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Centres of Mass (AQA A Level Maths: Mechanics)
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
Worked example
Examiner 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.
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