A uniform disc with a massless string wound around it and held by the string falls with acceleration 2/3g.
This is the same acceleration as the limiting case of the acceleration of a uniform disc down an incline as the angle approaches 90°.
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The total energy of a rolling object is the sum of it's rotational, kinetic and potential energies and is conserved. Check out KeysToMaths1 for more tutorials and solutions: https://www.youtube.com/channel/UCOYoe9L9R13HGUIhszjkeug

The acceleration of a uniform annulus rolling on an inclined plane is 2gSinƟ/(3+(b/r)^2) where r is the outer radius and b is the inner radius.
This is less than the acceleration of ANY uniform disc (2gSinƟ/3) rolling on the same incline.
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