Rolling: Energy in Two Places at Once

You'll learnhow a rolling body splits its energy between translating and spinning, and why shape decides the race.

A hoop, a disk, and a sphere leave the same height with the same energy — and don’t arrive together. Watch each shape’s budget split between going and spinning, and the race explains itself. The tie-breaker is the shape factor \(I/mR^2\), not the mass or the radius.

8 STEPS · 6 QUICK CHECKS · v2

ROLLING

Before you start

What you're looking at

A hoop, a solid disk, and a solid sphere at the top of identical ramps, beside three energy columns.

The question

Released together from the same height, which shape reaches the bottom first?

Watch for

Each body's energy column splitting between going and spinning — shape, not mass, breaks the tie.

What the symbols mean

Solid blue is translational K, striped green is rotational K, amber is unspent gravitational energy U_g (joules).

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