There is a problem : A straight smooth tube revolves with constant angular velocity W in a horizontal plane about one extremity which is fixed. If at zero time the tube be horizonal and a particle inside it be at a distance a from the fixed end and moving with velocity along the tube, find the distance at time t.
Now a similar problem is solved by taking the radial acceleration 0. But this problem has been solved taking the radial acceleration as -g sin Wt. The final answers also came different. Please help me in figuring out how to choose the radial acceleration in such problems.
It seems that the second formula you suggested holds for motion in a vertical plane under the influence of gravity. The radial acceleration would not have varied as a simple harmonic equation in case the motion was horizontal as g holds constant at a given height. But it seems some more info is required as radial acceleration in such cases can never be zero. Circular motion necesitates the presence of centripetal force and non-inertial centrifugal force., the second of which might result in displacement should there be no string or anything to hold the object to.