# Physical pendulum and meter stick

• bearhug
In summary, the conversation discusses finding the distance x for a physical pendulum with a meter stick and a period of oscillation of 1.656 seconds. The equation I=1/2mL^2 + mx^2 is used, but there may be an error in the factor for the moment of inertia. The correct factor for a rod may be 1/3 instead of 1/2.

#### bearhug

A physical pendulum consists of a meter stick that is pivoted at a small hole drilled through the stick a distance x from the 50. cm mark. The period of oscillation is observed to be 1.656 s. Find the distance x.

I know I have to find the moment of Inertia and I believe the equation for this is I=1/2mL^2 + mx^2 is this the right equation? Then use the equation T= 2pie(I/mgx)^1/2.

This is what I did but it's not right so if anyone can point out any errors will be greatly appreciated:
I=1/2mL^2 + mx^2
I=1/2m(0.5)^2 + mx^2
I=0.125m + mx^2

T=2pie(I/mgx)^1/2
1.656=2pie{(0.125m + mx^2)/(9.8mx)}^1/2
0.263= {(0.125+x)/9.8}^1/2
0.0692(9.8)=0.125+x
0.553=x

Is this right?

I believe the factor for your moment of inertia is off. I=(1/2)mL^2 is the moment of inertia of a disc. I think you should be using the moment of inertia for a rod, which turns out is just a different factor... it may be 1/3 instead of 1/2. You should look this up though, I'm not entirely positive.

Yes, your approach and calculations are correct. The distance x is indeed 0.553 meters. Good job!

## 1. What is a physical pendulum and meter stick?

A physical pendulum is a type of pendulum that consists of a rigid object suspended from a pivot point, while a meter stick is a long, thin object used to measure length.

## 2. How does a physical pendulum and meter stick work?

A physical pendulum works by utilizing the force of gravity to create a back-and-forth swinging motion, while a meter stick works by comparing the length of an object to the standard length of a meter.

## 3. What factors affect the period of a physical pendulum?

The period of a physical pendulum is affected by several factors, including the length of the pendulum, the amplitude of its swing, and the force of gravity.

## 4. How is a physical pendulum and meter stick used in scientific experiments?

A physical pendulum and meter stick are commonly used in experiments to study the properties of oscillatory motion, such as determining the acceleration due to gravity and measuring the period of a pendulum.

## 5. What are the advantages of using a physical pendulum and meter stick in experiments?

Physical pendulums and meter sticks are advantageous in experiments because they provide a simple and reliable way to measure time and length, and can be easily manipulated to investigate different variables and relationships in a controlled environment.

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