1. The problem statement, all variables and given/known data Please see the attached In this example my professor is trying to calculate the total KE of the hoop,and let since the velocity at the contact point of the hoop and tube is zero we have v = vt + aω.This is equivalent to (R-a)Θ. = - aω. However,he later said that it was wrong since the no-slip condition should be RΘ. = aω but he did not give any explanation.Though it makes sense if you think about it geometrically,I think both of them are correct but I am not sure which one is correct? 2. Relevant equations 3. The attempt at a solution I am not sure,the equation T = T' + 1/2MV^2 where S and S' are an inertial frame and the centre of momentum frame,V is the speed of S' wrt S,holds under Galilean transformation.I think the set of Cartesian coordinates at CM of hoop is somewhat rotating wrt to the observer/lab frame so that it is not a Galilean transformation and we couldn't calculate the KE in the way as shown in the attached?