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P8.4 Centre of Mass

GCSE Combined Science · AQA · Chapter P8: Forces in Balance

A free GCSE Combined Science: Trilogy lesson for AQA (8464) from OBA School: mass and weight, W = m g, the centre of mass and how to find it for a flat object. 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

  • Explain the difference between mass and weight, and calculate weight using W = m g
  • State that weight is directly proportional to mass and is measured with a newtonmeter
  • Define the centre of mass and locate it for a uniform ruler and for 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

Key words

  • Mass: The amount of matter in an object, in kilograms (kg). It is the same everywhere.
  • Weight: The force acting on an object due to gravity, in newtons (N). It acts downwards.
  • Gravitational field strength: The weight of each kilogram, g, in N/kg. Near the Earth’s surface g = 9.8 N/kg.
  • Newtonmeter: A spring balance with a scale in newtons, used to measure forces such as weight.
  • Centre of mass: The single point through which the weight of an object can be taken to act.
  • Uniform: Having the same thickness and material all the way through.
  • Plumb line: A string with a small weight on the end; it hangs vertically.

Mass and weight

The mass of an object is the amount of matter in it; it does not change if the object is moved to the Moon. The weight of an object is the force of gravity on it. A large body such as the Earth has a gravitational field that pulls on every mass near it. Weight is a non-contact force and a vector (it acts downwards, towards the centre of the planet).

weight = mass × gravitational field strength W = m g

W = weight in newtons, N; m = mass in kilograms, kg; g = gravitational field strength in N/kg

On the Earth g = 9.8 N/kg; on the Moon g = 1.6 N/kg (you are given the value you need).

Worked example: weight on the Earth and on the Moon

A student has a mass of 55 kg. On the Earth: W = 55 × 9.8 = 539 N.
A 2.5 kg rock sample on the Moon: W = 2.5 × 1.6 = 4.0 N. Its mass is still 2.5 kg.

Answer: 539 N and 4.0 N

Weight is measured with a newtonmeter (a calibrated spring balance). The heavier the object, the more the spring stretches.

The centre of mass

Every tiny part of an object has weight. We can replace all these tiny forces by one force – the weight of the object – acting through 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 or a cricket bat), the centre of mass is nearer the heavy end.

Symmetrical objects

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

Hanging objects and the plumb-line method

If you hang a flat object from a pin and let it swing, it always comes to rest with its centre of mass directly below the point of suspension. Only then do the weight (acting down through the centre of mass) and the upward pull of the pin act along the same vertical line, so they balance. If the object is pushed aside, its weight acts to one side of the pin and swings it back.

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.

Exam tip: Check your answer: the card should balance on the flat end of a pencil placed under the point you found. Thin lines, holes far apart and a card that swings freely all improve accuracy.

Common mistakes

  • Giving weight in kilograms. Weight is a force, so it is measured in newtons.
  • Saying an astronaut’s mass is smaller on the Moon. The mass is the same; only the weight changes.
  • Thinking the centre of mass must be inside the material. For a ring or a horseshoe it is in the empty space.
  • Drawing only one plumb line. You need at least two lines to find where they cross.

Revision questions

Try these, then check your answers below each one.

Question 1. Calculate the weight on the Earth of a 4.2 kg bag of rice. (g = 9.8 N/kg)

Answer: 41.16 N

Working: W = 4.2 kg × 9.8 N/kg = 41.16 N (about 41 N).

Question 2. The diagram shows a flat card hanging at rest from a pin. Which point, A, B, C or D, is the centre of mass of the card? (Choose from: A, B, C, D.)

Answer: B

Working: A freely suspended object comes to rest with its centre of mass directly below the point of suspension. Only B is vertically below the pin.

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 P8.4 (AGCSC3704) of our free GCSE Combined Science 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 Combined Science course.

 

 

 

 

 

 

 

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