FYKOS Year 29 Series 5 Problem 5 — rolling stones · FYKOS 29 #29.5.5
Physics · mechanics
Problem
There is a sphere with inhomogeneous distribution of density on an inclined plane. We know the angle of inclination of the plane α, the radius of the sphere R and the distance t of the centre of mass from its geometrical centre. If we label the centre of the sphere S, the point of touch with the plane D and the centre of mass T, then we can define the angle φ0=∠DST as the initial angle (before any motion begins). We also know that the centre of mass is situated in a plane given by the line segment DS (the normal to the inclined plane) and the down-sloping direction. Considering all the parameters given, carefully describe the time evolution of the sphere's state of motion. The sphere does not slip.