Length of Pendulum: Does COM Matter?

In summary, the length measurement of a pendulum can affect its time period, but it does not matter if the measurement is taken to the center of mass of the ball or to the bottom of the ball. Both measurements will result in the same time period, as shown by the example of a simple pendulum and a wooden ruler.
  • #1
AnthroMecha
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Homework Statement



Does it matter whether you measure the length of the pendulum to the center of mass of the ball or to the bottom of the ball


Homework Equations



T=2pi*root(L/g)


The Attempt at a Solution



I can see that L (length) is a factor, but I'm not sure why it matters if it's taken from the COM or not??

Any help is appreciated!
 
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  • #2
It is essential! A simple pendulum (small mass on the end of a massless string) of length 50cm will have the same time period as a wooden ruler of length 100cm (1 metre).
The 1m ruler must be pivoted as near the end as possible.
The centre of mass of a uniform wooden ruler is at the middle (50cm mark)
 
  • #3
Thank you! That clears it up perfectly.
 

FAQ: Length of Pendulum: Does COM Matter?

How does the center of mass affect the length of a pendulum?

The center of mass (COM) of a pendulum affects its length because it determines the location of the pendulum's pivot point. The length of a pendulum is measured from the pivot point to the center of mass. Therefore, a change in the location of the COM will result in a change in the length of the pendulum.

Can the length of a pendulum be altered by changing the position of the center of mass?

Yes, the length of a pendulum can be altered by changing the position of the center of mass. This is because the length of a pendulum is directly affected by the location of its pivot point, which is determined by the COM. Moving the COM closer or further away from the pivot point will result in a change in the pendulum's length.

Does the center of mass affect the period of a pendulum?

Yes, the center of mass does affect the period of a pendulum. The period of a pendulum is directly proportional to its length. As the length of the pendulum changes due to a change in the location of the COM, the period of the pendulum will also change.

Is the center of mass important to consider when determining the length of a pendulum?

Yes, the center of mass is an important factor to consider when determining the length of a pendulum. The length of a pendulum is directly related to its period, which is an important aspect to consider when studying pendulums. Additionally, the location of the COM can also affect the stability and accuracy of a pendulum.

How can the center of mass be changed in a pendulum?

The center of mass can be changed in a pendulum by altering the weight distribution of the pendulum. This can be done by adding or removing weight from different parts of the pendulum. The location of the pivot point can also be changed, which will also affect the position of the COM.

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