A Reuleaux triangle is a two-dimensional figure defined as the intersection of three identical disks placed so that the center of each disk lies on the boundary of the other two (see diagram).
The moment of inertia of a Reuleaux triangle rotating about its centre of mass is given by I = CMR², where M is its mass, R the radius of the circles and C is a numerical constant.
a) Consider a "wheel" in the shape of a Reuleaux triangle with uniform density, resting on a flat surface. What is the frequency of small oscillations of this wheel? Neglect any slipping.
b) Consider two logs with Reuleaux triangle cross-sections placed on a flat horizontal surface and supporting a long flat plank of wood, as shown. Assume no slipping and consider only the time period before one of the logs reaches the end of the plank. Sketch the height of the center of mass of the plank as a function of horizontal displacement.
c) Is there a configuration in part (b) for which the center of mass of the whole system (logs + plank) remains at constant height as the plank moves? Justify your answer.