Answered: Consider a particle moving at a…

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter8: Central-force Motion

Section: Chapter Questions

Problem 8.9P

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Areas and circular motion

A) Consider a particle moving at a constant speed in a straight line with no
forces acting on it. For an arbitrary observer located at a fixed point O, show mathematically that an imaginary line joining the observer to the particle sweeps out equal areas in equal time intervals.

B) Consider now instead a particle following a circular trajectory with constant angular velocity and an observer at the centre of the circle. Show that the imaginary line that joins the observer to the particle sweeps out equal areas in equal times.

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