Rolling race down an incline.

Ring, disc, sphere and a sliding block race down one incline; KE splits into translation and rotation by I/MR², so they arrive in a fixed order regardless of mass.

Predict and confirm the finishing order, then find the incline height at which the disc arrives at 4 m/s (h = 1.22 m).

Heavier or larger objects roll down faster.

• A particle is an idealised point mass with no size. Real bodies are extended, and an extended body is best seen as a system of particles.
• An ideal rigid body keeps a perfectly definite shape: the distance between every pair of its particles stays fixed. No real body is truly rigid, but wheels, tops, steel beams, molecules and planets can be treated as rigid when their bending, twisting and vibration are negligible.
• In pure translation every particle of the body has the same velocity at each instant, like a block sliding down an incline without turning.
• A cylinder rolling down the same incline is translating plus rotating: its particles have different velocities at the same instant, and if it rolls without slipping the point in contact with the incline is momentarily at rest.
• Fixed along a line, a body has only rotation open to it. Each of its particles then traces a circle whose plane is at right angles to the axis and whose centre lies on it; particles on the axis stay still. A ceiling fan and a potter's wheel turn this way, and so do the giant wheel and merry-go-round at a fair.
• In some rotations only one point is fixed and the axis moves: a spinning top's axis sweeps out a cone about the vertical through its tip (precession), and an oscillating table fan's axis swings about its pivot.
• Summary: a body that is not pivoted either translates or translates and rotates; a pivoted or fixed body rotates. This chapter treats rotation about a fixed axis only.

Teaching this idea? Put the simulation on your own page or LMS with this code.