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

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Homework Help Overview

The discussion revolves around understanding the dynamics of a rotating disk in the context of Newtonian mechanics, specifically focusing on the relationships between linear and angular motion, as well as the forces acting on the system involving a suspended mass.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning, Problem interpretation, Assumption checking

Approaches and Questions Raised

  • Participants explore the equations of motion for the system, questioning the assumptions about the velocities of the masses and the axis of rotation. There are discussions about using conservation of energy and angular momentum, as well as the implications of different axes for calculating moments.

Discussion Status

Several participants are actively engaging with the problem, proposing different approaches and questioning the validity of assumptions made about the system. There is a recognition of the complexity involved in relating linear and angular accelerations, and some guidance has been offered regarding the need for multiple equations to fully describe the dynamics.

Contextual Notes

Participants note the importance of considering the center of mass and the effects of forces applied off-center, as well as the potential for misunderstanding the nature of rotation in the absence of friction. The discussion reflects a mix of theoretical insights and practical considerations in analyzing the problem.

  • #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.
Newton.png
III in Principia.
 
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