MP moments Of Inertia - MasteringPhysics: Assignment Print...

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IUPhysicsP201F2009 Assignment 7b Due at 11:00pm on Sunday, October 26, 2008 Assignment Display Mode: View Printable Answers View Grading Details Introduction to Moments of Inertia and Rotational Kinetic Energy Description: Conceptual questions about moment of inertia; several basic computational questions on moment of inertia and kinetic energy for discrete mass distributions. (version for algebra-based courses) Learning Goal: To understand the definition and the meaning of moment of inertia; to be able to calculate the moments of inertia for a group of particles; to relate moment of inertia to kinetic energy. By now, you may be familiar with a set of equations describing rotational kinematics. One thing that you may have noticed was the similarity between translational and rotational formulas. Such similarity also exists in dynamics and in the work-energy domain. For a particle of mass moving at a constant speed , the kinetic energy is given by the formula . If we consider instead a rigid object of mass rotating at a constant angular speed , the kinetic energy of such an object cannot be found by using the formula directly, since different parts of the object have different linear speeds. However, they all have the same angular speed. It would be desirable to obtain a formula for kinetic energy of rotational motion that is similar to the one for translational motion; such a formula would include the term instead of . Such a formula can, indeed, be written: For rotational motion of a system of small particles or for a rigid object with continuous mass distribution, the kinetic energy can be written as . Here, is called the moment of inertia of the object (or of the system of particles). It is the quantity representing the inertia with respect to rotational motion. It can be shown that for a discrete system of particles, the moment of inertia (also known as rotational inertia ) is given by . Page 1 of 27 MasteringPhysics: Assignment Print View 10/13/2008
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In this formula, is the mass of the i th particle and is the distance of that particle from the axis of rotation. Part A On which of the following does the moment of inertia of an object depend? Check all that apply. Unlike mass, the moment of inertia depends not only on the amount of matter in an object but also on the distribution of mass in space . The moment of inertia is also dependent on the axis of rotation . The same object, rotating with the same angular speed, may have different kinetic energy depending on the axis of rotation. ANSWER: g f e d c linear speed g f e d c linear acceleration g f e d c angular speed g f e d c angular acceleration g f e d c b total mass g f e d c b shape and density of the object g f e d c b location of the axis of rotation Part B What is the moment of inertia of particle a?
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This note was uploaded on 11/30/2009 for the course PHYS physics taught by Professor Physics during the Spring '09 term at Abraham Baldwin Agricultural College.

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MP moments Of Inertia - MasteringPhysics: Assignment Print...

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