# What is the Minimum Distance x for an Interrupted Pendulum to Wrap Around a Rod?

• Bob Jagnaf
In summary, an interrupted pendulum is when the string of a pendulum strikes a rod below the pivot point, causing the pendulum bob to deviate from its circular trajectory and wrap around the rod. To calculate the minimum distance x in terms of L and θ for the bob to completely wrap around the rod, one must consider two separate phases: the first phase where the pendulum swings down towards the rod and the second phase where it rotates around the rod. The equation for the first phase can be used to find the minimum distance x, while the setup can be simplified in the second phase.
Bob Jagnaf
An interrupted pendulum is one in which the string strikes a rod directly below the pivot point causing the pendulum bob to deviate from its previous circular trajectory into a trajectory of a smaller radius. Depending on the original angle of displacement θ and where the rod is placed relative to the total length of the string, the bob may or may not wind itself completely around the rod.

Calculate the minimum distance x in terms of L and θ that will cause the pendulum bob to completely wrap around the rod. You should be careful here – the bob must have sufficient energy to completely circle the rod, and not enter a projectile motion pattern of free fall.

Any solutions is appreciated, steps to solutions are very valuable. Thanks!
1. Homework Statement

L= total length of string to center of mass from the inital point of the pendulum.

## Homework Equations

I found the period of a interrupted pendulum. That is all I have.

## The Attempt at a Solution

I am totally lost on how to do this. Can anyone guide me?[/B]

It is not enough to say you are completely lost. You must have done some previous work with pendulums, so should have some expressible thoughts.
I'll give you this tip: think of it as two separate phases.
In the first, the pendulum is swinging down towards the rod. Since the rod has not been reached, it plays no part. What equation describes this phase?
In the second, it has reached the rod and is starting to rotate about it. What part of the set up can be ignored in this phase?

## 1. What is a period of interrupted pendulum?

The period of interrupted pendulum refers to the time it takes for a pendulum to complete one full swing when interrupted by an external force or obstacle. This can be affected by factors such as the length of the pendulum, the mass of the pendulum, and the strength of the external force.

## 2. How does the length of the pendulum affect its period?

The length of the pendulum directly affects its period. As the length increases, the period also increases. This is because a longer pendulum has a larger swing arc, which takes more time to complete one full swing. This relationship is known as the pendulum's period-length relationship.

## 3. What is the formula for calculating the period of an interrupted pendulum?

The formula for calculating the period of an interrupted pendulum is T = 2π√(L/g), where T is the period, L is the length of the pendulum, and g is the acceleration due to gravity. This formula assumes that the amplitude of the pendulum's swing is small (less than 15 degrees).

## 4. Can the mass of the pendulum affect its period?

Yes, the mass of the pendulum can affect its period. A heavier pendulum will have a longer period compared to a lighter pendulum with the same length. This is because a heavier pendulum requires more energy to swing, which results in a longer period.

## 5. How does an external force affect the period of an interrupted pendulum?

An external force can affect the period of an interrupted pendulum by either increasing or decreasing it. If the external force provides additional energy to the pendulum, the period will decrease. However, if the external force hinders the pendulum's movement, the period will increase. This is known as the principle of conservation of energy.

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