**Kinetic Energy of a Dumbbell**This problem illustrates the two contributions to the kinetic energy of an extended object: rotational kinetic energy and translational kinetic energy. You are to find the total kinetic energy \( K_{\text{tot}} \) of a dumbbell of mass \( m \) when it is rotating with angular speed \( \omega \) and its center of mass is moving translationally with speed \( v \). **Diagram Description:**The diagram shows a dumbbell with two spherical masses connected by a rod. The rod's center is marked and labeled as the axis of rotation. The dumbbell is rotating with angular speed \( \omega \), and the diagram shows an arrow representing the direction of rotation.**Note:**- If you approximate the spheres as point masses of mass \( m/2 \) (each located a distance \( r \) from the center) and ignore the moment of inertia of the connecting rod, then the moment of inertia of the dumbbell is given by \( I_{\text{cm}} = mr^2 \), but this fact will not be necessary for this problem.---**Part A**- **Objective:** Find the total kinetic energy \( K_{\text{tot}} \) of the dumbbell.- **Expression Requirements:** Express your answer in terms of \( m \), \( v \), \( I_{\text{cm}} \), and \( \omega \).- **Input Field:** \( K_{\text{tot}} = \) [_______]- **Submit Button**---**Part B**- Complete previous part(s)**Provide Feedback**

Mass of sphere = "m" Angular speed = "w" translational speed = "v" moment of inertia "Icm Total kinetic energy of dumbbell is= Translational energy + rotational energy ... Eq(1) Where , Translational energy = 1/2 mv² And Rotational energy = 1/2 Icm × w² . Now put these value in eqn (1) KE(total) = 1/2 mv²+ 1/2 Icm w²

Science

Physics

Kinetic Energy of a Dumbbell This problem illustrates the two contributions to the kinetic energy of an extended object: rotational kinetic energy and translational kinetic energy. You are to find the total kinetic energy Kotal of a dumbbell of mass m when it is rotating with angular speed w and its center of mass is moving translationally with speed v. (Figure 1)Denote the dumbbell's moment of inertia about its center of mass by Im. Note that if you approximate the spheres as point masses of mass m/2 each located a distance r from the center and ignore the moment of inertia of the connecting rod, then the moment of inertia of the dumbbell is given by Im = mr?, but this fact will not be necessary for this problem. Part A Find the total kinetic energy Klet of the dumbbell. Express your answer in terms of m, v, Icm, and w. • View Available Hint(s) Kot = Submit Part B Complete previous part(s) Provide Feedback Figure < 1 of 1>

Kinetic Energy of a Dumbbell This problem illustrates the two contributions to the kinetic energy of an extended object: rotational kinetic energy and translational kinetic energy. You are to find the total kinetic energy Kotal of a dumbbell of mass m when it is rotating with angular speed w and its center of mass is moving translationally with speed v. (Figure 1)Denote the dumbbell's moment of inertia about its center of mass by Im. Note that if you approximate the spheres as point masses of mass m/2 each located a distance r from the center and ignore the moment of inertia of the connecting rod, then the moment of inertia of the dumbbell is given by Im = mr?, but this fact will not be necessary for this problem. Part A Find the total kinetic energy Klet of the dumbbell. Express your answer in terms of m, v, Icm, and w. • View Available Hint(s) Kot = Submit Part B Complete previous part(s) Provide Feedback Figure < 1 of 1>

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

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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