AQA A Level Maths: Mechanics复习笔记4.1.3 Centres of Mass

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

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