John Taylor Classical Mechanics Chapter 1 Problem 46

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SUMMARY

The discussion focuses on Problem 46 from John Taylor's Classical Mechanics, which involves analyzing the motion of a frictionless puck on a rotating turntable. The puck is launched from the center of the turntable in a straight line, and the task is to express its polar coordinates (r, φ) in the inertial frame and the rotating frame (S'). The participants conclude that the puck's path appears curved to an observer on the turntable due to the effects of angular velocity, and they discuss the implications for the inertial nature of frame S'.

PREREQUISITES
  • Understanding of inertial reference frames and Newton's laws of motion.
  • Familiarity with polar coordinate systems and their applications in physics.
  • Knowledge of angular velocity and its effects on motion in rotating systems.
  • Basic skills in sketching motion paths and interpreting physical scenarios.
NEXT STEPS
  • Study the derivation of polar coordinates in rotating frames using classical mechanics principles.
  • Explore the concept of fictitious forces in non-inertial reference frames.
  • Learn about the Coriolis effect and its implications in rotating systems.
  • Review examples of motion in rotating frames, including applications in engineering and physics.
USEFUL FOR

Students of physics, particularly those studying classical mechanics, educators teaching motion in rotating systems, and anyone interested in the application of inertial and non-inertial reference frames in real-world scenarios.

karmonkey98k
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Homework Statement


Problem 27 Experiment needed first: The hallmark of inertial ref. frames is that any object subject to 0 net force travels in straight line at a constant speed. Consider the following experiment: I am standing on the ground (which we shall take to be an inertial frame) beside a perfectly flat horizontal turntable, rotating with constant ang. velocity w. I lean over and shove a frictionless puck so that it slides across turntable, straight through center. The puck is subject to 0 net force, and, as seen from my inertial frame, travels in straight line. Describe puck's path as observed by someone sitting at rest on turntable.
Now Problem 46: Consider experiment of Problem 27, where a frictonless puck is slid straight across a rotating turntable through the center O. a. Write polar coordinates r, phi, of the puck as functions of time as measured in the inertial frame S of an observer on the ground (Assume puck was launched along axis phi=0 at t=0). b. Now write down the polar coordinates rprime, phiprime of the puck as measured by an observer (Frame Sprime) at rest on tunrtable. (choose these coordinates so that phi and phiprime coincide at t=0). Describe and sketch path as seen by this second observer. Is frame Sprime inertial?


The Attempt at a Solution


I had tried to find which polar coordinates would coincide with the regular cartesian ones; that's really all i can describe about my attempt
 
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hi karmonkey98k! :wink:

show us how far you have got :smile:

(btw, you can write S' for Sprime etc)
 

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