Edit View History Window Help Thu 7:28 PM Nasser A ani chegg.com Item 16 kinetic

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Edit View History Window Help Thu 7:28 PM Nasser A ani chegg.com Item 16 kinetic energy of an e his anegylatiKspeed energy and translational kinetic energy. You are to find the total kinetic energy K total of a dumbbell of mass m when it is rotating with angular speed mass is moving tra the two to the Ktot = 0.5mt,2 + 0.51,m4,2 SubmitMy Answers Give Up w and,its center of with speed v-(Figure 1 the dumbbell's moment of inertia about its center of mass by lem. Note that if you a 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 ofthe dumbbell is given by 1mr2but this fact will Correct Part B of 1 the translational kinetic energy term is called the kinetic energy of the center of mass. the kinetic energy in the center of mass plus decomposition exists for angular and linear You found that the total kinetic energy is the sum of the kinetic energy of the center of mass. A similar bodies like a dumbbel It is important to m. There are also related decompositions that work for systerms of masses, not just rigid the applicability of the formula Ktot K, + K1. Which of the following conditions are necessary for the formula to be valid? Check all that apply. The velocity vector um ust be perpendicular to the axis of rotation. The moment of inertia must be taken about an axis through the center of mass are to find the total kinetic energy Ktotal of a dumbbell of mass m when it is rotating with d its center of mass is moving t lationally with speed v. (Figure 1) Denote the dumbbell's moment gf

Explanation / Answer

from the coordinats of Center of mass and relation with its angular coordinates

we have Vcm = RW

where R is radius of Circular motion

and W is angular velocity

and for this Circular motion to happen, Velocity must be perpendicualr to axis of rotation,

and the MOI must be taken through CoM

parallel component of velocity will make it go in linear path

hence option 3 is true . and option 1 and 2 are wrong.

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