4.4MechanicsStretch
Centres of Mass
A non-uniform rod has its weight acting at an unknown point. By taking moments about a support, you can locate this centre of mass from the equilibrium conditions.
What you'll be able to do
- Understand centre of mass for non-uniform rods
- Take moments to locate it
- Combine with equilibrium equations
- Interpret the result
1
Non-uniform rods
For a rod the weight acts at the centre. For a rod the weight acts at an unknown distance from one end — this is what you solve for.
Take moments to find the unknown distance.
1At the balance point, moments are equal either side.
2The centre of mass is at the support.
AnswerCentre of mass is at the balance point (1.2 m).
Tip — If a rod balances on a single support, its centre of mass is directly over that support.
Formula recap
Symmetric body.
Locate the centre of mass.
Common mistakes to avoid
Assuming a non-uniform rod’s weight acts at the centre.
Its weight acts at an unknown point you must find.
Ignoring the rod’s weight entirely.
Include the weight as a force at the centre of mass.
Key takeaways
- Uniform rod: weight at the centre.
- Non-uniform rod: centre of mass is unknown — find it by moments.
- Balancing on a single support ⇒ centre of mass is above it.
Test yourself
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