Question goes something like: A cylindrical particle is placed in a certain metre long, frictionless tube, where it can slide back and forth. If the particle is not positioned in the centre of the tube, then as the tube is turning at a constant angular velocity of U, determine the acceleration of the particle along the tube. I understand from my textbook that the equation to use in such case should be a_r = r "doubledot" (second derivative w.r.t time) - r x U^2 where r = the distance between the particle to the centre of the tube. But I do not know how to work out r "doubledot". Any help is much appreciated.