# A problem about spherical pendulum that filled with water

1. Jun 26, 2008

We have a hollow spherical pendulum that is filled with water. The sphere has a hole under it. If it starts to oscillate and at the beginning it was full of water, how it’s period would be by passing time and empting sphere?

2. Jun 26, 2008

### Hootenanny

Staff Emeritus

Well I suppose the first question to ask yourself is that what property changes as the water empties from the sphere?

3. Jun 27, 2008

the mass and the inertia of the sphere changes

4. Jun 27, 2008

### Hootenanny

Staff Emeritus
Indeed it does. However, the problem is greatly simplified because usually a spherical pendulum is seen as a generalisation of a simple pendulum in three-space, which means that we can ignore the moment of inertia of the sphere and just consider the pendulum as a point mass suspended by a massless string.

EDIT: So, now you need to decide how the position of the centre of mass of the sphere varies with time.

Last edited: Jun 27, 2008
5. Jun 27, 2008

### atavistic

We only need to find the effective "l" for the pendulum which is the distance of the centre of mass from the point of attaching of the string.

6. Jun 27, 2008

### PhysicsDruid

Hence... the problem. This sounds like some sort of twisted related rates problem. From the sort of question you posted, I imagine you know how to calculate your moments of inertia (and maybe are familiar with the tensor forms even)... sounds like you just need to express the rate of change of mass for the volume of water within the sphere. Neglecting the mass of the sphere itself, as Hottenanny already mentioned.

7. Jun 27, 2008

i am graduated student in physics and i knonw how to calculate its moments of inertia but and how to simply ignore it as a point mass but i cant reach its answer that is first its period becomes large and then becomes smaler and without ignoreing the inertial momentom of the sphere solving becomes very complicated and did not look a meaning ful answer

8. Jun 27, 2008

### Hootenanny

Staff Emeritus
Consider where the centre of mass of the hollow sphere is located at the following points:

(a) When it is full of water
(b) When it is half full of water
(c) When it is empty

Last edited: Jun 27, 2008
9. Jun 28, 2008