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A pendulum is made of a rod of mass 3.1 kg and length 3.1 m whose moment of inertia about its center of mass is - M L² and a thin cylindrical disk of mass 2.2 kg and ra- dius 1.8 m whose moment of inertia about its center of mass is , M R². 12 3.1 kg 1.8 m 2.2 kg What is the moment of inertia of the pen- dulum about the pivot point? 3.1 m

A pendulum is made of a rod of mass 3.1 kg and length 3.1 m whose moment of inertia about its center of mass is - M L² and a thin cylindrical disk of mass 2.2 kg and ra- dius 1.8 m whose moment of inertia about its center of mass is , M R². 12 3.1 kg 1.8 m 2.2 kg What is the moment of inertia of the pen- dulum about the pivot point? 3.1 m

College Physics
College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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### Pendulum Moment of Inertia Analysis A pendulum consists of two components: 1. **Rod:** - Mass: 3.1 kg - Length: 3.1 m - Moment of Inertia about its center of mass: \(\frac{1}{12} M L^2\) 2. **Thin Cylindrical Disk:** - Mass: 2.2 kg - Radius: 1.8 m - Moment of Inertia about its center of mass: \(\frac{1}{2} M R^2\) ### Diagram Description The diagram illustrates a pendulum system with two main parts attached to a fixed horizontal support: - A rod extending vertically downwards with a length of 3.1 meters. - At the bottom of the rod, a thin cylindrical disk is attached. **Measurements in the Diagram:** - The rod is labeled with a mass of 3.1 kg. - The disk is labeled with a mass of 2.2 kg and a radius of 1.8 m. - The overall system is free to oscillate with angular motion denoted by the symbol \(\omega\). ### Problem Statement Calculate the moment of inertia of the combined pendulum system about the pivot point (top of the rod). This setup involves using principles of rotational dynamics to determine the pendulum's moment of inertia, essential for analyzing its oscillatory motion.
Transcribed Image Text:### Pendulum Moment of Inertia Analysis A pendulum consists of two components: 1. **Rod:** - Mass: 3.1 kg - Length: 3.1 m - Moment of Inertia about its center of mass: \(\frac{1}{12} M L^2\) 2. **Thin Cylindrical Disk:** - Mass: 2.2 kg - Radius: 1.8 m - Moment of Inertia about its center of mass: \(\frac{1}{2} M R^2\) ### Diagram Description The diagram illustrates a pendulum system with two main parts attached to a fixed horizontal support: - A rod extending vertically downwards with a length of 3.1 meters. - At the bottom of the rod, a thin cylindrical disk is attached. **Measurements in the Diagram:** - The rod is labeled with a mass of 3.1 kg. - The disk is labeled with a mass of 2.2 kg and a radius of 1.8 m. - The overall system is free to oscillate with angular motion denoted by the symbol \(\omega\). ### Problem Statement Calculate the moment of inertia of the combined pendulum system about the pivot point (top of the rod). This setup involves using principles of rotational dynamics to determine the pendulum's moment of inertia, essential for analyzing its oscillatory motion.
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