# How Do You Calculate the Length of a Swinging Rod in a Physical Pendulum?

• mikefitz
In summary, to find the length of the rod acting as a physical pendulum with a period of 1.74 s, you can use the formula T = 2Pi * sqrt (I / mgh) and solve for 'h'. To get 'h', you need to calculate 'I' using the mass and length of the rod. Once you have 'I', you can express it in terms of the length of the rod and use the given information to solve for the length. However, it's important to note that h is not equal to 2L, as h represents the distance from the pivot point to the center of mass of the rod.
mikefitz
A rod suspended on its end and acting as a physical pendulum swings with a period of 1.74 s. What is its length? (g = 9.80 m/s2)

Ok so in order to solve this I need to use the physical pendulum formula:

T = 2Pi * sqrt (I / mgh) ==> I am looking for 'h'

To get 'h' I need to first calculate 'I' which requires mass for a rod.

So, taking it from here I'm not sure where to begin. I've tried rearranging the formulas I've been given with no luck - any ideas?

h is the distance from the pivot point to the center of mass of the rod. You can express that in terms of the length of the rod and you can express I in terms of the length of the rod.

Ok let me try this:
1.74=2Pi * sqrt ((1/12*mL^2) / (m*9.81*2L)
=> .27=sqrt((1/12L / 19.62))
1/12L = 1.504
L=~18m ??

This is wrong. I canceled out m and L in my early steps, did this throw my calculations off?

The stick is suspended from its end, not its middle.

1.74=2Pi * sqrt((1/3L^2) / (m(9.81)(2L)

*question: I haven't had algebra for a while, but you can just cancel the m's and cancel the L's, leaving only one 'L' in the numerator, correct?

If that assumption is correct I get L=4.51m - my book disagrees with this answer though; any idea why?

Looks like you are setting h = 2L, which isn't right. As OlderDan explained, h is the distance from the pivot point to the center of mass of the rod.

## 1. What is a physical pendulum?

A physical pendulum is a rigid body suspended from a fixed point that is allowed to swing freely back and forth under the influence of gravity.

## 2. What is the formula for the period of a physical pendulum?

The formula for the period of a physical pendulum is T = 2π√(I/mgd), where T is the period, I is the moment of inertia, m is the mass of the pendulum, g is the acceleration due to gravity, and d is the distance from the point of suspension to the center of mass of the pendulum.

## 3. How is the physical pendulum formula different from the simple pendulum formula?

The physical pendulum formula takes into account the shape and mass distribution of the pendulum, while the simple pendulum formula assumes a concentrated mass at the end of a massless string. This makes the physical pendulum formula more accurate for real-world applications.

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

The period of a physical pendulum can be affected by the length of the pendulum, the mass distribution, the angle of oscillation, and the acceleration due to gravity. Friction and air resistance can also have a small impact on the period.

## 5. How is the physical pendulum formula derived?

The physical pendulum formula can be derived using the principles of rotational dynamics and energy conservation. By analyzing the forces and torques acting on the pendulum, we can derive the equation for the period of a physical pendulum.

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