# Oscillations with fluid and pendulum

• LCSphysicist
In summary, the conversation discusses the influence of water in liquid state on the motion of a hollow sphere with inertia moment equations provided. The participants also mention the effect of water on the torque exerted on the sphere and the parallel axis theorem for calculating the moment of inertia. They also reference a similar question regarding the period of a pendulum with a disk mass.
LCSphysicist
Homework Statement
A pendulum is constructed as a light thin-walled sphere of
radius R filled up with water and suspended at the point 0 from a
light rigid rod (Fig. 4.1.1). The distance between the point 0 and the
centre of the sphere is equal to 1. How many times will the small
oscillations of such a pendulum change after the water freezes? The
viscosity of water and the change of its volume on freezing are to
be neglected
Relevant Equations
All below

That's a good question, i am not sure how the water in liquid state will influence in the motion, but i imagine that can not exert any torque, i would say in the first case:

Hollow sphere inertia moment: 2mr²/3 + ml²
(2mr²/3 + ml²)θ'' = -mglθ (1)

In the second case, otherwise, we will have
2(m+m')r²/5 + (m+m')l² = -(m+m')glθ

Anyway, i am certain that have some error in (1), something say to me that the water can indeed exert a torque although it doesn't contribute to inertia moment, but, as i don't know the mechanics of a fluid, i am not sure.

LCSphysicist said:
Hollow sphere inertia
The shell is light and can be ignored.
The water does not exert a torque about its centre, but it still exerts a torque about the point of suspension. What does the parallel axis theorem give for its MoI about that point?

Last edited:

## 1. What is an oscillation with fluid and pendulum?

An oscillation with fluid and pendulum is a type of movement where a pendulum is immersed in a fluid, such as water or air, and is allowed to swing back and forth. This creates a repetitive pattern of motion known as an oscillation.

## 2. How does the fluid affect the pendulum's oscillation?

The fluid surrounding the pendulum creates resistance, which slows down the pendulum's motion and causes it to eventually come to a stop. This resistance also affects the frequency and amplitude of the oscillation.

## 3. What factors affect the oscillation of a pendulum in fluid?

The oscillation of a pendulum in fluid is affected by the mass of the pendulum, the length of the pendulum, the density and viscosity of the fluid, and the initial angle of release.

## 4. What is the relationship between the frequency and amplitude of an oscillation with fluid and pendulum?

The frequency and amplitude of an oscillation with fluid and pendulum are inversely proportional. This means that as the amplitude increases, the frequency decreases, and vice versa.

## 5. How is the oscillation of a pendulum in fluid different from a pendulum in a vacuum?

In a vacuum, there is no resistance to the pendulum's motion, so it will continue to swing back and forth indefinitely. In fluid, the resistance causes the pendulum's motion to eventually come to a stop. Additionally, the frequency and amplitude of the oscillation will be different in a vacuum compared to in fluid.

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