Finding the Centre of Mass (Oxford AQA IGCSE Physics)

Revision Note

Finding the Centre of Mass

  • The centre of mass of an object is

The point in an object at which the mass can be thought to be concentrated

  • For a symmetrical object of uniform density (such as a symmetrical cardboard shape), the centre of mass is located at the point of symmetry

    • The shape needs to have more than one line of symmetry

Centre of mass of a symmetrical object

Centre of mass of symmetrical objects for IGCSE & GCSE Physics revision notes
The centre of mass of a regular shaped object can be found using symmetry
  • For non-symmetrical objects, the centre of mass can be found using suspension

  • When an object is suspended from a point, the object will always settle with its centre of mass directly below the point of suspension

Centre of mass of a non-symmetrical object

Hang an irregularly shaped object using a thread and a plumb line. Mark the plumb line on the shape. Suspend the object from another location and repeat. The centre of mass will be the point at which the two lines cross.
For irregularly shaped objects, the centre of mass can be found using suspension
  • The irregular shape (also called a plane lamina or thin lamina) is suspended from a pivot and allowed to settle

  • A plumb line (weighted thread) is then held next to the pivot and a pencil is used to draw a vertical line from the pivot (the centre of mass must be somewhere on this line)

  • The process is then repeated, suspending the shape from two additional points

  • The centre of mass is located at the point where all three lines cross

Worked Example

A student wishes to find the centre of mass of an isosceles trapezium.

Isosceles trapezium for IGCSE & GCSE Physics revision notes

Describe a suitable method for the student to use.

Answer:

Step 1: Determine the correct method to use

  • An isosceles trapezium is a symmetrical shape

  • However, it only has one line of symmetry

Single line of symmetry drawn on the isosceles trapezium
  • Therefore, the suspension method must be used

Step 2: Describe the method

  • Suspend the shape using a thread

  • Align a plumb line with the suspension thread and mark the plumb line on the shape (or use the line of symmetry as the first line)

Suspension thread attached to the corner of the base of the trapezium and a plumb line positioned
  • Suspend the shape from a second point, align the plumb line and mark on the shape

A suspension thread positioned at the other bottom corner of the trapezium and a plumb line held in place
  • Suspend the shape from a third point, align the plumb line and mark on the shape

A suspension thread positioned at the other bottom corner of the trapezium and a plumb line held in place
  • The centre of mass is the point at which all three lines cross

The centre of mass labelled as the point at which the three lines cross

Examiner Tip

Make sure that you can describe how to find the centre of mass of a thin lamina with an irregular shape, as you may be asked to this in your exam.

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