Ball on a rotating turntable Hugh Hunt http://www.eng.cam.ac.uk/~hemh

The dynamics of a ball on a rotating table have been understood for decades. An elegant and compact vectorial treatment can be found in Milne, E. A.”VECTORIAL MECHANICS”. The analyses given here (top right and bottom left) are based on this vectorial approach. The analysis given
above (top left) for a ball on a horizontal rotating table is purely
Cartesian and is easier for those less skilled in vector manipulation to
follow. It makes use of _{} is the velocity of
point P and p is the linear momentum of the ball. A feature of a rolling ball is that the
centre of mass G is always directly above the contact point P so that _{} where _{} is the velocity of
the centre of mass. So _{} since _{}. Therefore, since Q_{P}
= 0 (all forces pass through P) we have
_{} or h_{P}
is constant ie . This is beautiful.moment of momentum is conserved about the moving point P |