Suppose we have a merry-go-round of radius 10 meters. There's a thin glass tube with cross-sectional density d going radially from the center of the merry-go-round to the edge. In the glass tube one meter away from the center, there's a marble of mass m. The merry-go-round completes one counter-clockwise rotation every 2pi seconds, and the glass tube is frictionless. At time t, the marble is at rest. I want to find the trajectory of the marble.(adsbygoogle = window.adsbygoogle || []).push({});

I'm taking the center of the merry-go-round to be at the origin and the marble's initial position to be at (0, 1); obviously its initial velocity is 0. Since the tube rotates counter-clockwise every 2pi seconds, I can define the marble's position at t as <r(t)cos(t), r(t)sin(t)>. What I'm having trouble with is finding the force acting on the marble. I know the normal force on the marble from the glass tube is in the direction <-sin(t), cos(t)>, perpendicular to the tube. However, I don't know how to determine its magnitude. I initially assumed it was constant, but this leads to an incorrect answer.

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# Homework Help: Setting up a centrifugal force question

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