True or false? The centre of mass of an object must always be inside the material of the object.

Answer: False

Working: False. For a ring the centre of mass is at the centre of the hole, where there is no material.

Related lessons

Continue in the full course

This lesson is section 8.6 (AGCPH0806) of our free GCSE Physics course for AQA. In the full course you get every video for this section, a self-marking practice quiz, a printable worksheet with a mark scheme, chapter tests, and your progress saved. Go to the full GCSE Physics course.

 

 

 

 

 

 

 

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