Period of oscillations of the disk

[cupcake]

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?

 

[Delzac]

I am afraid its not correct. You have to calculate the new moment of inertia. Use parallel axis theorem to help you.

 

[Delzac]

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?

 

[cupcake]

why this is not a uniform circular motion?
is it because the disk is not moving in constant speed?

 

[Delzac]

You are right. Because it is not moving at constant linear velocity. So angular velocity is always changing too, v=rw.