Talk (October 19, 2019) on Relational Mechanics presented in Prague, Czech Republic, at the Conference Physics Beyond Relativity. Video of the presentation (1 hour): https://www.youtube.com/watch?v=UNleL0Wynkg and https://science21.cz/conference/?p=878. Abstract: We present Galileo's free fall experiment and its interpretation in Newtonian mechanics. We also discuss Newton's bucket experiment. In this case we have a bucket partially filled with water hanging by a rope. When the bucket and the water are at rest relative to the ground, the surface of the water is flat. When the bucket and the water rotate together relative to the ground, the surface of the water becomes concave (the water rises towards the sides of the bucket, acquiring a parabolic shape). In Newtonian mechanics the curvature of the water surface is not due to its rotation relative to the bucket, relative to the Earth, nor relative to the distant stars and galaxies. According to Newton, this experiment proved the existence of empty and free space, which he called absolute space. According to him, the curvature of the water was due to its rotation relative to absolute space. We then discuss the criticisms of Ernst Mach against Newtonian mechanics. An emphasis is given in Mach's ideas according to which the inertia of any body is due to its gravitational interaction with the distant masses in the universe. Einstein's theories of relativity do not implement Mach's principle. This fact is one of the reasons why we are totally against Einstein’s special and general theories of relativity. Finally, we present Relational Mechanics, a theory which implements quantitatively Mach's ideas about the origin of inertia utilizing Weber's law for gravitation. We discuss Galileo's free fall experiment and Newton's bucket experiment from the point of view of Relational Mechanics. We also present experimental tests in order to distinguish Relational Mechanics from Einstein’s general theory of relativity. Slides of this presentation: https://www.ifi.unicamp.br/~assis/Relational-Mechanics-19-10-2019.pdf.