Final answer:
Galileo's work on pendulum motion and acceleration underpinned the development of classical mechanics. His discoveries about motion refuted Aristotelian physics and supported Newton's laws of motion. His promotion of the Copernican system also brought him into conflict with the Church.
Step-by-step explanation:
Galileo Galilei's penal theory which is likely referring to his work on the law of pendulum motion and the theory of acceleration, posits that the period of a simple pendulum, or the time it takes to complete a cycle, is independent of the mass of the pendulum and the amplitude of its swing, assuming small angular displacements.
This principle is tied to physics and mechanics. Moreover, Galileo made profound discoveries including that for objects starting from rest, the distance covered is proportional to the square of the time elapsed.
He also stated that objects will maintain their velocity unless acted upon by an external force, a concept which helped lay the groundwork for Newton's First Law of Motion.
Galileo's advocacy for the Copernican heliocentric system over the geocentric model placed him in conflict with the Church and marked a significant moment in the history of science.
His work in mechanics and the understanding of motion challenged the long-held Aristotelian view that objects have a natural tendency to come to rest and shifted the perspective towards the relativity of motion.
Galileo's innovative approach placed emphasis on experimentation and empirical evidence over philosophical speculation. His insights into the nature of motion directly contributed to the eventual advent of classical mechanics.