What was Newton's insight on rotational motion in Principia?

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Newton's insight on rotational motion in "Principia" involves understanding the relationship between linear and angular motion, particularly in systems with multiple bodies. The discussion highlights the complexities of calculating velocities and accelerations when a disk rotates while a mass is suspended from it, emphasizing the need for multiple equations to describe the system's dynamics. Participants express confusion over the correct application of conservation laws and the role of the center of mass in determining motion. The conversation also touches on the axis of rotation, with arguments presented about whether the disk rotates about its center or another point. Ultimately, the challenge lies in accurately modeling the interactions and motions involved in such systems.
  • #31
The more I read about Newton and what he did the more impressed I am. He had the critical insight on this problem as Definition III in Principia.
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III in Principia.
 
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