Pendulum Problem and steiner' law

In summary, a uniform circular disk with a radius of 14.3 cm is being used as a physical pendulum. The period of the pendulum is found using the equation T= 2pi radical ( I / mgh ). In Part A, the period is calculated to be 0.849 seconds. Part B requires finding the radial distance r < R where a pivot point would give the same period. This can be found using Steiner's law to express the moment of inertia through a parallel axis, and then equating the period of the disk to that of a simple pendulum. The answer should be provided in cm.
  • #1
ChazyChazLive
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Homework Statement


A uniform circular disk whose radius R is 14.3 cm is suspended as a physical pendulum from a point on its rim. (a) What is its period? (b) At what radial distance r < R is there a pivot point that gives the same period? (give answer in cm)

Homework Equations


T= 2pi radical ( I / mgh )

The Attempt at a Solution


Okay, I already found part A using T= 2pi radical ( I / mgh )
Any help would be greatly appreciated =]

Part A: 0.849 s <-- It's correct.
I'm just stuck on Part B.
 
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  • #2
Use steiner' law to express the I through a parallel axis..
 
  • #3
You can find the radial distance by equating period of the disk to that of a simple pendulum.
 

FAQ: Pendulum Problem and steiner' law

What is the Pendulum Problem?

The Pendulum Problem is a physics problem that deals with the motion of a pendulum due to gravity. It involves calculating the period of oscillation (time for one complete swing) of a pendulum, given its length and the acceleration due to gravity.

What is Steiner's Law?

Steiner's Law, also known as the Parallel Axis Theorem, states that the moment of inertia of a rigid body about any axis is equal to the moment of inertia of the body about a parallel axis through the center of mass, plus the product of the mass of the body and the square of the perpendicular distance between the two axes.

How are the Pendulum Problem and Steiner's Law related?

The Pendulum Problem can be used to demonstrate Steiner's Law. By changing the axis of rotation of a pendulum, the moment of inertia also changes, and the period of oscillation of the pendulum can be affected. This relationship is used in many real-world applications, such as in designing mechanical systems and calculating the stability of structures.

What are some examples of the Pendulum Problem and Steiner's Law in action?

Some examples include pendulum clocks, cranes, and balance scales. The period of oscillation of a pendulum in a clock is affected by the distance between the pivot point and the center of mass of the pendulum, which follows Steiner's Law. Cranes use counterweights to balance their load, and this also follows the principles of Steiner's Law. Balance scales use a pivot point and different weights on either side to find balance, demonstrating the Pendulum Problem and Steiner's Law in action.

How can understanding the Pendulum Problem and Steiner's Law benefit scientists?

Understanding the Pendulum Problem and Steiner's Law can help scientists in various fields such as engineering, physics, and mechanics. It can aid in designing more efficient and stable structures, predicting the behavior of mechanical systems, and calculating the motion of objects in motion. Additionally, these principles can also help in understanding more complex concepts such as rotational motion and energy conservation.

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