Period of oscillations of the disk

In summary, the conversation discusses a problem involving a circular disk of uniform density pivoting about a fixed point and the calculation of its period of oscillations when released from a small angle. The equations used include F=ma, a=v^2/R, and v=2*R*pi/T. The attempt at a solution involves calculating the new moment of inertia using the parallel axis theorem and determining the characteristic of a uniform circular motion, which is not applicable in this situation due to the disk not moving at a constant speed.
  • #1
cupcake
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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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  • #2
I am afraid its not correct. You have to calculate the new moment of inertia. Use parallel axis theorem to help you.
 
  • #3
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?
 
  • #4
why this is not a uniform circular motion?
is it because the disk is not moving in constant speed?
 
  • #5
You are right. Because it is not moving at constant linear velocity. So angular velocity is always changing too, v=rw.
 

Related to Period of oscillations of the disk

What is the period of oscillations of a disk?

The period of oscillations of a disk refers to the amount of time it takes for the disk to complete one full cycle of oscillation, or one back-and-forth motion.

What factors affect the period of oscillations of a disk?

The period of oscillations of a disk is affected by several factors, including the mass of the disk, the stiffness of the material it is made of, and the distance from the center of the disk to the point of rotation.

How is the period of oscillations of a disk calculated?

The period of oscillations of a disk can be calculated using the equation T=2π√(I/k), where T is the period, I is the moment of inertia of the disk, and k is the spring constant of the material the disk is made of.

What is the relationship between the period of oscillations and the frequency of a disk?

The frequency of a disk is the number of oscillations it completes in a given amount of time, while the period is the amount of time it takes to complete one oscillation. They are inversely related, meaning that as the frequency increases, the period decreases.

How does damping affect the period of oscillations of a disk?

Damping, which is the gradual decrease in amplitude of oscillations over time, can affect the period of oscillations of a disk. As damping increases, the period also increases, meaning that the disk takes longer to complete one oscillation.

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