Frozen Pendulum: How Does it Affect Oscillations?

[durt]

A pendulum is constructed as a light thin-walled sphere of radius $$R$$ filled up with water and suspended at the point $$O$$ from a light rigid rod. The distance between the point $$O$$ and the center of the sphere is equal to $$l$$. How many times will the small oscillations of such a pendulum change after the water freezes? The viscosity of the water and the change in its volume on freezing are to be neglected.

Why is the period of a solid pendulum different from that of a liquid one? Is it because the water shifts around inside the sphere? I need a hint.

 

[arildno]

Why is the period of a solid pendulum different from that of a liquid one? Is it because the water shifts around inside the sphere? I need a hint.

Quite so!
In liquid form, the moment of intertia of the whole pendulum will change over time, wheres in the solid form, the moment of inertia is a constant.

 

[durt]

In liquid form, the moment of intertia of the whole pendulum will change over time, wheres in the solid form, the moment of inertia is a constant.

But how and why does this occur? The shape and mass of the pendulum are constant.

 

[Harmony]

The distribution of mass is different throughout time.

 

[vijay123]

yes, they are constandt...but the angular accelerationa and rotational energy are not. in soldi form, like wut arildno said, the moment of inertia is constant and is concentrated at the bottom of the ball.now, moment of inertia means measure of the tenddency to make the angular acceleration of the ball as minimal as possible. hence, i think that when frozen, the pendulum would sway much slower than that in liquid form.thats the rotational part, hope you can do the rest of the part involving osscilations

 

[durt]

Ok, I think I understand now. When its solid, the mass of water does not rotate about the center of the sphere, but it does as a liquid. So its like there's a hinge in the middle of it. Is this the right idea? I'll run through the calculations later. I don't see how this changes any moments of inertia though.

 

[arildno]

The moment of inertia effectively represents the object's mass distribution with respect to the rotation axis.