# Moment of inertia of a double physical pendulum

• AF Fardin
In summary, the conversation discusses finding the moment of inertia of the second rod and whether it is related to the first rod. The speaker initially thought it was not related, but simplifying the equation by treating the first rod as constant showed that there is no chaos involved. The approach to solving the equation of motion for a double "physical" pendulum is also discussed, with emphasis on the incorrect assumption of the kinetic energy equation. The moderator also notes that the motion of the second rod is not independent of the first rod's angle. An exam problem with different coordinates for a double pendulum is mentioned as an example of this concept.
AF Fardin
Homework Statement
My task is to solve the equation of motion for a double "physical" pendulum!
Relevant Equations
L=T-V
$\tau=Fr=I\alpha I am having trouble to find the moment of inertia of the second rod! Is it related to the first rod?? At the beginning I thought It's not! But when took those as constant,the equation had become way much simpler and there is nothing about chaos! My approach is given below Use the fact that the kinetic energy of either rod is the sum of two contributions: (1) the kinetic energy due to the motion of the center of mass of the rod: ##\frac {1}{2} M V_{cm}^2 ## (2) the kinetic energy due to rotation about the center of mass: ##\frac{1}{2} I_{cm} \omega^2## AF Fardin AF Fardin said: Homework Statement:: My task is to solve the equation of motion for a double "physical" pendulum! Relevant Equations:: L=T-V$\tau=Fr=I\alpha

My approach is given below
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AF Fardin

AF Fardin and Delta2
The big problem here is the assumption that
$$T = \frac 12 (I_1\dot\theta_1^2 + I_2\dot\theta_2^2)$$
The kinetic energy cannot be written on this form. Note that the second rod will also move when ##\theta_1## changes.

Note: The angles are the angles each rod make with the vertical. This does not mean that the motion of rod 2 is independent of ##\theta_1##.
I made an exam problem with different coordinates for a double pendulum… that really threw some people off …

AF Fardin, BvU and Delta2

## 1. What is the moment of inertia of a double physical pendulum?

The moment of inertia of a double physical pendulum is a measure of its resistance to rotational motion. It is a mathematical property that depends on the mass distribution and shape of the pendulum.

## 2. How is the moment of inertia of a double physical pendulum calculated?

The moment of inertia of a double physical pendulum can be calculated using the formula: I = m1r1^2 + m2r2^2, where m1 and m2 are the masses of the two pendulum bobs and r1 and r2 are the distances of their respective centers of mass from the pivot point.

## 3. Why is the moment of inertia of a double physical pendulum important?

The moment of inertia of a double physical pendulum is important because it affects the pendulum's period of oscillation. A higher moment of inertia will result in a longer period, while a lower moment of inertia will result in a shorter period.

## 4. How does the moment of inertia of a double physical pendulum change with different configurations?

The moment of inertia of a double physical pendulum can change with different configurations, such as changing the length or mass of the pendulum bobs. As the distance of the masses from the pivot point increases, the moment of inertia also increases.

## 5. Can the moment of inertia of a double physical pendulum be measured experimentally?

Yes, the moment of inertia of a double physical pendulum can be measured experimentally using a variety of methods, such as a torsion pendulum or a ballistic pendulum. These experiments involve measuring the period of oscillation and using it to calculate the moment of inertia.

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