Read Physical Pendulums: Optimise the Effective Length
For a rod pivoted away from its centre, the time period is controlled by I about the pivot divided by the torque lever arm. Both change when the pivot is moved.
Minimum Period of a Physical Pendulum is the central idea in this question pattern. Identify the condition in the stem before applying the method below.
Start with the condition
Let x be pivot-to-centre distance.
Minimise it for x greater than zero.
Build the governing relation
The minimum occurs where the two contributions balance. Confirm it is a minimum by checking that the effective length grows at both very small and very large x.
Finish with a physical check
Check the limiting case before selecting an option: remove the special feature in the diagram or make the relevant parameter very large or very small. The result should reduce to a familiar relation.
OlympIQ exam lens
- ✓State the physical condition before choosing a formula.
- ✓Keep direction, sign and constraint information explicit.
- ✓Test one limiting case before committing to an option.
Minimising the moment of inertia alone would put the pivot at the centre, where the restoring torque is zero.
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