Edexcel International A Level Maths: Mechanics 1

Revision Notes

4.1.3 Centres of Mass

Test Yourself

Uniform Rods & Laminae

What is meant by the centre of mass of an object?

  • The centre of mass of an object is the point at which the weight of the object may be considered to act
  • For a uniform object the centre of mass is at the centre of the object where the lines of symmetry intersect
    • For a uniform rod this will be at its midpoint
    • For a uniform rectangular lamina this will be where the diagonals intersect

  • For a non-uniform object the centre of mass is not necessarily at the centre of the object

4.1.3 Centres of Mass Diagram 1, downloadable Edexcel A Level Mechanics revision notes

How can I solve problems involving uniform rods?

  • If you are told that a rod is uniform then you can draw the weight at the midpoint of the rod
  • If a rod lies on a support or peg then there will be a normal reaction force which acts perpendicular to the rod at that point
  • If the rod is suspended by strings or cables then there will be tensions in the strings which keep the rod in place

Worked example

4.1.3_WE_Centre of Mass_1

4-1-3-centres-of-mass-example-solution-1

Exam Tip

  • If there are two supports with unknown reaction forces then choosing the pivot to be at one of the supports will help to find the force at the other support. The same method works with strings too.

Non-uniform Rods

How do I find the centre of mass of a non-uniform rod in equilibrium?

  • Step 1: Label the weight of the rod at a random point on the rod
  • Step 2: Call the perpendicular distance between the pivot and the weight x
    • Or any letter of your choice

  • Step 3: Form a moment equation using the fact that the rod is in equilibrium
  • Step 4: Solve the equation to find x

Worked example

4.1.3_WE_Centre of Mass_2

4-1-3-centres-of-mass-example-solution-2

Exam Tip

  • Make sure you read carefully which distance you are asked to find.

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Dan

Author: Dan

Dan graduated from the University of Oxford with a First class degree in mathematics. As well as teaching maths for over 8 years, Dan has marked a range of exams for Edexcel, tutored students and taught A Level Accounting. Dan has a keen interest in statistics and probability and their real-life applications.