Triangular Joints

MediumrotationPractice ProblemsSolved by 2

Three identical thin rods, each of mass

m

and length

L

, are joined at their ends to form an equilateral triangle. In gravity-free space the triangle spins at constant angular speed

\omega

about an axis through its centroid perpendicular to its plane. What is the magnitude of the total force that one rod exerts on the other at each joint?

$An equilateral triangle drawn as three plain straight rods meeting at three vertices, one side horizontal at the bottom. Small filled dots at the three vertices mark the joints. Label one side with $L$ (dimension along the side) and $m$ (beside a different side). At the centroid, a small circle-with-dot marking the rotation axis coming out of the page, with a curved arrow around it labelled $\omega$. No force arrows, no median or radius lines, no named points.$

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