# The Length of Pendulum Strings: Motion Effects

• anantchowdhary
In summary: The time period as viewed from another rest frame would be the T = \gamma T_0?where T is the time period as viewed by the rest frame and T_0 ,Tthe time period as viewed by the moving frame.PLease help.I would really ,like to know whether the above reasoning is correct or not!
anantchowdhary
When a pendulum is moving

will the length of the string that the bob is attached to appear to be contracted?I have this doubt as the string is sometimes in direction of motion and at one point absolutely not in the direction of motion

Appear to be contracted from whom's point of view?

From an observer's point of view whoo is in an inertial frame.If he wants to calculate the time period of the pendulum,how will he measure the length as it changes from position to position

Please sum1 help me out here!

anantchowdhary said:
When a pendulum is moving

will the length of the string that the bob is attached to appear to be contracted?I have this doubt as the string is sometimes in direction of motion and at one point absolutely not in the direction of motion
Each infinittesimal portion of the string is a linie segment which is moving perpendicular to its motion. According to SR the length of the string will remain unchanged.

Pete

I assume that the OP meant that the swinging pendulum was in a moving rocket (say) being observed from the earth.

Doc Al said:
I assume that the OP meant that the swinging pendulum was in a moving rocket (say) being observed from the earth.
That's the usual way. Another way is to to have a charged particle on a string at a fixed distance from a charged plate. But you're right, he was probaby speaking of in a grav-field or in a rocket shift.

Pete

Doc Al said:
I assume that the OP meant that the swinging pendulum was in a moving rocket (say) being observed from the earth.

No,i just meant to have an experiment of a pendulum,moving at a constant velocity relative to a frame.Now the string of the pendulum,once is perpendicular to the direction of motion,and when it is at its maxima,it has some component in the direction of velocity,so my question was,wouldnt this affect the length of the string?

Also the time period as viewed from another rest frame would be the
$$T = \gamma T_0$$?

where T is the time period as viewed by the rest frame and $$T_0$$ ,$$T$$the time period as viewed by the moving frame.

Last edited:

## 1. What is a pendulum and how does it work?

A pendulum is a simple device consisting of a weight suspended from a pivot point that is able to swing back and forth. The motion of a pendulum is governed by the principles of gravity and inertia. When the weight is pulled to one side and released, it will swing back and forth in a regular pattern, known as its period. This motion can continue indefinitely as long as there is no external force acting on the pendulum.

## 2. How does the length of a pendulum string affect its motion?

The length of a pendulum string has a direct effect on its motion. According to the laws of physics, the longer the pendulum string, the longer the period of its swing. This means that a longer pendulum string will take more time to complete one swing than a shorter pendulum string. This relationship is known as the "pendulum length effect."

## 3. What other factors can affect the motion of a pendulum?

In addition to the length of the pendulum string, there are other factors that can affect its motion. These include the weight of the pendulum, the angle at which it is released, and the air resistance it encounters. These factors can influence the period and amplitude of the pendulum's swing, making its motion more complex.

## 4. How is the length of a pendulum string measured?

The length of a pendulum string is typically measured from the pivot point to the center of the weight. It is important to measure from the center of the weight rather than the bottom or top of the weight, as this can affect the accuracy of the measurement. The length can be measured using a ruler or measuring tape.

## 5. How is the length of a pendulum string related to its frequency?

The length of a pendulum string is inversely proportional to its frequency. This means that as the length of the pendulum string increases, the frequency decreases, and vice versa. This relationship is described by the equation: frequency = 1/period. Therefore, as the length increases, the period of the pendulum's swing also increases, resulting in a lower frequency.

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