Angular velocity at Isaac Newton's house

I finally made it to Isaac Newton's house at Woolsthorpe in Lincolnshire. This exhibit was in the science centre. You push the ball round the circle and it decays into the centre. I am thinking about the shape. If it represents gravitational potential in the Solar System, then perhaps it is a 1/r shape. The photograph exposures should represent equal time periods. Thus we can comment on the angular velocity as the ball moves from the outside to the centre. In the top photograph, it manages 90 degrees. By the second photograph, the trace of the ball is twice as long - the angular velocity has doubled. In the final photograph, it has doubled again to complete a full 360 degrees. It is true for the Solar System that angular velocity is bigger closer in. I will look in to making measurements of radial distance from the photographs to quantify the relastionship.