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**[SOLVED] Vertical circular motion help!**

## Homework Statement

A 17.4 g steel marble is spun so that it rolls at 171.0 rpm around the inside of a vertically oriented steel tube. The tube, shown below, is 13.0 cm in diameter. Assume that the rolling resistance is small enough for the marble to maintain 171.0 rpm for several seconds. What is the force of static friction required for the marble to not spiral down the inside of the tube? (For steel on steel μK=0.600 and μS=0.800.)

## Homework Equations

## The Attempt at a Solution

I figured the vertical component of static friction must be equal to the weight of the object. The normal force on the centripetal axis can be found from the angular velocity, that is, F(n) = m x (angular velocity)^2 x r. Then I calculated the kinetic friction force on the tangential axis using this normal force, F(kinetic friction) = 0.6 x N. Finally, because the ball moves with a constant angular velocity for a few seconds I figured the magnitude of the tangential static friction force muse be equal to the magnitude of the tangential kinetic friction force. I summed the two static friction forces using Pythagorean theorem, but didn't get the correct answer.

I have correctly converted units, etc. I just need to know if my approach is sound? Thanks in advance for any help