Rate of Rotation of a Pendulum

In summary: I mistyped it.In summary, the given conversation discusses deriving a formula for calculating the rate of rotation for a pendulum at any location on Earth using data from four different locations. The suggested method is to plot latitude against rotational frequency and determine whether there is a linear dependence or a trigonometric dependence. The data points provided are 3600/24 Hr at the North Pole, 226/24 Hr at the Smithsonian in Washington D.C., 0/24 Hr at the Equator, and 220.5/24 Hr at the California Academy of Sciences. The conversation also mentions two models to explain pendulum motion rotation and how they can be verified from a visual frame of reference. Lastly, there
  • #1
Kee10016
2
0

Homework Statement


The rate of rotation for a pendulum was found for the following locations. Using these data, derive a formula for calculating the rate of rotation for a pendulum at sea level for any location on Earth.
• North Pole = 3600/24 Hr
• Smithsonian, Washington, D.C. = 2260/24 Hr
• Equator = 00 /24 Hr
• California Academy of Sciences (370 46.2’) = 220.50/24 Hr


Homework Equations


n= (360)(sin theta)


The Attempt at a Solution


My teacher said we could use Graphical Analysis, but I don't know why I should use that. Should I try finding the rate of rotation for each location?

Homework Statement


The data from question # 1 indicates that no rotation occurs at the equator. This suggests two models to explain pendulum motion rotation. Explain and diagram each model. Explain how each model can be verified from its visual frame of reference.


Homework Equations





The Attempt at a Solution



Homework Statement


3. Explain and show mathematically that a simple pendulum exhibits simple harmonic motion.

Homework Equations


Is there an equation I can use to figure this out?

The Attempt at a Solution


 
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  • #2
Kee

The only obvious difference between these different locations is their latitude.

So, as suggested by your teacher, plot latitude (0° to 90°) along the X axis of a graph and rotational frequency (0 to 3600) on the Y axis. Put into the four data points and see whether you get a straight line or a curve.

If it's a straight line, bingo, it's a linear dependence on latitude and you should be able to formulate an expression for that quite easily. If it's not a straight line then we'll have to check for dependence on the latitude angle in terms of trigonometic functions (sin,cos,tan,etc..)

BTW are you sure your numbers are correct - 2260 and 220.5 ?
 
  • #3
Sorry it's 226 and 220.5
 

Related to Rate of Rotation of a Pendulum

1. What is the rate of rotation of a pendulum?

The rate of rotation of a pendulum refers to the speed at which the pendulum swings back and forth. It is measured in units of time, typically seconds, and is influenced by factors such as the length of the pendulum, the force of gravity, and the angle of release.

2. How is the rate of rotation of a pendulum calculated?

The rate of rotation of a pendulum can be calculated using the formula T = 2 * π * √(L/g), where T is the period (time for one complete swing), π is pi, L is the length of the pendulum, and g is the acceleration due to gravity. This formula assumes a small amplitude swing and no air resistance.

3. Does the rate of rotation of a pendulum change over time?

In a perfect scenario, with no air resistance, the rate of rotation of a pendulum will remain constant. However, in real-world situations, factors such as air resistance and changes in the length of the pendulum can cause the rate of rotation to change over time.

4. How does the rate of rotation of a pendulum relate to its period?

The rate of rotation of a pendulum is directly related to its period. The shorter the period, the faster the pendulum will rotate. This is because a shorter period means the pendulum will complete more swings in a given amount of time.

5. How does the rate of rotation of a pendulum differ on different planets?

The rate of rotation of a pendulum is influenced by the gravitational force of the planet it is on. On planets with a stronger gravitational force, such as Jupiter, the pendulum will have a faster rate of rotation. On planets with a weaker gravitational force, such as the Moon, the pendulum will have a slower rate of rotation.

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