Physical Pendulums
Hang shapes from different pivots. Builds on Simple Harmonic Motion and Moment of Inertia.
You have a uniform meter stick (100 cm). You can hang it from either end (pivot at 0 cm) or from a point 25 cm from one end (pivot at 25 cm).
Which pivot point gives a SHORTER period (faster swing)?
Pivoting at 25 cm makes the stick swing faster! There's actually an optimal pivot point that minimizes the period — and it's NOT at the end.
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Drag the pivot point along the stick. Watch how the period changes — find the sweet spot!
T = 2π√(I/mgd)
There exists an optimal pivot point that minimizes the period — it's not at the end or the center
The pendulum's pivot and mass distribution are precision-tuned for exact timing
Your leg swings as a physical pendulum — its natural frequency sets comfortable walking speed
The center of percussion is where impact feels 'perfect' — related to physical pendulum physics
“Real objects swing differently from ideal pendulums. The shape matters, the pivot matters, and there's always a sweet spot.”
Pendulum Shapes
Hang different shapes from adjustable pivot points. Discover how shape and pivot location affect the swing.
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Try a ring, a disk, and a rod. For each shape, find the pivot point that gives the fastest swing. Are they all at the same relative position?
Every shape has a unique 'sweet spot' pivot that minimizes its period. This is the point where I/(md) is smallest.