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Course: OCR A Level Physics A H556
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OCR A Level Physics A H556

1. Development of Practical Skills in Physics

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2. Foundations in Physics

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3. Forces and Motion

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4. Electrons, Waves and Photons

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OCR H556 chapter questions and answers

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Text lesson

3.4.3 Centre of Mass

3.4.3 Centre of Mass: Define centre of mass, locate it for symmetrical and irregular objects, and relate its position to the stability of an object.

3.4.3 Centre of Mass

The weight of an extended object can be treated as acting at a single point.

Definition
  • The centre of mass is the point through which the weight of an object appears to act.
Uniform shapes
  • For a uniform symmetrical object, the centre of mass is at its geometric centre.
May lie outside
  • The centre of mass need not be inside the object, as with a ring or a hollow shape.
Centre of gravity
  • In a uniform gravitational field the centre of gravity is at the same point as the centre of mass.
1

Make three small holes near the edge of a flat, thin card of irregular shape.
2

Hang the card freely from a pin through one hole, and let it settle.
3

Hang a plumb line from the same pin and mark its vertical line on the card.
4

Repeat from the other holes; the lines cross at the centre of mass.
5

Check by balancing the card on a pin at that point, which should leave it horizontal.
Stability
Stable
  • An object is stable when its centre of mass is low and its base is wide.
Toppling
  • An object topples when the vertical line through its centre of mass falls outside its base.
Low position
  • Lowering the centre of mass means the object has to be tilted further before the line leaves the base.
Wide base
  • A wider base means the line through the centre of mass stays inside the base for larger tilt angles.
Object feature Effect on stability
Low centre of mass More stable
Wide base More stable
High centre of mass Less stable
Narrow base Less stable

Question: A uniform metre rule is balanced on a pivot at the 40.0 cm mark when a 0.100 kg mass is hung at the 10.0 cm mark. Find the mass of the rule.

  1. The weight of the rule acts at its centre, the 50.0 cm mark, which is 10.0 cm from the pivot.
  2. The mass is 30.0 cm from the pivot on the other side.
  3. Moments: m × 10.0 = 0.100 × 30.0, so m = 3.00 ÷ 10.0 = 0.300 kg.

Answer: The rule has a mass of 0.300 kg.

3.4.3 – Key Points for the Exam

  • Centre of mass: The point through which the weight of an object appears to act.
  • Plumb line: A string with a weight that hangs vertically.
  • Lamina: A thin flat sheet of material.
  • Stable: Tending to return to its original position when tilted slightly.
  • Base: The area of an object that is in contact with the surface.

Common Mistakes

  • Thinking the centre of mass must be a point inside the object.
  • Marking a single plumb line and claiming that it gives the centre of mass; two lines at least are needed.
  • Saying a heavy object is always more stable; the position of the centre of mass and the base width matter.
  • Measuring distances to the wrong end of the rule rather than from the pivot.
YOUR STUDY PATH

3.4.3 Centre of Mass

OCR A Level Physics A H556 / 3. Forces and Motion

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