Question

The two spheres of equal mass $m$ are able to slide along the horizontal rotating rod. If they are initially latched in position a distance $r$ from the rotating axis with the assembly rotating freely with an angular velocity $\omega_{0},$ determine the new angular velocity $\omega$ after the spheres are released and finally assume positions at the ends of the rod at a radial distance of $2 r$. Also find the fraction $n$ of the initial kinetic energy of the system which is lost. Neglect the small mass of the rod and shaft.

          The two spheres of equal mass $m$ are able to slide along the horizontal rotating rod. If they are initially latched in position a distance $r$ from the rotating axis with the assembly rotating freely with an angular velocity $\omega_{0},$ determine the new angular velocity $\omega$ after the spheres are released and finally assume positions at the ends of the rod at a radial distance of $2 r$. Also find the fraction $n$ of the initial kinetic energy of the system which is lost. Neglect the small mass of the rod and shaft.

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Added by Shawn W.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Deepanshu Kumar

03/17/2022

Step 1

Initially, the system has angular momentum $I\omega_{0}$, where $I$ is the moment of inertia of the system. After the spheres move to the ends of the rod, the new angular momentum is $2mr^{2}\omega$, where $m$ is the mass of each sphere. Therefore, we Show more…

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The two spheres of equal mass $m$ are able to slide along the horizontal rotating rod. If they are initially latched in position a distance $r$ from the rotating axis with the assembly rotating freely with an angular velocity $\omega_{0},$ determine the new angular velocity $\omega$ after the spheres are released and finally assume positions at the ends of the rod at a radial distance of $2 r$. Also find the fraction $n$ of the initial kinetic energy of the system which is lost. Neglect the small mass of the rod and shaft.

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