Frozen Pendulum: How Does it Affect Oscillations?

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In summary: In liquid form, the moment of inertia is distributed more uniformly throughout the sphere, as the water rotates more freely. When frozen, the moment of inertia is concentrated near the center of the sphere, due to the increased mass at that location.
  • #1
durt
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A pendulum is constructed as a light thin-walled sphere of radius [tex]R[/tex] filled up with water and suspended at the point [tex]O[/tex] from a light rigid rod. The distance between the point [tex]O[/tex] and the center of the sphere is equal to [tex]l[/tex]. 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. :smile:
 
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  • #2
durt said:
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. :smile:
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.
 
  • #3
arildno said:
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.
 
  • #4
The distribution of mass is different throughout time.
 
  • #5
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
 
  • #6
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.
 
  • #7
The moment of inertia effectively represents the object's mass distribution with respect to the rotation axis.
 

Related to Frozen Pendulum: How Does it Affect Oscillations?

1. How does the length of the pendulum affect its oscillations?

The length of a pendulum directly affects the time it takes for one complete oscillation, also known as its period. The longer the pendulum, the slower the oscillations and the longer the period. This is because the longer pendulum has a greater distance to travel and thus a slower velocity. The relationship between length and period is described by the equation T=2π√(L/g), where T is the period, L is the length, and g is the acceleration due to gravity.

2. What role does gravity play in the oscillations of a pendulum?

Gravity is the force that pulls the pendulum back to its resting position. As the pendulum swings away from its resting position, gravity pulls it back towards the center, causing the pendulum to oscillate. Without the force of gravity, the pendulum would not have any oscillations and would simply hang in a static position.

3. How does the weight of the pendulum affect its oscillations?

The weight of a pendulum does not have a direct effect on its oscillations. The period of a pendulum is determined by its length and the force of gravity, not its weight. However, a heavier pendulum will require more force to set it in motion and may have a slightly slower oscillation due to air resistance. Additionally, a heavier pendulum may have a greater potential energy, which can affect the amplitude of its oscillations.

4. Can the materials used for the pendulum affect its oscillations?

The materials used for a pendulum can have a slight effect on its oscillations. For example, a pendulum made of a lighter material may experience less air resistance and thus have a slightly faster oscillation. However, as long as the materials are strong enough to support the weight of the pendulum, the type of material should not have a significant impact on its oscillations.

5. How does temperature affect the oscillations of a frozen pendulum?

Temperature can have a significant effect on the oscillations of a frozen pendulum. As the pendulum is frozen, the materials used will become stiffer and less elastic, resulting in a shorter period and faster oscillations. The decrease in temperature may also reduce air resistance, resulting in a more consistent oscillation pattern. However, extreme temperatures may cause the pendulum to become too rigid and affect its ability to oscillate altogether.

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