Period of oscillations of the disk

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Homework Help Overview

The problem involves calculating the period of oscillations of a circular disk that pivots about a fixed point on its circumference when displaced by a small angle. The subject area includes dynamics and rotational motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants discuss the application of the moment of inertia and the parallel axis theorem. There is a focus on the characteristics of uniform circular motion and how they relate to the problem at hand.

Discussion Status

Some participants have raised concerns about the initial approach to the problem, suggesting that the moment of inertia needs to be recalculated. Others are exploring the differences between uniform circular motion and the motion of the disk, indicating a productive examination of the underlying concepts.

Contextual Notes

There is an emphasis on understanding the dynamics of the disk's motion, particularly regarding the changing angular velocity and the implications for the period of oscillation. Participants are questioning the assumptions made in the original poster's calculations.

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Homework Statement



A circular disk of radius R and uniform density is free to pivot about a fixed point P on its circumference. Calculate the period of oscillations of the disk, in the plane of Figure I, when it is displaced by a small angle about its pivot and released.


Homework Equations



F=ma
a=v^2/R
v=2*R*pi/T

The Attempt at a Solution



F=mv^2/R
mg=mv^2/R
g=v^2/R

where v= 2*R*pi*/T

thus, T= 2*pi*root(R/g)

can anyone advise?
 

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I am afraid its not correct. You have to calculate the new moment of inertia. Use parallel axis theorem to help you.
 
And the problem here is, this is not a uniform circular motion.

What is the characteristic of a uniform circular motion? And how does it NOT fit into this situation?
 
why this is not a uniform circular motion?
is it because the disk is not moving in constant speed?
 
You are right. Because it is not moving at constant linear velocity. So angular velocity is always changing too, v=rw.
 

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