Rolling
▶︎ Watch it animatedinteractive step-through · ~3 min · optionalA body that rolls without slipping does two things at once: its center moves and it spins, locked together by v = Rω. Its kinetic energy is the sum of both motions, K = ½mv² + ½Iω², and how that energy splits between moving and spinning is set by the shape, not the mass.
Three things have to stay in view at once: both energy terms and the constraint. Rolling kinetic energy is never just ½mv² and never just ½Iω² — the body moves and spins together. The spin and the speed aren't independent; v = Rω binds them. And which object wins a race down a ramp is set by the shape factor I / mR², not by mass or radius.
Rolling without slipping
3 ways in · any order
Lesson
Rolling
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Rolling without slipping: the constraint v = R omega, the two-term kinetic energy one half m v squared plus one half I omega squared, energy conservation down an incline, and why the shape factor I over m R squared, not the mass or radius, decides which body is fastest. Includes the static friction that does no work in rolling without slipping. Closes with a ten-scenario skill check.
Diagnostic
10-item topic check
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Ten items across the four Topic 6.5 mistakes: counting only one of the two kinetic-energy terms, misusing the rolling constraint v = R omega, ranking an incline race by mass or radius instead of the shape factor, and treating the static friction in rolling without slipping as if it removed energy. Take it cold to see what still trips you up, or after the lesson to confirm it does not.
Targeted Practice
Drill a single misconception
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Pick one mistake you keep making and drill it on its own. Two correct in a row clears it and you move on.