Centres of Mass (Edexcel International AS Maths) : Revision Note

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

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

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