OCR AS Physics

Revision Notes

3.4.3 Centre of Mass

Centre of Mass

  • The centre of mass of an object is the point at which the weight of the object may be considered to act
  • The position of the centre of mass of uniform regular solid is at its centre
    • For example, for a person standing upright, their centre of mass is roughly in the middle of the body behind the navel, and for a sphere, it is at the centre
  • For symmetrical objects with uniform density, the centre of mass is located at the point of symmetry

Point of symmetry, downloadable AS & A Level Physics revision notes

The centre of mass of a shape can be found by symmetry

Stability

  • The position of the centre of mass of an object affects its stability
  • An object is stable when its centre of mass lies above its base

Stability, downloadable AS & A Level Physics revision notes

The object on the right will topple, as its centre of mass is no longer over its base

  • The wider base an object has, the lower its centre of mass and it is more stable
  • The narrower base an object has, the higher its centre of mass and the object is more likely to topple over if pushed

Stability and base, downloadable AS & A Level Physics revision notes

The most stable objects have wide bases and low centres of mass

Finding the Centre of Mass

  • When an object is suspended from a point, the object will always settle so that its centre of mass comes to rest below the pivoting point
  • This can be used to find the centre of mass of an irregular shape:

Finding Centre of Mass, downloadable AS & A Level Physics revision notes

Diagram showing an experiment to find the centre of mass of an irregular shape

  • The irregular shape (a plane laminar) is suspended from a pivot and allowed to settle
  • A plumb line (a lead weight) 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 or three different points
  • The centre of mass is located at the point where all three lines cross

Centre of gravity v Centre of mass

  • In a uniform gravitational field, the centre of gravity is identical to the centre of mass
  • The centre of mass does not depend on the gravitational field
  • Since weight = mass × acceleration due to gravity, the centre of gravity does depend on the gravitational field
  • When an object is in space, its centre of gravity will be more towards the object with the larger gravitational field
    • For example, the Earth’s gravitational field on the Moon:

Centre of gravity vs centre of mass, downloadable AS & A Level Physics revision notes

The Earth’s stronger gravitational field pushes the Moons centre of gravity closer to Earth

Exam Tip

Since the centre of mass is a hypothetical point, it can lie inside or outside of a body. The centre of mass will constantly shift depending on the shape of a body. For example, a human body’s centre of mass is lower when leaning forward than upright

Close

Join Save My Exams

Download all our Revision Notes as PDFs

Try a Free Sample of our revision notes as a printable PDF.

Join Now
Already a member?
Go to Top